Guidelines for the Development and Application of Crash Modification Factors (2022)

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6 This chapter presents the research conducted under each of the three major tasks presented above. Each task follows a consistent format in the use of subtasks. For each task, the report presents a series of subtasks on the findings based on the: • Review of literature and existing studies • Framework as conceived at the end of Phase 1 that would direct the Phase 2 activities • Potential data sources identified for use in Phase 2 • Activities that were planned for research in Phase 2 • Research activities in Phase 2 and how they led to the developed guidelines material Task 2 Guidelines for Calibration of Existing CMFs for Different Site Characteristics Many studies in recent years have produced CMFs on a variety of safety treatments. Likewise, many safety practitioners are realizing the benefits of using CMFs and have begun employing them in areas of practice such as project prioritization, countermeasure selection, and benefit– cost analysis. However, one recurring issue is the question of the transferability of CMFs. In research studies, CMFs are developed using data from a sample of sites, either a group of inter- sections or road segments where a countermeasure was implemented. Additionally, a CMF may be available for a countermeasure but is focused only on one road type. Many practitioners want to know if a CMF developed under one set of conditions (e.g., state, roadway type, geography, and agency design practices) can be applied to a site with another set of conditions. Overview of Task and Products The objective of Task 2 was to develop a process that practitioners can use to identify and apply an appropriate CMF for a particular situation. The primary audience for these guidelines is safety practitioners who must often adopt CMFs developed in other geographic areas and apply those CMFs to their own situations. This section presents the activities that were under- taken to develop this process. The guidelines and supporting material produced from Task 2 are presented in Appendix A. The project team also developed two Excel spreadsheet tools to facilitate the implementation of the procedures from this task. • Excel Spreadsheet Tool 1—CMF Regression Software. This tool supports the procedure in Appendix A. It can be used to evaluate two or more CMFs associated with a common treatment. The evaluation can consist of (1) computing the overall average CMF, (2) computing CMFs by crash type or severity category using reported aggregate CMFs, or (3) computing CMFs as a C H A P T E R   3 Findings and Applications

Findings and Applications 7   function of site characteristics. A user guide for the CMF Regression Software is presented in Appendix D. • Excel Spreadsheet Tool 2—CMF Combination Tool. This tool is a spreadsheet implementa- tion of the homogeneity testing and CMF combining procedures presented in Appendix A. This tool can be used to test two or more CMFs for the same treatment to determine whether they are similar enough to be combined into a single CMF value. If so, the tool produces a value for the combined CMF. It also gives cautions for the use of the combined value. While the CMF Regression Software provides this same functionality, the CMF Combination Tool was developed as a pared-down, simpler version that would be directed at users who simply want to compare two or more CMFs to determine whether they can be combined and to calculate the combined value. A user guide for the CMF Combination Tool is presented in Appendix E. Subtask 2.1 Literature Review One objective of the review of the literature was to identify methods that are currently being used for calibration of current CMFs to assess treatment effectiveness at sites for which key site characteristics may be different. The review of the literature did not reveal any documented methods that are used to calibrate existing CMFs. Hence, the review focused on the following topics: • Transferability of CMFs—Determine if there are existing methods for assessing whether a CMF developed under one condition/jurisdiction applies to another condition/jurisdiction. If the CMF can be transferred from one condition/jurisdiction to another, then there is no need for calibration/adjustment. • Influential factors—Identify candidate treatments from the literature for which a range of site characteristics are known to have some influence on treatment effectiveness. This included studies that estimate crash modification functions (CMFunctions) using data from both cross-sectional and before-after evaluations. The following sections present further discussion about the findings on these two topics. Transferability of CMFs The review indicated that very few studies have been conducted specifically on the transfer- ability of CMFs. A recent report published by the Organization for Economic Cooperation and Development (OECD), “Sharing Road Safety: Developing an International Framework for Crash Modification Functions” (OECD 2012), was the main source. This report discusses the challenges and opportunities for transferability (of CMFs), assessing transferability of road safety evaluation studies, and provides a quantitative framework for enhancing transferability of CMFs and CMFunctions. The focus of this document is the international transferability of CMFs. However, many of the concepts and issues discussed in this document are applicable even for the transferability of CMFs within a particular country. One of the challenges identified by the OECD report regarding transferability is there is not a lot of uniformity in how safety studies are conducted and reported. The recent report titled Recommended Protocols for Developing Crash Modification Factors published as part of NCHRP Project 20-07 provides some guidelines to researchers on conducting and reporting CMF studies and hence addresses this challenge (Carter et al. 2012). More guidelines may be available as part of the ongoing NCHRP Project 17-72 Update of Crash Modification Factors for the Highway Safety Manual that will recommend CMFs for the 2nd edition of the HSM. Another challenge is that the nature of the roadway system, vehicle population, and interrelationship between driver behavior and the roadway environment is probably different in different parts of the world and even within the United States.

8 Guidelines for the Development and Application of Crash Modification Factors The OECD report argues that to assess the international transferability of CMFs from evalu- ation studies, many studies should have been reported in many countries during a long period, and the study findings should not vary systematically between countries or over time. The report presents an approach for determining whether the study findings vary systematically between countries over time. The approach involves cumulative meta-analysis by combining the results of each study one by one starting with the earliest study (although the framework discusses international transferability, a similar argument could be made for transferability within the United States; many studies within the United States over a long period are needed to assess the transferability of CMFs within the different jurisdictions in the United States). If the study findings do vary systematically between countries (or jurisdictions) over time, then it is neces- sary to determine the sources of variation in the study findings. If the sources of variation are primarily due to differences in methodology (e.g., cross-sectional vs. before-after study design), then assessment of transferability becomes difficult. However, if the sources of variation are primarily due to other reasons such as site characteristics or differences in the characteristics of the treatment, then a CMFunction needs to be estimated. Influential Factors The literature review identified candidate treatments for which a range of site characteristics are known to have some influence on treatment effectiveness and studies that have developed CMFunctions in addition to CMFs. The CMF Clearinghouse was used to identify the appropriate studies. Further description of the individual studies and the findings on influential factors is provided in the discussion under Subtask 2.6. Subtask 2.2 Develop Framework for Guidelines The team’s initial framework for the guidelines was presented as a flow chart in the interim report for this project. Figure 1 shows the flowchart as it was initially conceived. As shown in the flow chart, the guidelines were envisioned to consist of several steps, several of which were known to be necessary items for development under this project (denoted in gray boxes in the flowchart). This provided the roadmap for the work to be conducted in Phase 2 of the project. The final flow- chart is presented in the guidelines in Appendix A. The final flowchart of the procedure is provided in Appendix A, Figure A1. Subtask 2.3 Identify Potential Data Sources for Phase 2 The team identified data sets to be used in developing the required procedural steps presented in Figure 1. The intent of the team was to conduct data analysis at two levels. One level would be to use the information available from the CMF Clearinghouse. This was only for treatments where CMFs have been estimated in many studies. The goal of this analysis was to determine whether the CMFs from the various studies for a specific treatment are similar (apart from random varia- tion). If the CMFs are not similar, then the team would estimate CMFunctions and determine the reasons for the differences between the CMFs. The second level was intended for more detailed disaggregate data that are available for indi- vidual locations within studies for the purpose of estimating CMFunctions and determining the effect of location-specific characteristics such as traffic volume on CMFs. The following list provides the treatments and data sets initially identified for consideration for the second-level analysis. • Two-way to multi-way stop control. Data from 53 locations in North Carolina were used to determine the CMF for converting from two-way to multi-way stop control (Simpson and Hummer 2010). This was a before-after empirical Bayes study. The study also conducted a

Findings and Applications 9   limited analysis of the effect of flashers, speed limits, and major and minor road annual average daily traffic (AADT) on the CMF. • Improved curve delineation. Data from Connecticut and Washington were used to examine the safety impacts of improved curve delineation on rural two-lane roads (Srinivasan et al. 2009). This information from the Connecticut data set was used to conduct a limited disag- gregate analysis of the effect of curve radius, roadside hazard rating, and the number of signs that were improved or added with a curve. • Stop to signal conversion. Harkey et al. (2008) developed CMFs for the conversion of stop control to traffic signals in rural areas using data from California. An ongoing project with NCDOT is developing CMFs for the same treatment for intersections on two-lane roads in rural and suburban areas. Combining the two data sets would allow the team to examine the effect of major and minor road AADT, speed limit, and other site characteristics. Identify treatment of interest and subject site Identify site characteristics Identify existing CMFs for treatment of interest One or more CMFs found? (exact or category) Yes No Conduct before- after study of treatment at subject sites and similar sites Identify influential factors for each CMF Match site characteristics on large-effect factors Multiple CMFs No Match found at large effect level? (exact or category) One CMF Combine CMFs to obtain one CMF Are CMFs homogeneous? Yes No Select the one CMF that is a best match to the subject site characteristics or develop CMFunction Adjust CMF for differences in site characteristics Document conclusions and recommended CMF value How many CMFs? Yes Test CMFs for homogeneity This initial flowchart showed that the project team’s research in Phase 2 should concentrate on these areas. Figure 1. Initial flowchart of a process for selecting and adjusting CMF.

10 Guidelines for the Development and Application of Crash Modification Factors • Signal to roundabout conversion. A recent study (Srinivasan et al. 2011) developed CMFs for the signal to roundabout conversion using data from 28 intersections from different states in the country. The team plans to estimate CMFunctions using the data from this evaluation to get further insight into the effect of traffic volume and other site characteristics (e.g., number of legs) on the safety impact of this conversion. • Application of centerline and shoulder rumble strips. Data from Pennsylvania, Kentucky, and Missouri were used to evaluate the combination of centerline and shoulder rumble strips on rural two-lane roads. In some cases, a shoulder rumble strip was present previously; in others, they were not. The database has many variables that may influence the effectiveness of the treatment, including AADT, lane width, shoulder width, shoulder type, and the location of the shoulder rumble strip (on lane line or offset into shoulder). • Improving pavement friction. Under Phase VI of the FHWA Evaluation of Low Cost Safety Improvements Pooled Fund Study, team members used data from Minnesota, North Carolina, Pennsylvania, and California to evaluate the safety impacts of various pavement treatments. The analysis did show some evidence that the safety benefits vary by AADT, precipitation levels, urban vs. rural environment, and the expected crash frequency before treatment. This is a rich database that can be suitable for developing and demonstrating methods for developing CMFunctions. • Multiple treatments. Team members are working on NCHRP Project 17-62, which is collecting data to estimate crash type and severity models for all the HSM chapters for both segments and intersections. These data will include many variables and could be very useful for demonstrating the development of CMFunctions from cross-sectional regression. • Modifying the change interval at traffic signals. For a study performed by Persaud et al. (2012), geometric, traffic volume, signal timing, and crash data for 135 treatment and 31 reference sites were acquired from the states of California (1992 to 2002) and Maryland (1992 to 2002) to facilitate the analysis. Specifically, data were obtained in California from the cities of San Diego and San Francisco and in Maryland from the counties of Howard and Montgomery. There were indications that a CMFunction could be estimated based on the difference between the change interval and the Institute of Transportation Engineers (ITE) recommended practice. Additional variables in the database that could be considered, especially if the data are supplemented with additional sites, are the number of intersection approaches, type of left-turn phasing, area type, posted speed on major and minor approaches, number and width of approach lanes, and pres- ence and width of the median on approach. Subtask 2.4 Develop Plan for Phase 2 Based on the framework conceived in Subtask 2.2, the team developed a plan for the activities in Phase 2. Those necessary items for development in Phase 2 consisted of the following: • Identify influential factors for the CMF. One of the first steps was to identify the character- istics of the subject site or region in terms of the key influential factors. A list of key influential factors was identified and assembled for this purpose. This can serve as an initial resource for practitioners. The documented process of how the influential factors were identified can also serve as a guideline for practitioners to identify other influential factors that would not be identified under this project. • Test CMFs for homogeneity. The process requires the user to conduct a test of homogeneity if there are multiple CMFs that describe the treatment effect for the subject site (or region). In this step, the analyst determines whether the variability in CMF values is likely due to random sources (i.e., a homogeneity test). A test was needed to compare CMFs based on homogeneity and determine whether they are similar enough to be combined. • Adjust CMF for differences in site characteristics. This step was initially conceived as adjusting a CMF specific to differences in physical site characteristics. Through the process of

Findings and Applications 11   developing the guidelines, the team postulated that differences in the crash type and severity distributions between the two sites (site where CMF was developed and site where it is intended to be applied) were the priority for adjustment. The wide range of types of physical charac- teristics and the limited availability of data meant that adjusting for crash type and severity distributions would be more reliable and more widely applicable. Thus, this step of the pro- cedure became a step of adjusting the CMF to account for differences in crash type and severity distributions. Further discussion and rationale for this approach is presented below in the sections under Subtasks 2.5 and 2.6. Subtask 2.5 Collect and Assemble Data The collection of data needed to develop the required procedures is documented with the discussions in Subtask 2.6 on the development of these procedures. Subtask 2.6 Develop Guidelines and Demonstrate Their Use Following the needs shown in the initial flowchart (Figure 1), the following procedures and tools were developed in NCHRP Project 17-63 for practitioners to be able to implement the suggested guidelines: • Subtask 2.6a—Identification of CMF influential factors. • Subtask 2.6b—Homogeneity test and procedure for combining CMFs. • Subtask 2.6c—Converting aggregate CMFs to specific crash type and severity (initially con- ceived as adjustment for site conditions). • Subtask 2.6d—Excel spreadsheet tools. The process of selecting and adjusting a CMF, presented in Appendix A, uses all these proce- dures. The sections below describe the steps undertaken by the project team in developing these procedures as well as the rationale behind them. Subtask 2.6a Identification of CMF Influential Factors A practitioner who is seeking a CMF to use in a particular situation will search the existing resources and literature (e.g., CMF Clearinghouse, HSM, and state-specific “in-house” CMF lists) to find existing CMFs that address the countermeasure of interest. It is often the case that an existing CMF may have been developed under conditions that do not exactly match the conditions of the site where it is desired to be applied. These conditions include factors such as the number of lanes, area type (urban vs. rural), traffic volume level, and other characteristics. If the site characteristic significantly affects the effect of the countermeasure, it is referred to as an influential factor. “Influential factor” is further clarified in these guidelines as a site characteristic that is continu- ous from before treatment to after treatment and that is believed to exert some influence on the safety effect of the treatment. For example, characteristics such as the number of lanes, degree of curvature, and area type would fit this definition of influential factors, assuming that the counter- measure of interest is not changing these factors. Influential factors are those site characteristics under which the countermeasure is expected to have a different effect. For example, a certain type of lane marking may have a different effect (e.g., may be more effective) when applied to two-lane roads than to four-lane roads. Contrasted to this is the concept of differences in countermeasure implementation. That is, if the countermeasure of interest is adding lanes to a road, then the number of lanes is not a CMF influential factor but rather a difference in the type of treatment being performed. Converting a two-lane road to a four-lane road should be considered a wholly different countermeasure

12 Guidelines for the Development and Application of Crash Modification Factors than converting a four-lane road to a six-lane road. The number of lanes is not simply a CMF influential factor, but rather, it is integrated as part of the countermeasure itself. In most cases, a difference in prior (base) condition is a difference in countermeasure implementation rather than an influential site characteristic. Another example of a difference in base conditions of the site would be the difference in these countermeasures: “change signal phasing from permissive left turn to protected left turn” vs. “change signal phasing from permissive-protected left turn to protected left turn.” The base condition in one is a permissive left turn whereas the other is a permissive-protected left turn. The other defining characteristic of a difference in countermeasure implementation would be a difference in how or to what extent the countermeasure was enacted. For example, if the counter measure of interest pertains to changing the clearance interval of a signal, there is a dif- ference between changing the clearance interval to attain a certain timing standard vs. not attain- ing that timing standard. The amount of change is a difference in the way the countermeasure is implemented. The research team assembled a list of known influential factors to serve as a resource for practitioners who would be using the guidelines produced in this project. This list is non- comprehensive, in that it does not cover all potential countermeasures and all potentially influential factors of those countermeasures, but it does provide a starting point of known information. The influential factors were identified by several methods, as listed below. The full list of information identified on influential factors is presented in Appendix A, Step 4. Existing literature on the influence of site characteristics. Some previous studies provided information regarding influential factors, either through general statements in their results and discussion or in the form of CMFunctions. These CMFunctions were identified through an analysis of data from the CMF Clearinghouse. For example, a study by Ksaibati et al. (2009) produced a CMFunction for paving an unpaved road. The function showed that the CMF value was dependent on the traffic volume, V (Equa- tion 1). Thus, the level of traffic volume was seen to be an influential factor in the effectiveness of paving an unpaved road. e V Equation 1CMF 0.1123 0.0003= − where V = traffic volume in vehicles per day The following studies were used in this manner to identify CMF influential factors, either through CMFunctions produced by the study or by conclusions drawn by the authors in the report. • Safety Evaluation of Hybrid Mainline Toll Plazas (Abuzwidah et al. 2014) • Safety Evaluation of Permanent Raised Pavement Markers (Bahar et al. 2004) • Horizontal Curve Accident Modification Factor with Consideration of Driveway Density on Rural Four-Lane Highways in Texas (Fitzpatrick et al. 2009) • Prediction of the Expected Safety Performance of Rural Two-Lane Highways (Harwood et al. 2000) • WRRSP: Wyoming Rural Road Safety Program (Ksaibati et al. 2009) • Safety Effects of Cross Section Design on Urban and Suburban Roads (Le and Porter 2012a) • Safety Evaluation of Geometric Design Criteria 3 for Entrance-Exit Ramp Spacing and Auxiliary Lane Use (Le and Porter 2012b)

Findings and Applications 13   • Development of Adjustment Functions to Assess Combined Safety Effects of Multiple Treat- ments on Rural Two-Lane Highways (Park and Abdel-Aty 2015) • Exploration and Comparison of Crash Modification Factors for Multiple Treatments on Rural Multilane Roadways (Park et al. 2014) • Developing Crash Modification Functions to Assess Safety Effects of Adding Bike Lanes for Urban Arterials with Different Roadway and Socio-Economic Characteristics (Park et al. 2015) • Safety Evaluation of Installing Center Two-Way Left-Turn Lanes on Two-Lane Roads (Persaud et al. 2007b) • Evaluating the Need for Surface Treatments to Reduce Crash Frequency on Horizontal Curves (Pratt et al. 2014) • Developing Crash Modification Functions for Pedestrian Signal Improvement (Sacchi et al. 2015) • Safety Evaluation of Improved Curve Delineation (Srinivasan et al. 2009) • Accident Effects of Sideslope and Other Roadside Features on Two-Lane Roads (Zegeer et al. 1988) Homogeneity Test. Under NCHRP Project 17-63, the team developed a homogeneity test to determine whether the reported CMF values for a common treatment, crash type category, and crash severity category have differences that are so large as to be likely caused by underlying differences in circumstances among the locations studied. Appendix A, Step 6a, provides a full description of the homogeneity test. This homogeneity test was used to identify the influential factors by comparing CMFs in such a way as to determine whether a significant difference in the CMFs could be attributed to a difference in a key site characteristic. Table 1 shows two CMFs from a study that evaluated the effect of converting an intersection from signal control to roundabout (Srinivasan 2011). In addition to these two CMFs, this study produced many other disaggregate CMFs, which allowed the potential for comparing them using the homogeneity test. The two CMFs in Table 1 were selected because they were similar in all reported site characteristics (e.g., area type, states of origin, and traffic volume) but were dif- ferent in intersection geometry. One was developed at four-leg intersections; the other at three- leg intersections. The homogeneity test concluded that the CMFs had differences large enough that they could not be reliably combined into a single value. Given that the only difference in the development of these two CMFs is the number of intersection legs, it can be reasonably assumed CMF ID Number 4264 4262 CMF Value 0.759 1.066 Standard Error of CMF 0.052 0.163 Intersection Geometry 4-leg 3-leg Crash Type All Crash Severity All Area Type Urban and suburban State CO, FL, IN, MD, MI, NY, NC, SC, VT, WA Major-Road Traffic Volume, Vehicles Per Day 5,322 to 43,123 Number of Lanes 1 to 2 Table 1. Example of CMFs compared using homogeneity test and found to be significantly different.

14 Guidelines for the Development and Application of Crash Modification Factors that number of intersection legs is an influential factor in the effectiveness of converting a traffic signal to a roundabout. The team conducted similar homogeneity tests for countermeasures for which there were sufficient disaggregate CMFs to allow for matching on all site characteristics except the one of interest. In situations where the homogeneity test concluded that the CMFs were similar enough to be combined, the team concluded that the site characteristic of interest (the characteristic that differed between the CMFs being tested) could not be considered a CMF influential factor. CMFs evaluated using the homogeneity test were assembled for the following countermeasures: • Convert signal to a roundabout • Install Safetyedge • Provide a left-turn lane on both major-road approaches • Provide a left-turn lane on one major-road approach • Provide flashing beacons at stop-controlled intersections Data Analysis to Identify Influential Factors. Reviewing existing literature and conduct- ing homogeneity tests of difference on existing CMFs revealed some information about influen- tial factors. However, the project team desired to fill more gaps in the knowledge about influential factors by conducting additional analyses. The project team conducted analyses of the following data sets to develop CMFunctions and identify influential factors. Using CMF Data Reported in Study Reports • Evaluation of the Effectiveness of Shoulder Rumble Strips on Rural Multi-Lane Divided High- ways in Minnesota (Carrasco et al. 2004) NCHRP Report 641: Guidance for the Design and Application of Shoulder and Centerline Rumble Strips (Torbic et al. 2009) Using Raw Data Obtained for Various Countermeasure Installations: NCHRP Project 17-63 Analyses • Centerline and shoulder rumble strips: disaggregate data from 2000 sites in three states. • Reflective pavement markings on edge lines and lane lines (freeways): disaggregate data from 705 sites in three states. • Signal to roundabout conversions: disaggregate data from 10 states from NCHRP Project 17-35 and other projects. The latter three data sets were compiled and analyzed primarily to investigate specific state- to-state differences of countermeasure effects, though they yielded findings on other influential factors as well. State-to-State Differences. The issue of transferability of CMFs between states in the United States was a priority to many parties interested in the results of this project. Many state practi- tioners desire to know whether a CMF developed in one state would have a greater, lesser, or equal magnitude in a different state. To address this question, the team first examined the results of existing studies that involved data from multiple states. The studies in Table 2 were identified initially through a data analysis of CMFs from the CMF Clearinghouse. These studies were identified as those that used data from multiple states in the evaluation of a single countermeasure. Table 2 provides a summary of the findings related to state-to-state differences. The examination of existing studies yielded little in the way of conclusions about the effect of the state of origin. Thus, the team also conducted specific analyses to attempt to isolate and

Findings and Applications 15   identify state-to-state differences in CMFs. These analyses were conducted on data sets obtained for the evaluation of three countermeasures • Centerline and shoulder rumble strips • Reflective pavement markings on edgelines and lane lines (freeways) • Signal to roundabout conversions These analyses yielded some indications that the state of origin sometimes appeared to be an influential factor. However, it was more often the case that other site characteristics, such Study Title Countermeasure States Involved Findings on State-to-State Significant Effects on CMF Reference NCHRP Report 650: Median Intersection Design for Rural High- Speed Divided Highways Convert 4-leg intersection into two 3- leg intersections IA and OR Insufficient data to draw conclusions (only one site per state). Maze et al. 2010 Safety Evaluation of Lane and Shoulder Width Combinations on Rural, 2-Lane, Undivided Roads Decrease lane width PA and ID The authors compared results by state but did not identify or quantify the significance of differences; the general conclusion was that the results from PA and TX, but not from WA, were very similar. Gross et al. 2009 Safety Evaluation of Increasing Retroreflectivity of STOP Signs Increase stop sign visibility CT and SC The authors noted that there was no effect from state differences when results were disaggregated by the number of legs and AADT; they reported inconclusive effect from state differences when results were disaggregated by area type. Persaud et al. 2007a NCHRP Report 641: Guidance for the Design and Application of Shoulder and Centerline Rumble Strips Install centerline rumble strips, install edgeline rumble strips, install shoulder rumble strips, and widen outside shoulder MN, PA, and WA The authors did not make conclusions about state-to-state effects. Torbic et al. 2009 The J-Turn Intersection: Design Guidance and Safety Experience Install J-turn intersection MD and NC Insufficient data to draw conclusions (only two sites per state). Hochstein et al. 2009 Safety Evaluation of Transverse Rumble Strips on Approaches to Stop- Controlled Intersections in Rural Areas Install transverse rumble strips on stop-controlled approaches in rural areas IA and MN The authors did not make conclusions about state-to-state effects; also, the application of transverse rumbles was different by state. Srinivasan et al. 2010 Safety Evaluation of Installing Center 2-Way Left-Turn Lanes on 2- Lane Roads Install TWLTL NC, IL, CA, and AR The authors conclude that the effect was smaller for NC than for CA, IL, or AR. Lyon et al. 2008 Safety Evaluation of the Safety Edge Treatment Installation of safety edge treatment GA and IN The authors did not make conclusions about state-to-state effects. Graham et al. 2011 Table 2. Review of studies using data from multiple states.

16 Guidelines for the Development and Application of Crash Modification Factors as AADT and expected crashes in the before period, were found to be influential factors. The details of these analyses are provided in Appendix A, Section A.4. The fact that state of origin was only occasionally a significantly influential factor supports the approach discussed in Sub- task 2.6c, which concludes that crash type and severity distributions are the dominant factors in the transferability of CMFs. The findings on influential factors for these three countermeasures were incorporated into the assembled information on influential factors presented in Appendix A, Step 4. Related Work under Southeastern Transportation Center. A related effort by Srinivasan and Lan (2016) was conducted simultaneously with NCHRP Project 17-63 and shared many common goals. The objective of this related study was to investigate the performance of three different forms of CMFunctions. The authors compared two traditional forms (normal and lognormal) with a new negative binomial regression approach. Data from the results of a before- after empirical Bayes evaluation from North Carolina were used for this investigation. The treat- ment was the introduction of traffic signals at locations that were controlled by stop signs of minor roads. Unlike the traditional approach of using the CMF from a site (or group of sites) as a dependent variable, this study investigated the use of observed crashes (the numerator of the CMF calculation) as the dependent variable and expected crashes (the denominator of the CMF calculation) as an offset in the estimation of CMFunctions using negative binomial regression. The findings of this work produced knowledge on several factors that were shown to influ- ence the effectiveness of installing a traffic signal. Traffic volume, number of intersection legs, the speed limit on the major road, and expected crashes in the before period were all found to be influential factors. This knowledge was incorporated into the assembled information on influential factors in Appendix A, Step 4. Subtask 2.6b Homogeneity Test and Procedure for Combining CMFs The team developed a test based on homogeneity for comparing CMFs to determine whether they can be combined into a single value. The homogeneity test can be used to determine whether the reported CMF values for a common treatment, crash type category, and crash severity category have differences that are so large as to be likely caused by underlying differences in circumstances among the locations studied (Griffin and Flowers 1997). If the differences in CMF value are small, then they are likely due to random variation, and the CMFs can be combined into a single CMF value that represents the best estimate of treatment effect. This test is for CMFs that address the same countermeasure. If the differences are large, then they are likely due to systematic influences that affect the treatment’s effectiveness at a given location. In this latter case, further investigation of location circumstances may lead to the identification of some of these influences. In turn, these findings may lead to the development of (1) a set of unique CMF values for specified circumstances, or (2) a CMFunction that includes variables that quantify the effect of different circumstances on the CMF value. The homogeneity test is described in Appendix A, Step 6a. It produces a test statistic that is chi-square distributed. This statistic is used to test the null hypothesis that the CMF values are equal. To apply the homogeneity test, two or more CMF values (and their associated standard error) are needed. Typically, each CMF used in the test represents results from a group of sites with certain site characteristics. More detail on this test is provided by Woolf (1955) and by Fleiss (1973). Appendix C also describes the procedure for combining CMFs when the homogeneity test indicates that the CMFs can be combined. An Excel spreadsheet tool (CMF Combination Tool) for conducting the homogeneity test and combining the CMFs was also developed as part of NCHRP Project 17-63. A user guide for the CMF Combination Tool is found in Appendix E.

Findings and Applications 17   Subtask 2.6c Converting Aggregate CMFs to Specific Crash Type and Severity Many geometric and traffic control elements associated with a roadway facility influence its safety (as defined by its crash frequency or severity distribution). CMFs are typically used to quantify the change in safety associated with a change in the size or presence of one of these elements. Changes to make the facility safer are often referred to as “treatments” or “counter- measures.” However, it is recognized that some changes to a facility may also make the facility less safe. The word “treatment” is used in this report in its most general context—as a change in the size or presence of a geometric or traffic control element of a facility. It is not meant to imply that the change will always improve safety. Changes to some geometric and traffic control elements are recognized to influence the fre- quency or severity of specific crash types. For example, a road with a narrow (or nonexistent) median is likely to have more frequent head-on crashes. So, widening (or adding) a median is likely to reduce head-on crash frequency. Similarly, a road with wide shoulders is likely to have less frequent single-vehicle run-off-road crashes. In fact, the distribution of crash type and severity at a given facility is typically used to identify appropriate treatments. For example, the addition of shoulder rumble strips may be used at a location with frequent single-vehicle run-off-road crashes. Some of the CMFs reported in the literature are quantified in terms of their effect on crashes of a specific type or severity. This approach recognizes that certain treatments have a significant effect on certain crash types, and negligible (or no) effect on other crash types (in fact, this rec- ognition is exploited in the diagnostic and countermeasure-selection steps of the safety manage- ment process). This approach also recognizes that the effect of certain treatments may vary by crash severity category. For example, the addition of a median barrier will likely reduce severe crashes but may increase property-damage-only crashes. In recent years, there has been more interest by transportation professionals in developing CMFs that are specific to a given crash type or severity category. In some cases, the CMFs devel- oped are specific to a specific crash type and crash severity; in other cases, they may be specific to just a subset of crash types or a subset of crash severity categories. Regardless, this direction recognizes that more reliable safety estimates are obtained through the evaluation of treatment effects at a disaggregate level. In this manner, a given treatment’s overall safety effect is deter- mined by first computing its effect on each crash type and severity category, and then aggregat- ing the results to a single estimate for the overall site. In recognition of the benefit of using a disaggregate approach to safety evaluation, the ongoing NCHRP Project 17-62: Improved Predic- tion Models for Crash Types and Crash Severities, is charged with developing models to support disaggregate safety evaluation. Parts B and C of the HSM describe predictive methods that are used to estimate the overall safety of a roadway facility. The methods of Part B are based on safety performance functions (SPFs) that predict aggregate (i.e., total) or partly aggregate (e.g., KABC crashes of all types) crash frequency. Each of the methods in Part C includes an SPF and a series of CMFs that are used together to estimate the aggregate crash frequency for a specific facility type (e.g., urban signalized intersection). Most of the CMFs documented in Part C are “aggregate” CMFs such that they quantify treatment effect on overall safety (i.e., all crash type and severity categories combined). There are a few “disaggregate” CMFs in Part C that recognize that some treatments have a significant effect on some crash types. For example, the Lane Width CMF in Chapter 10 of Part C of the HSM recognizes that a change in lane width is likely to significantly influence only specific crash types. The following equation is provided in the HSM to convert the disaggregate CMFs (associated with specific crash types) into an aggregate CMF: CMF CMF pr ra ra Equation 21.0 1.01 ( )= − × +

18 Guidelines for the Development and Application of Crash Modification Factors where CMF1r = CMF for the effect of lane width on total crashes of all types and severities CMFra = CMF for the effect of lane width on related crashes (single-vehicle run-off-road, head-on, opposite-direction sideswipe, and same-direction sideswipe) pra = proportion of total crashes that are related An important point to note regarding Equation 2 is that the value of CMF1r will vary with the value of the proportion pra. Thus, the aggregate CMF value can vary among sites simply because the proportion pra varies among sites. A key drawback of aggregate CMFs is that they reflect the crash distribution at the sites used for their calibration; they cannot be adjusted to reflect the dis- tribution representative of the site of interest (Equation 2 is a rare exception). The most notable issue is that the value of an aggregate CMF can vary among locations due to differences in crash type and severity distribution. The long-term solution is to move safety evaluation in the direction of disaggregate analysis. However, there are limited numbers of CMFs and prediction models currently available to support disaggregate analysis. Hence, the focus of the discussion is the development of a procedure for estimating aggregate CMFs based on the crash distribution representative of the site of interest. In this manner, the aggregate CMFs are “locally calibrated” to the site of interest. A related topic is the influence of crash location distribution on the value of an aggregate CMF. In this situation, the reported CMF is aggregated over the entire facility when only a por- tion of the facility is treated. The rest of this section provides two case studies and their respective examples. Case Study 1 is devoted to the discussion of aggregate CMF variation by crash type and severity distribution. Case Study 2 is devoted to the discussion of aggregate CMF variation by crash location distribu- tion. The procedure for estimating aggregate CMFs that are locally calibrated (using the crash distribution representative of the site of interest) and the procedure for estimating the disaggre- gate CMFs needed for a disaggregate safety evaluation of a specified treatment are available in Appendix A, Steps 5 and 7. The team also developed an Excel spreadsheet tool called the CMF Regression Software for implementing these procedures, which was delivered as a product of Project 17-63. A user guide for CMF Regression Software is found in Appendix D. Case Study 1—Variation Represented by Crash Type and Severity Distribution. Table 3 is based on a hypothetical example. Two different values of aggregate CMFs are shown (i.e., 0.75 and 0.80). The analyst would like to know which CMF applies to a site in Iowa. The disaggregate CMF values in Columns 3 and 4 were not reported by the authors who developed the aggregate CMF values in Column 2, but the crash type distribution was reported. Using the reported aggregate CMFs and crash distribution, the disaggregate CMF values were computed using the following equation: CMF CMF p CMF pagg Equation 31 1 2 2( ) ( )= × + × where CMFagg = aggregate CMF CMF1 = disaggregate CMF for crash category 1 p1 = proportion of crash category 1 CMF2 = disaggregate CMF for crash category 2 p2 = proportion of crash category 2 (= 1 − p1) To obtain the CMF values in Columns 3 and 4, Equation 3 is written twice. The first equa- tion is populated with the Oregon values in Table 3. The second equation is populated with the

Findings and Applications 19   Florida values. A closed-form solution for the two disaggregate CMF values emerges from these two equations, given the number of study locations and equation variables. If additional CMFs were identified from the literature, then the regression approach described in Appendix A, Step 5, is more appropriate for quantifying the average disaggregate CMF values. The computed disaggregate CMF values in columns 3 and 4 indicate that the CMFs for each crash category are constant and that the variation in the two aggregate CMF values is due to differences in crash type distribution. Logically, the two disaggregate CMF values can be used with Equation 3 to “locally calibrate” an aggregate CMF for the subject site in Iowa (using a representative crash distribution for the Iowa site). For example, if the crash distributions for the Iowa site are 0.4 and 0.6 for categories 1 and 2, respectively, then the aggregate CMF is 0.70 (= 0.40 × 0.40 + 0.90 × 0.60). Case Study 1—Example. This subsection describes the results from an evaluation of the safety effect of adding shoulder rumble strips to road segments (Torbic et al. 2009). The researchers evaluated the addition of shoulder rumble strips to urban freeways, rural freeways, rural multi- lane highways, and rural two-lane highways in three states. About 250 miles of roadway were treated. The estimates of safety effect were computed using the empirical Bayes before-after study method. The CMF values obtained from Tables 26 through 28 of the final report by Torbic et al. (2009) are listed in Table 4. The first nine rows list the computed CMF values based on all crash type and severity categories combined (referred to as “TOT,” or total, crashes by the report authors). The remaining rows list the computed CMF values for various combinations of crash type and severity. Regarding the CMFs in the first nine rows, Torbic et al. (2009) note that most combinations “. . . suggest an increase in TOT crashes when shoulder rumble strips are installed” (p. 67). More importantly, the authors found that fatal-and-injury crashes typically decrease after the installa- tion of shoulder rumble strips (as indicated by the CMFs in rows 10 to 18). The CMF values in Table 4 for a common combination of crash type and severity vary widely among the three states. For example, the CMFs for rural multilane highways in Rows 4, 5, and 6 vary from 0.8671 to 1.2200. Similarly, those for rural two-lane highways in Rows 7, 8, and 9 vary from 0.7560 to 1.4049. Supplemental analyses were conducted to determine whether this variation could be explained by differences in heavy vehicle percentage, the extent of adverse weather, and lighting levels among sites. The final report from Torbic et al. (2009) also included the crash type and severity distribu- tion asso ciated with each of the CMF values reported in Table 4. These distributions were used to determine best estimates of the following four underlying disaggregate CMFs: multiple-vehicle fatal-and-injury, single-vehicle fatal-and-injury, multiple-vehicle property-damage-only, and single-vehicle property-damage-only. Study Location CMF Crash Type Distribution Aggregate, CMFagg Crash Category 1, CMF1 Crash Category 2, CMF2 Portion 1, Category p1 Portion 2, Category p2 Oregon 0.75 0.40 0.90 0.30 0.70 Florida 0.80 0.40 0.90 0.20 0.80 Table 3. CMF variation due to differences in crash type distribution.

20 Guidelines for the Development and Application of Crash Modification Factors Area Type Roadway Type Median State Crash Type Severity CMF Urban Freeway Divided Pennsylvania All All 0.9862 Rural Freeway Divided Missouri All All 1.0789 Pennsylvania All All 1.0033 Multilane Divided Minnesota All All 1.1022 Missouri All All 1.2200 Pennsylvania All All 0.8671 2-lane Undivided Minnesota All All 1.1438 Missouri All All 1.4049 Pennsylvania All All 0.7560 Urban Freeway Divided Pennsylvania All Fatal-and- Injury 0.8399 Rural Freeway Divided Missouri All Fatal-and- Injury 0.9416 Pennsylvania All Fatal-and- Injury 0.8739 Multilane Divided Minnesota All Fatal-and- Injury 0.7779 Missouri All Fatal-and- Injury 0.9475 Pennsylvania All Fatal-and- Injury 0.5988 2-lane Undivided Minnesota All Fatal-and- Injury 1.0513 Missouri All Fatal-and- Injury 0.8076 Pennsylvania All Fatal-and- Injury 0.8203 Urban Freeway Divided Pennsylvania SV-ROR All 0.9419 Rural Freeway Divided Missouri SV-ROR All 0.9209 Pennsylvania SV-ROR All 0.8229 Multilane Divided Minnesota SV-ROR All 1.3836 Missouri SV-ROR All 1.4478 Pennsylvania SV-ROR All 0.7454 2-lane Undivided Minnesota SV-ROR All 1.1072 Missouri SV-ROR All 1.1687 Pennsylvania SV-ROR All 0.5641 Urban Freeway Divided Pennsylvania SV-ROR Fatal-and- Injury 0.9257 Rural Freeway Divided Missouri SV-ROR Fatal-and- Injury 0.8436 Pennsylvania SV-ROR Fatal-and- Injury 0.7680 Multilane Divided Minnesota SV-ROR Fatal-and- Injury 0.8971 Missouri SV-ROR Fatal-and- Injury 1.0016 Pennsylvania SV-ROR Fatal-and- Injury 0.8014 2-lane Undivided Minnesota SV-ROR Fatal-and- Injury 0.6759 Missouri SV-ROR Fatal-and- Injury 0.5541 Pennsylvania SV-ROR Fatal-and- Injury 0.6334 Abbreviation: SV-ROR, single-vehicle run-off-road crash. Table 4. Reported safety effect of shoulder rumble strips.

Findings and Applications 21   A regression model was developed to estimate the disaggregate CMFs, where the number of observations equaled the number of rows in Table 4 (i.e., 36). The details of this analysis are described in Appendix A, Step 5. The analysis results indicate that 49% of the CMF value variability in Table 4 is explained by a combination of differences in (1) crash type and severity distribution, (2) roadway type, and (3) state. The best-fit disaggregate CMF values for two-lane highways in Pennsylvania are • Multiple-vehicle fatal-and-injury 0.887 • Single-vehicle fatal-and-injury 0.781 • Multiple-vehicle property-damage-only 1.117 • Single-vehicle property-damage-only 0.966 Based on the regression results, each CMF value in the bullet list is increased by 1.3% when applied to freeway sites and by 14% for multilane highway sites. They are increased by 12% when applied to sites in Minnesota or Missouri. The CMF value of 0.781 for single-vehicle fatal- and-injury crashes can be compared with the Pennsylvania CMF shown in the last row of Table 4 (i.e., 0.6334). A closer agreement might be achieved if differences in heavy vehicle percentage, the extent of adverse weather, and lighting level among sites were factored into the regression analysis. These results imply that some of the variability in the aggregate CMF values in Table 4 can be “explained” simply by differences in crash type and severity distribution among states. Other systematic differences may be explained by roadway type (or, more precisely, the design and traffic control elements associated with each roadway type). The consistently lower CMF values associated with Pennsylvania may be related to differences in the method of treatment site selec- tion, heavy vehicle percentage, the extent of adverse weather, and lighting level, but the original data would be needed to confirm this possibility. The best-fit disaggregate CMFs described above are intended to illustrate how the crash type and severity distribution can influence the value of aggregate CMFs. They are not intended to replace the recommendations of Torbic et al. (2009). Case Study 2—Variation Represented by Crash Location Distribution. CMFs typically describe the safety effect of a treatment that is applied to both travel directions on a given road- way facility. For example, CMFs have been developed for the case where a median is widened for the length of a given segment. They also describe the safety effect of a treatment that is applied to all legs of an intersection. For example, CMFs have been developed for the case where an inter- section is converted from two-way stop-control to signal-control. In this regard, the treatment is presumed to affect both travel directions for the length of the segment and all intersection legs. Hence, the CMF is accurately represented as a spatially aggregate CMF because the treatment influences the safety of the entire site. On the other hand, some treatments are only applied to one travel direction of a two-way roadway or just one leg of an intersection. The most accurate approach for quantifying the effect of these treatments is to quantify their effect on the treated portion of the facility. In this manner, the CMF produced would be a spatially disaggregate CMF. It would be used in a disaggregate safety evaluation to separately evaluate each travel direction (or each intersection leg) and then combine the results to obtain a spatially aggregate estimate of overall site safety. In general, spatially aggregate CMFs are reported in the literature and the HSM, regardless of whether the treatment for which they were derived was applied to only a portion of the facility. A comparison of spatially aggregate CMF values for which the treatment was only applied to a portion of the facility will show some unexplained differences due partly to unmeasured site characteristics and partly to leg volume variation. On a rational basis, these influences on safety

22 Guidelines for the Development and Application of Crash Modification Factors are undoubtedly reflected in the crash “location” distribution (i.e., distribution of crashes by travel direction or intersection leg). For example, an intersection with one leg having a relatively high volume or an unmeasured element that increases crash risk will show a larger proportion of crashes associated with this leg. Thus, the intersection will show a larger safety improvement when a treatment is applied to the subject leg than when the same treatment is applied to a dif- ferent leg. A spatially disaggregate safety evaluation (based on the use of spatially disaggregate CMFs) is one approach for indirectly including the effect of differences in leg volume and differences in unmeasured site characteristics on the estimate of a given site’s overall safety. However, because most SPFs predict spatially aggregate crashes, another approach for considering exposure and unmeasured site characteristics is to use a locally representative crash location distribution to “locally calibrate” the spatially aggregate CMF for the site of interest. This second approach is illustrated in the Case Study 2 Examples. Case Study 2 Examples Intersection Case. Consider the spatially aggregate CMF values shown in the second column of Table 5. Two different values are shown (i.e., 0.90 and 0.82). These CMFs correspond to the addition of one left-turn bay at an urban signalized intersection. The analyst would like to know which CMF applies to a site in Iowa. The spatially disaggregate CMF values in Columns 3 through 6 were not reported by the authors who developed the CMF values in Column 2, but the crash location distribution was reported. Using the reported spatially aggregate CMF values, crash distribution, and knowledge of which legs were treated, the disaggregate CMF values in Column 3 are computed using the following equation: CMF CMF p CMF p CMF p CMF psp agg sp int sp int sp int sp int Equation 4,1 ,1 ,2 ,2 ,3 ,3 ,4 ,4( ) ( ) ( ) ( )= × + × + × + ×− where CMFsp-agg = spatially aggregate CMF CMFsp,i = spatially disaggregate CMF for intersection leg i (i = 1, 2, 3, 4) pint,i = proportion of crashes associated with intersection leg i (i = 1, 2, 3, 4) Equation 4 was used to compute the spatially disaggregate CMF for the northbound leg. A value of 1.0 is used for the spatially disaggregate CMF for each of the other, untreated legs. A closed-form solution for the disaggregate CMF value emerges from each equation. Both equations indicate that the disaggregate CMF is 0.60. If these two values had differed, or if multiple CMFs and crash categories are identified, then the regression approach described in Appendix A, Step 5, is more appropriate for quantifying the crash category CMFs. The computed spatially disaggregate CMF values in Column 3 indicate that the CMF for treating a given leg is constant at 0.60 and that the variation in the two spatially aggregate CMF values is due to differences in crash location distribution. Logically, the two disaggregate CMF Study Location Intersection CMF, spatially aggregate CMF by Intersection Leg Crash Distribution by Intersection Leg NB SB EB WB NB SB EB WB Oregon 0.90 0.60 1.00 1.00 1.00 0.25 0.25 0.25 0.25 Florida 0.82 0.60 1.00 1.00 1.00 0.45 0.45 0.05 0.05 Abbreviations: EB, eastbound; NB, northbound; SB, southbound; WB, westbound. Table 5. CMF variation due to differences in crash location distribution.

Findings and Applications 23   values can be used with Equation 4 to “locally calibrate” a spatially aggregate CMF for the sub- ject site in Iowa (using a representative crash distribution for the Iowa site). For example, if the crash distribution for the site in Iowa is 0.3, 0.3, 0.2, and 0.2 for the NB, SB, EB, and WB legs, respectively and the NB and SB legs are treated, then the aggregate CMF is 0.76 (= 0.60 × 0.30 + 0.60 × 0.30 + 1.0 × 0.20 +1.0 × 0.20). Segment Case. The concepts described in the previous paragraphs can equally be applied to the two travel directions of a roadway when only one direction of travel is treated and the crash location distribution varies by direction (for example, because there is an unequal distribution of daily volume or some variation in unmeasured site characteristics that make one direction of travel safer than the other). The following equation would be used to compute the spatially aggregate CMF. CMF CMF p CMF psp agg sp seg sp seg Equation 5,1 ,1 ,2 ,2( ) ( )= × + ×− where CMFsp-agg = spatially aggregate CMF CMFsp,i = spatially disaggregate CMF for travel direction i (i = 1, 2) pseg,i = proportion of crashes associated with segment travel direction i (i = 1, 2) If only one direction of travel is treated, then a spatially disaggregate CMF value of 1.0 is used for the untreated direction. If the treatment effect is the same in each direction and both direc- tions are treated, then Equation 5 reduces to CMFsp-agg = CMFsp. In other words, if the literature indicates that the CMF value for adding shoulder rumble strips to both shoulders is 0.769 (i.e., CMFsp-agg = 0.769), then the spatially disaggregate CMF value is also equal to 0.769. This result simplifies the task of determining the spatially disaggregate CMF values for segment treatments. Case Study 3—Adding Turn Bays at Intersections. This subsection describes the results from an evaluation of the safety effect of adding turn bays at intersections (Harwood et al. 2002). Harwood et al. evaluated the addition of left- and right-turn bays to urban and rural intersections having signalized or 2-way stop control. They collected data for 280 intersections at which one or more turn bays were added. The recommended estimates of safety effect were based on the empirical Bayes before-after study method. The CMF values for fatal-and-injury crashes in Tables C-18 and C-21 of the final report by Harwood et al. are listed in Table 6. The first six rows of the table correspond to left-turn bays. The last six rows correspond to right-turn bays. Within each group of rows, the CMFs vary by area type, traffic control type, and level of aggregation. The CMF values obtained from Tables C-18 and C-21 are listed in Column 5. The CMF values in the first two rows correspond to left-turn bays added to urban signalized intersections. The spatially aggregate CMF in the “intersection” row is 0.716 (from Table C-18). It represents the average effect at 39 intersections for which 121 legs were treated (for an average of 3.1 bays per intersection = 121/39). The spatially disaggregate CMF in the “treated approach” row is 0.647 (from Table C-21). It represents the average effect on crashes on the 121 treated legs. This description applies to each pair of rows in the table. The values in the last two columns of Table 6 were computed using Equation 4. Specifically, the disaggregate CMF in the “treated approach” row was used with the two proportions p to compute two estimates of the aggregate CMF. To accommodate the non-integer nature of the “average bays/site” variable, 10 intersections were assumed to be treated and the number of treated legs was adjusted slightly at each intersection to produce the “average bays/site” value listed in the table. The resulting aggregate CMFs shown in the last two columns are considered

24 Guidelines for the Development and Application of Crash Modification Factors to represent a reasonable range of possible values for the aggregate CMF, depending on the proportion of crashes associated with the treated legs. This range is comparable to the aggregate CMF value in Column 5. The calculation for left-turn bays at urban signalized intersections (corresponding to the first two rows of Table 6) is shown with the following 10 equations developed using Equation 4 for the case p = 0.45: The first equation includes the CMF “0.647” for each of the four terms, which indicates that a bay was installed on each of the four legs. The second through tenth equations include “0.647” for three terms and a “1.000” for the fourth term. This pattern indicates that bays were installed on only three legs for nine intersections. All total, 31 bays were installed at the 10 intersections for an average of 3.1 bays per site. The average aggregate CMF for the 10 intersections is 0.66 (= [0.647 + 9 × 0.665]/10). The other values shown in the last two columns were computed using a similar technique. A comparison of the aggregate CMF (i.e., the “intersection” CMF) in Column 5 with the range in Columns 6 and 7 yields several observations. First, it indicates that the value in Column 5 is either within the range or slightly smaller than the lower value of the range. The general agree- ment between the aggregate CMF in Column 5 and the range in Columns 6 and 7 is an indi- cation that Equation 4 provides a reasonable estimate of the aggregate CMF. More generally, it illustrates the influence that the crash distribution proportion has on the magnitude of the aggregate CMF and highlights the importance of a disaggregate safety evaluation. The fact that four of the six aggregate CMFs have values that are smaller than the lower value of the range suggests that there may be a small (beneficial) interaction between the addition of a Eq A Eq B Eq J . : 0.647 0.647 0.45 0.647 0.45 0.647 0.05 0.647 0.05 . : 0.665 0.647 0.45 0.647 0.45 0.647 0.05 1.000 0.05 : : : : : : : : : . : 0.665 0.647 0.45 0.647 0.45 0.647 0.05 1.000 0.05 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = × + × + × + × = × + × + × + × = × + × + × + × Area Type Control Type Crash Location Average Bays/Site CMF Implied Intersection CMFagga p = 0.45 p = 0.25 Left-Turn Bay Urban Signal Intersection 3.1 0.716 0.66 0.73 Treated approach 1 0.647 -- -- Unsignalized Intersection 2 0.921 0.95 0.97 Treated approach 1 0.948 -- -- Rural Unsignalized Intersection 1.8 0.366 0.51 0.73 Treated approach 1 0.390 -- -- Right-Turn Bay Urban Signal Intersection 2.2 0.794 0.80 0.88 Treated approach 1 0.778 -- -- Unsignalized Intersection 1.5 0.466 0.72 0.85 Treated approach 1 0.589 -- -- Rural Unsignalized Intersection 1.5 0.841 0.84 0.91 Treated approach 1 0.757 -- -- a Assumptions: Intersection has four legs. Bays are installed on major-road legs first, before being installed on minor-road legs. The proportion “0.45” corresponds to an intersection with 45% of the crashes occurring on each of the two major legs and 5% of the crashes occurring on each of the two minor legs. The proportion “0.25” corresponds to an intersection with 25% of the crashes occurring on each leg. Table 6. Reported safety effect of intersection turn bays.

Findings and Applications 25   bay on one leg and the frequency of crashes within the intersection (but not on the treated leg). For example, the addition of a bay may improve sight lines to (and gap-acceptance decisions by) drivers on other legs and, thereby, indirectly influence overall crash frequency within the intersection. Subtask 2.6d Excel Spreadsheet Tools The team developed two Excel spreadsheet tools to facilitate the implementation of the pro- cedure for selecting and adjusting CMFs. Excel Spreadsheet Tool 1—CMF Regression Software. This tool supports the procedures in Appendix A. It can be used to evaluate two or more CMFs associated with a common treat- ment. The evaluation can consist of (1) computing the overall average CMF, (2) computing CMFs by crash type or severity category using reported aggregate CMFs, or (3) computing CMFs as a function of site characteristics. A user guide for the CMF Regression Software is presented in Appendix D. Excel Spreadsheet Tool 2—CMF Combination Tool. This tool is a spreadsheet implemen- tation of the homogeneity testing procedure presented in Appendix A, Step 6. This tool can be used to test two or more CMFs for the same treatment to determine whether they are similar enough to be combined into a single CMF value. If so, the tool produces a value for the com- bined CMF. It also gives cautions for the use of the combined value. While the CMF Regression Software provides this same functionality, this tool was developed as a simpler version that would be directed at users who only want to compare two or more CMFs to determine whether they can be combined. A user guide for the CMF Combination Tool is presented in Appendix E. Task 3 Quantifying the Effect of Multiple Treatments at a Single Location Transportation agencies frequently implement more than one treatment at a given location, either sequentially or simultaneously, to address specific safety concerns. These agencies need to estimate the expected safety impact of the combined treatments, and CMFs are one tool to support this effort. While there are more than 5,000 CMFs available from the CMF Clearing- house, many of these are for individual treatments. The issue is that relatively few CMFs exist for specific combinations of treatments, and it would take a tremendous effort to develop CMFs for all likely combinations of treatments. An alternative to developing CMFs for each possible combination of treatments is to combine individual CMFs to estimate the combined treatment effect. Before this project, there were limited guidelines on the application of multiple CMFs, and the guidelines that did exist had not been rigorously tested. Overview of Task and Products The objective of Task 3 was to develop guidelines for estimating the combined effect of mul- tiple different treatments (not to be confused with estimating a single CMF from multiple CMFs for the same treatment). The primary audience for these guidelines is transportation profes- sionals who consider the safety effects that would result from the application of multiple safety treatments at a location. Using the product of this task, agencies will be able to estimate the combined effect of multiple treatments for which individual CMFs were developed in isolation from previous research.

26 Guidelines for the Development and Application of Crash Modification Factors The product of Task 3 includes a recommended method for combining single-effect CMFs to estimate the joint effect of multiple treatments. Guidelines are provided to help determine the likelihood of overlapping effects and the appropriate method to account for the interaction among multiple treatments. The guidelines also identify a method for estimating the standard error of the joint effect based on the standard errors of the individual CMFs. Finally, the guide- lines provide examples for common combinations of treatments to demonstrate how the recom- mended method can be used to estimate the combined CMF. The procedure and guidelines produced from Task 3 are presented in Appendix B. Subtask 3.1 Literature Review The first subtask identified existing methods and known issues related to the combination of single-effect CMFs to estimate the joint effect of multiple treatments. Based on a thorough literature review and discussions with practitioners, the study team identified existing methods for combining single-effect CMFs and assessed the strengths and limitations of those methods. A summary of the existing methods and related issues is provided below. Existing Methods Several existing methods for estimating the combined treatment effect were summarized pre- viously in a white paper by Gross and Hamidi (2011). The white paper provided a foundation for this task, and additional methods were added based on a review of the literature. This section provides a summary of existing methods for estimating the combined effect of multiple treat- ments. (Note that not all methods “combine” single-effect CMFs. For example, some methods are based on engineering judgment. In addition, not all the methods are explored further in this research. For example, the first method is an additive effects approach, which has been shown through other work to be inappropriate for this type of analysis.) Additive Effects. The additive effects approach assumes that CMFs are independent, and estimates the combined effect by adding the individual effects as follows: Equation 6CMF 1 1 CMF 1 CMF . . . 1 CMFt 1 2 n[ ]( ) ( ) ( )= − − + − + + − where CMFt = CMF for the combined treatments CMF1 = CMF for the most effective treatment CMF2 = CMF for the second most effective treatment CMFn = CMF for the nth most effective treatment The primary limitation of this approach is that the combined effect could exceed 100% if enough treatments were implemented or if the expected crash reductions were relatively large for just a few treatments. Another limitation is that the treatment effects may not be indepen- dent (i.e., there may be overlapping effects). As such, this method was excluded from further investigation. Additive Effects with Systematic Reduction of Subsequent CMFs. This method is like the additive effects approach but reduces the effect of each subsequent treatment by a set amount (e.g., one-half, two-thirds). Equation 7CMF 1 1 CMF 1 CMF 2 . . . 1 CMF n t 1 2 n( )= − − + −    + + −       

Findings and Applications 27   While this method reduces the effect of each subsequent treatment, it still suffers from the primary limitation of the additive effects approach (i.e., the combined effect could exceed 100%). As such, this method was excluded from further investigation. Dominant Effect. The dominant effect approach applies the CMF for only the most effec- tive countermeasure (i.e., lowest CMF value). This method is an over-simplified approach to estimating the combined effect of multiple treatments. By only applying a single CMF, this method avoids the issue of independence. The primary limitation of this method is that it is likely to underestimate the combined treatment effect if subsequent treatments improve safety. Multiplicative. The multiplicative approach assumes that CMFs are independent and esti- mates the combined effect by multiplying the individual CMFs as follows: Equation 8CMF CMF CMF . . . CMFt 1 2 n= ∗ ∗ ∗ The primary limitation of this approach is that the combined effect may be underestimated or overestimated if the treatment effects are not independent. Limited Multiplicative. The limited multiplicative approach is like the multiplicative approach but limits the number of CMFs to two or three. Equation 9CMF CMF CMFt 1 2= ∗ This method helps to limit the potential for overlapping effects but still may underestimate or overestimate the combined effect if the treatment effects are not independent. There is also no rationale for this approach. One might expect that for some treatments three CMFs should be multiplied, for others two, and for some only one is best. Multiplicative with Generalized Reduction of Combined Effect. This method is like the multiplicative approach but reduces the total combined effect by a set amount. As an example, Turner and Tziotis (2008) suggest that a factor of two-thirds be applied to reduce the combined effect as follows: Equation 10CMF 1 2 3 1 CMF CMFt 1 2( )( )= − − ∗   The primary limitation of this method is that there is limited theoretical or empirical evidence for the generalized reduction. Turner and Tziotis (2008) developed this factor based on limited data from New Zealand. Therefore, the general applicability of this factor, or any single factor for that matter, remains questionable. There are likely merits to this method, but there is a need for additional research. For example, the generalized reduction may vary depending on the number or type of treatments. Multiplicative with Systematic Reduction of Subsequent CMFs. This method is like the multiplicative approach but reduces the effect of each subsequent treatment by a set amount (e.g., one-half or two-thirds). CMF CMF 1 1 CMF 2 . . . 1 1 CMF n t 1 2 n Equation 11= ∗ − −    ∗ ∗ − −    While this method reduces the effect of each subsequent treatment, the primary limitation is that there is no theoretical or empirical evidence for the systematic reductions. There are likely merits to this method, but there is a need for additional research to refine the specific reductions.

28 Guidelines for the Development and Application of Crash Modification Factors Multiplicative with Empirical-Based Reduction of Combined Effect. This method is like the multiplicative approach with generalized reduction but reduces the total combined effect by a set amount based on empirical research conducted as part of this project. The empirical-based reduction factor is applied to reduce the combined effect as follows: ii n Equation 12CMF 1 1 CMFt 1∏( )= − β − = This will help to overcome the primary limitation of the previous two methods in that there will be additional empirical evidence for the reduction. The following equations provide alterna- tive forms for combining CMFs based on the empirical investigation. ii n i Equation 13CMF CMFt 0 1∏= β β= CMF CMFt 0 1 i Equation 14∑= β + β ∗= ii n Dominant Common Residuals. This method, proposed by Elvik (2009), is like the mul- tiplicative method, except the non-independent CMFs (i.e., common residuals) are raised to the power of the most effective CMF (i.e., dominant common residual). The combined effect of multiple treatments is estimated as follows: CMF Equation 15CMF CMF CMF . . . CMFt 1 2 n 1( )= ∗ ∗ ∗ The primary limitation of this method is that there is no theoretical justification. However, it does provide a more conservative estimate of the combined effect than the multiplicative method (i.e., common residuals methods) as noted by Elvik (2009). Another limitation is mani- fest when the individual CMFs are greater than 1.0, particularly those of the most effective treat- ments. In these cases, the combined CMFs are raised to a power greater than 1.0, intensifying the effect rather than dampening it. As such, this method is not appropriate for CMFs greater than 1.0. Dominant Effect for Overlapping Crash Types. This method is like the dominant effect method but applies the CMF for only the most effective countermeasure (i.e., lowest CMF value) where there is overlap among the treatment effects. Otherwise, the CMFs are applied separately to the target crashes. If the expected crashes after treatment (N) is the product of Nbase and the applicable CMF, and Nbase is composed of multiple crash types (A, B, and C), it can be shown by the distributive property that: N N CMF A B C CMF A CMF B CMF C CMFbase Equation 16( )= ∗ = + + ∗ = ∗ + ∗ + ∗ Now, consider the combined effect of two treatments where CMF1 is associated with the more effective treatment and applies to target crash types A and B. CMF2 is associated with the less effec- tive treatment and applies to target crash types B and C. The expected target crashes for the two treatments are as follows: Equation 17N A Bbase1 = + N B Cbase2 Equation 18= +

Findings and Applications 29   CMF1 is applied to Nbase1 (A+B) to estimate the expected crashes after treatment (N1). CMF2 is applied to Nbase2 (B+C) to estimate the expected crashes after treatment (N2). N N CMF A B CMF A CMF B CMF1 base1 1 1 1 1 Equation 19( )= ∗ = + ∗ = ∗ + ∗ N N CMF B C CMF B CMF C CMF2 base2 2 2 2 2 Equation 20( )= ∗ = + ∗ = ∗ + ∗ The overlap between the two treatments is target crash type B. Applying this method, the expected effect on any overlapping crash types would be based only on the treatment with the greatest effect. In this case, the expected crashes after treatment (N) would be computed as follows: N N N overlap A CMF B CMF C CMF1 2 1 1 2 Equation 21= + − = ∗ = ∗ + ∗ This method accounts for potential overlapping treatment effects, but the primary limitation is that it may be difficult to identify the specific crashes that overlap between treatments. Estimating the Combined Effect When Interaction is Unknown. This method is used to estimate the combined effect of multiple treatments when the interaction is unknown or cannot be quantified. This may be the case when the CMFs for individual treatments apply to more general conditions or the treatments are applied to different locations (e.g., different intersection approaches). The premise of this approach is to isolate a given treatment’s effect on crash distribution, as opposed to total crashes. Then, for multiple treatments, estimate the combined treatment effect on crashes in each distribution as the product of CMFs. The computed CMFs are applied to the appropriate crash distribution category, where the crash distribution used is that for the subject site. This approach will limit the double-counting of crashes when multiplying CMFs to just those crashes in each distribution category. Further details and an example are provided in Subtask 3.4: Develop Framework for Phase 2. Meta-Analysis. The meta-analysis approach incorporates the standard error of the CMFs to estimate the combined effect using the following equation: CMF CMF 1 S t unbiased,i Si=1 n i 2 i=1 n i 2 Equation 22∑ ∑ = where CMFt = unbiased CMF for the combined treatments CMFunbiased,i = unbiased CMF for treatment i si = adjusted standard error of the unbiased CMF for treatment i n = number of CMFs to be combined This method is used to combine multiple CMF estimates for the same treatment and does not apply in general to estimating the combined effect of different treatments. As such, it was excluded as an alternative in this context. Crash Modification Functions. The CMFunction approach is not a method for combining individual CMFs, but rather a possibility for estimating the combined effect of multiple treat- ments. There are many examples in the HSM, CMF Clearinghouse, and other sources where CMFs are derived from regression-based models. If a regression model contains independent

30 Guidelines for the Development and Application of Crash Modification Factors variables for the treatments of interest, then a CMFunction may be derived to estimate the com- bined effect of those treatments. One advantage of using regression-based models is that there are many CMFs for which a before-after evaluation is seldom possible. The primary limitation of this method is that regres- sion-based models are only able to show correlation (not causation) between the independent and dependent variables. Another limitation is that the treatments of interest would need to be included in the model, and the model would need to be properly developed to accurately reflect the effects of those treatments. It is unlikely that these two conditions will be met in practice, so this method was excluded from further consideration. Engineering Experience and Judgment. This method allows the engineer to assess the crash patterns at the location of interest and consider the applicable CMFs. The engineer then uses their judgment to determine a combined treatment effect. This method is highly dependent on the experience of the engineer and is not as defensible as a quantitative method for estimating the combined treatment effect. Standard Error of Combined Treatment Effect. There is also interest in estimating the standard error or variance of the combined treatment effect. There is scant literature on the topic, but two methods were identified from the literature review. The first method is based on the meta-analysis approach to combining CMFs. Equation 23 has been used to estimate the standard error when multiple CMFs for the same treatment are combined in a meta-analysis (Bahar 2010). Equation 23 is shown for completeness but does not apply when CMFs of several different treatments are combined into one CMF. Equation 23S 1 1 S i2i 1 n∑ = = where S = standard error of the combined unbiased CMF value Si = adjusted standard error of the unbiased CMF from study i n = number of CMFs to be combined The second method was defined by Lord (2010) and applies to the following two scenarios: • Combined estimate of baseline crash prediction models and CMF(s) • Combined estimate from multiplying two or more CMFs The variance is estimated using the theory of multiplying independent random variables. If Equation 24 is used to estimate the combined effect of independent random variables, then Equation 25 is used to estimate the variance of the combined variables. In this case, single- effect CMFs represent independent random variables. This method provides a reasonable upper bound on the variance estimate; however, it does not explicitly recognize correlation among the CMF values. If the correlation is not zero, which is likely to be the case, the true variance will be smaller than predicted by Equation 25. Equation 24CMF CMF CMF . . . CMFcombined 1 2 n= ∗ ∗ ∗ Variance CMF CMF Var CMF . . . CMF Var CMF CMFcombined 12 1 n2 n combined 2 Equation 25 [ ]( ) ( )( ) ( )( ) ( )= + ∗ ∗ + − To apply this method, the variance must be reported for all components included in the computation (i.e., each CMF). In practice, the variance of the CMF may not be readily available.

Findings and Applications 31   As such, it is important to encourage the estimation of variance during CMF development and consistent reporting of the results. The methodology also assumes that the CMFs are indepen- dent random variables, which may or may not be the case. It will be necessary to compare theory with empirical evidence of the variance of combined effects. If the estimated variance from Equation 25 is inconsistent with the variance of combined treatment effects, then it may be necessary to develop an adjustment factor to better align theory and practice. Also, Equation 25 applies when the combined CMF is defined by Equation 24. If the combination is better defined by some other method (e.g., by a model with parameters), then it will be necessary to explore and develop alternatives for estimating the variance of the combined CMF. The methods presented in Chapter 6.2 of Hauer (1997) will be explored in this case. Known Issues There are known limitations associated with various existing methods for estimating the com- bined effect of multiple treatments. The white paper by Gross and Hamidi (2011) provided a foundation for this task, and additional limitations were defined based on a review of existing methods and discussions from the literature. The following is a list of specific issues, followed by a detailed discussion of each. • Expression of safety effect • Assumption of independence • Logic of added benefit versus fallacy of additive effects • Lack of consistency (judgment) • Applicability of CMFs • Lack of detailed CMF information • Computing a confidence interval Expression of Safety Effect. The first issue is whether the safety effect of a treatment is better described by an additive effect or a multiplicative effect. This issue was identified by Hauer (1997) but remains unexamined. To emphasize the importance of this issue, note that virtually all the entire literature in other fields deals with the estimation of the additive effect (δ)—the “effect size.” A CMF (θ) is multiplicative (e.g., a countermeasure effect is estimated to be a percentage decrease or increase in crashes) and is an oddity in terms of representing the effect of a treatment. While Hauer (1997) identifies an empirical method to examine the suitability of δ, θ, or something different in highway safety analysis, this question is beyond the scope of the current project. Further, the profession has adopted the use of CMFs (θ), so this research will focus on how to combine existing CMFs to estimate the combined effect of multiple treatments. Assumption of Independence. The overarching issue with combining multiple CMFs is the possibility that the safety effects of the treatments may not be independent of one another. In other words, the effect of the simultaneous or sequential application of treatments may not be equal to the product of the CMFs for the individual treatments. Due to correlations among the CMFs, the true combined effect of multiple treatments may be greater than, less than, or equal to the simple product. Consider a basic situation in which there are two treatments represented by CMF1 and CMF2. The parameter of interest is the true safety effect of the combination of these two treatments ( 12CMF ). If the treatments are assumed to be independent, the current practice is to multiply the two CMFs as was shown in Equation 8 and described in the HSM (AASHTO 2010). This assumption may lead to three different scenarios as characterized by Equation 26 through Equation 28. The true safety effect of the combination of treatments may be overestimated (i.e., Equation 26), underestimated (i.e., Equation 27), or accurately estimated (i.e., Equation 28).

32 Guidelines for the Development and Application of Crash Modification Factors > ∗12 1 2 Equation 26CMF CMF CMF Equation 2712 1 2< ∗CMF CMF CMF Equation 2812 1 2= ∗CMF CMF CMF where 12CMF = true safety effect of applying treatments 1 and 2 (i.e., parameter) CMF1 ∗ CMF2 = simple product of two CMFs (i.e., parameter estimate) Examples of the first and third scenarios may be more familiar than examples of the second scenario. An example of the first scenario would be the implementation of two or more treat- ments that redundantly address the same crash type. For instance, consider the installation of roadway lighting and enhanced pavement marking retroreflectivity. Since both treatments tar- get nighttime crashes, it is possible that the crash reduction associated with the two treatments would be less than the value suggested by the product of the two CMFs. Examples of the second scenario would be the implementation of two or more treatments that complement each other such that the combined crash reduction is greater than the product of the individual CMFs. For instance, consider enhanced pavement markings and shoulder rumble strips. Applying these two treatments in combination (i.e., edgeline rumble strip) creates a ver- tical face to the pavement marking, which is more visible than a standard pavement marking during wet weather conditions. As such, the combined effect of these two treatments may be greater than the product of the CMFs for the individual treatments. Examples of the third scenario include the implementation of treatments that target different crash types. For instance, installing right- and left-turn lanes on the major approaches of an inter- section will target specific, separate crash types. Since the target crash types are mutually exclu- sive, the combined effect may be computed accurately as the product of the individual CMFs. In the case of three or more treatments, one may encounter another scenario in which the net combined effect of the treatments approximately equals the product of the individual treatments, but only because of offsetting correlations among pairs of treatments. For example, suppose three treatments are considered for implementation: CMF1, CMF2, and CMF3. The following scenario is possible: Equation 29CMF CMF CMF12 1 2>> ∗ Equation 30CMF CMF CMF23 2 3<< ∗ Equation 31CMF CMF CMF13 1 3= ∗ Equation 32Such that CMF CMF CMF CMF123 1 2 3= ∗ ∗ where CMF12 = true safety effect of applying treatments 1 and 2 (i.e., parameter) CMF23 = true safety effect of applying treatments 2 and 3 (i.e., parameter) CMF13 = true safety effect of applying treatments 1 and 3 (i.e., parameter) CMF123 = true safety effect of applying treatments 1, 2, and 3 (i.e., parameter) CMF1 ∗ CMF2 = simple product of CMF 1 and 2 (i.e., parameter estimate) CMF2 ∗ CMF3 = simple product of CMF 2 and 3 (i.e., parameter estimate)

Findings and Applications 33   CMF1 ∗ CMF3 = simple product of CMF 1 and 3 (i.e., parameter estimate) CMF1 ∗ CMF2 ∗ CMF3 = simple product of CMF 1, 2, and 3 (parameter estimate) The scenario of three or more treatments, and its various permutations, are noteworthy because decision-makers may be given the false impression that the contributions made by each pair of treatments can be estimated accurately as the product of the individual CMFs. As the above scenario demonstrates, two of the three treatments may account for most of the reduction in crashes (i.e., one of the treatments was relatively ineffective and therefore not cost-effective). This study focused on the combination of two treatments but considered the implications of combining three or more treatments. To avoid potential complications, users should only com- pare two CMFs at a time. These scenarios raise the question of how to determine when treatments are independent. One suggested approach is to compare the target crash types for each treatment (CMF Clear- inghouse 2011a). In theory, if the treatments target different crash types, then it may be safe to assume independence and apply the multiplicative approach. If treatments target the same crash types, then there is a distinct possibility of dependency and the need to account for the potential overlapping effects. It may be difficult to establish independence for two treatments due to the difficulty in defin- ing target crashes. Target crashes include all crashes that may be affected by a treatment and not just those targeted for mitigation. For example, a roadway may be resurfaced to improve friction with the intent to mitigate wet weather crashes; however, resurfacing may also impact speed and thereby affect both the frequency and severity of all other crashes. Several other examples in which treatments affect various (sometimes difficult to foresee) crash types are provided in the literature (Hauer 1997). Logic of Added Benefit Versus Fallacy of Additive Effects. The Dominant Effect method does not consider the effects of multiple treatments. Instead, the method applies a single CMF (e.g., the CMF for the treatment with the greatest effect) to estimate the expected reduction in crashes. The primary concern with this method is that it will likely underestimate the potential effects of the project when it is reasonable to assume an added benefit of additional treatments. While there may be an added benefit of applying more than one treatment at a given location, the effects for the treatments are not additive because the total crash reduction cannot be greater than 100%. Recall the two additive effects methods presented above. The combined effect esti- mated from either of these methods could exceed 100% if enough treatments were implemented or if the expected crash reductions were relatively large for just a few treatments. Lack of Consistency (Judgment). Several of the identified methods rely on engineering experience and judgment to select an appropriate CMF for each treatment. One of the methods relies solely on engineering experience and judgment to estimate the combined effect of multiple treatments. While engineering experience and judgment are a necessary component of highway safety, they are also open to interpretation and may result in inconsistencies among or within agencies. For example, CMFs can be used to estimate the expected reduction in crashes, which can then be used as an input in a benefit–cost analysis. If an agency uses the results of benefit– cost analyses (or similar measures) in the allocation of funding, all divisions within that agency must use a consistent method so a fair comparison can be made among projects. Applicability of CMFs. CMFs may be related to total crashes or specific crash types and/or severities. The crash type and severity associated with a CMF define the crashes for which the CMF applies. It is not appropriate to apply a CMF for a specific crash type or severity to other crash types and severities because a treatment may reduce certain crash types or severities while

34 Guidelines for the Development and Application of Crash Modification Factors increasing other crash types and severities. Even if multiple treatments are independent, the respective CMFs may be related to different crash types and/or severities. If this is the case, the CMF for a particular crash type and/or severity must only be applied to the crashes expected for that crash type and/or severity. In other words, practitioners should be careful to consider crash type and severity when combining CMFs because simply multiplying the CMFs together without doing so would likely lead to erroneous results. CMFs are also related to specific condi- tions. As discussed in other sources (CMF Clearinghouse 2011b), CMFs should not be applied to scenarios for which they do not apply. Examples of specific roadway characteristics include area type, number of lanes, functional classification, and traffic volume. Lack of Detailed CMF Information. Some agencies are calculating expected reductions by crash type and summing the reductions to estimate project-level benefits. This method is likely to have less overlap than combining CMFs for total crashes, but there is still the risk that multiple treatments will address the same crash type (which relates to the assumption of inde- pendence). For instance, consider shoulder widening and the installation of shoulder rumble strips. Even if the CMFs for the specific crash types are applied separately, the combined effect will likely be overestimated as the two treatments both address run-off-road crashes. Further, there is the potential that a CMF has not been developed for a specific crash type for a given treatment. In these cases, the agency would not be able to apply a CMF for the specific crash type. There are currently more than 4,100 CMFs in the CMF Clearinghouse, only 2,600 of which are for specific crash types. Computing a Confidence Interval. A confidence interval provides highly useful informa- tion about a parameter. It provides the range of values that contains the parameter with a certain level of probability (e.g., 90%, 95%, or 99%). When working with a CMF, the confidence interval indicates whether a treatment has a statistically significant effect on crashes. If the confidence interval includes 1.0, then it can be concluded that the treatment does not have a statistically sig- nificant effect on crashes with a certain degree of confidence (e.g., 95%). If the confidence inter- val excludes 1.0, then it can be concluded that the treatment does have a statistically significant effect on crashes with a certain degree of confidence. More importantly, it is necessary to deter- mine whether the effect is different from zero, and this depends on how well the magnitude of the effect is “known.” The decision-making process will be improved (whether to implement or not implement a treatment) as the magnitude of the effect is better “known” (i.e., small standard error and small confidence interval). Therefore, it is important to understand the importance of the standard error and be able to compute a confidence interval for a CMF. To compute the confidence interval, one needs to identify the desired level of confidence and know either the standard error or variance associated with the CMF. (Note that the standard error and variance are directly related, and one may be computed from the other.) Equation 23 provides a means for computing the standard error of a combined CMF where multiple CMF estimates are combined for a single treatment. Equation 25 provides a means for computing the variance of a combined CMF where multiple CMF estimates are combined for different treatments. Equation 25 will provide a starting point for the current research, but it will be necessary to further explore the validity. For example, the method assumes that the combined CMFs are independent random variables, which may or may not be the case. It will be necessary to compare the theoretical values from Equation 25 with empirical evidence of the variance of the combined effects. If the theoretical and empirical values differ, then it may be necessary to develop an adjustment factor to better align theory and practice. Other methods such as those presented in Chapter 6.2 of Hauer (1997) may also be applicable if the combination of CMFs is better defined by some other method (e.g., by a model with parameters).

Findings and Applications 35   Subtask 3.2 Develop Framework for Guidelines The second subtask proposed a general framework for the guidelines. The following is an annotated outline of the proposed sections for the guidelines. 1. Background. What are the considerations for combining single-effect CMFs to estimate the joint effect of multiple treatments? 2. Recommended Method. The most appropriate method(s) for combining single-effect CMFs and the respective standard errors will be identified based on the results of the assessment and described in this section. a. Combined Effect. What is the recommended method for combining single-effect CMFs to estimate the joint effect of multiple treatments? b. Standard Error of Combined Effect. What is the recommended method for estimating the standard error of the combined CMF? 3. Examples. The guidelines will provide step-by-step procedures and examples for selecting and applying the appropriate method(s). 4. Combined Treatment Effects. Through the course of this project, the research team will produce or identify CMFs for specific combinations of treatments. These CMFs will be presented in the guidelines for future use by practitioners. 5. Interaction Effects. A separate section of the guidelines will describe the method(s) used in this research to quantify the interaction effect. This section of the guidelines will be written for other researchers to apply the method(s) to quantify the interaction of other CMF combina- tions. This section of the guidelines will also provide instructions for documenting individual projects for future validation of the recommended method(s), including the details of specific treatments, individual CMFs used for estimation purposes, and conditions before and after treatment (crash and exposure data). If the appropriate method is dependent on the specific scenario at hand, then it is envisioned that a flow chart will be developed and presented to guide users through the method selection process. An example flow chart is shown in Figure 2. Define Applicability of Individual CMFs (i.e., to what crash types and severities do the individual CMFs apply?) Same Crash Type and Severity Different Crash Type and Severity Define Categories for Individual Treatments (e.g., roadway, roadside, intersection) Define Categories for Individual Treatments (e.g., roadway, roadside, intersection) Same General Category Different General Category Large Potential Interaction Effect: Apply Method 1 Medium Potential Interaction Effect: Apply Method 2 Same General Category Different General Category Small Potential Interaction Effect: Apply Method 3 Negligible Potential Interaction Effect: Apply Method 4 Figure 2. Example flow chart for selecting appropriate method.

36 Guidelines for the Development and Application of Crash Modification Factors Subtask 3.3 Identify Potential Data Sources for Phase 2 The third subtask identified data sources from which to test various existing and proposed methods. This included a review of the CMF Clearinghouse to identify existing CMFs for the effect of combined treatments. This also involved a review of previous and current research related to CMF development to identify databases that could be used to develop CMFs for combined treatments. Several potential data sources could be used to support this research. Subtask 3.3 focused on the identification of potential data sources to facilitate the following: • Explore the magnitude and structure of interaction effects for combination treatments • Evaluate the potential for existing and proposed methods to estimate the combined effect of multiple treatments when CMFs are available for individual treatments CMF Clearinghouse The CMF Clearinghouse (www.cmfclearinghouse.org) was established to provide a regularly updated, online repository of CMFs. The Clearinghouse was used as a data source to iden- tify treatments for which CMFs exist for combination treatments as well as for the individual treatments. Where CMFs are available for individual and combination treatments, the results are considered to evaluate methods for combining individual CMFs to estimate the combined treatment effect. The Clearinghouse also identifies the reference to the underlying study, and the research team followed up with select authors to obtain the original databases for further analysis. Subtask 3.4 provides further details on CMFs that are related to combination and individual treatments as identified from the Clearinghouse. FHWA Evaluation of Low Cost Safety Improvements Pooled Fund Study (ELCSI-PFS) The FHWA ELCSI-PFS is a multi-phase project to develop CMFs for low-cost treatments. Several phases have been completed, and others are currently in progress. Phase II and Phase V of the ELCSI-PFS are of specific interest to this project. ELCSI-PFS Phase II. Phase II is complete and involved the development of CMFs for four treatments. One of the treatments is related to the allocation of lane and shoulder width for a given pavement width (Gross 2009). A multistate database was developed to evaluate the effects of lane and shoulder width. This database is used to facilitate additional analysis of the combined effects of lane and shoulder width to better understand the potential interactions. The results of the previous evaluation are also used to test existing and proposed methods for combining CMFs. ELCSI-PFS Phase V. Phase V is ongoing but has produced CMFs for four combination treatments, including (1) centerline and edgeline rumble strips, (2) median barrier and inside shoulder rumble strips on divided roads, (3) multiple low-cost treatments at signalized intersec- tions, and (4) multiple low-cost treatments at stop-controlled intersections. The results of these studies provide CMFs for the combined effects of multiple treatments. It was anticipated that these data sets would provide an opportunity to develop CMFs for the individual treatments (or subsets) if the treatments were implemented at various points in time. This was not the case, but these studies do provide an opportunity to test the methods by comparing the results (i.e., a CMF that represents the effect of multiple treatments) to the combined CMF based on CMFs developed for individual treatments. NCHRP Project 17-35: Evaluation of Safety Strategies at Signalized Intersections This project developed CMFs for several treatments identified in NCHRP Report 500: Guid- ance for Implementation of the AASHTO Strategic Highway Safety Plan; Volume 12: A Guide for

Findings and Applications 37   Reducing Collisions at Signalized Intersections (Srinivasan et al. 2011; Antonucci et al. 2004). One of the treatments was the installation of dynamic signal warning flashers (DSWFs) before signal- ized intersections. DSWFs provide drivers with advance notice of the phase change. Specifically, the DSWF is linked to the signal, and flashers are located before the intersection and actuated at a time when the driver would not be able to clear the intersection before the onset of the red phase. A multistate database was developed, including sites from Nevada, Virginia, and North Carolina. For all treatment sites in Nevada and most treatment sites in Virginia, it was dis- covered that the traffic signals and DSWFs were installed at the same time. This provides an opportunity for the current study to reanalyze the data, supplementing the database with addi- tional data from the participating states, to estimate the combined effect of installing a signal and DSWF at the same time. CMFs already exist for the individual effect of installing a signal and installing DSWFs (once a signal is in place). NCHRP Project 17-59: Safety Impacts of Intersection Sight Distance The objective of this project was to determine the relationships between available intersection sight distance (ISD) and safety through the development of CMFs and CMFunctions. Since available ISD is rarely changed at an intersection, a cross-sectional approach was used for data collection and analysis. Available ISD, intersection angle, and many other roadway and traffic characteristics were collected in the field and via desktop for more than 800 intersection approaches in North Carolina, Ohio, and Washington. The data set is available at the approach direction level for rural and urban, three- and four-leg intersections with two and four lanes on the major road approaches. This data set provides an opportunity to consider intersection angle and available ISD in isola- tion and in combination at unsignalized intersections with stop control on the minor approaches. Due to the extensive data collection for NCHRP Project 17-59, no additional data collection is necessary for this analysis. While both treatments are continuous, the data can be combined into categories for simplification of application. NCHRP Project 03-106: Traffic Control Device Guidelines for Curves This project developed CMFunctions for advance and in-curve horizontal alignment warning signs for isolated and series applications. The data set includes roadway, traffic, sign, and crash data for isolated curves and series curves on rural, two-lane highways in Florida, Ohio, Oregon, and Tennessee. Three years of data were collected via desktop for 272 isolated curves and 270 series curves. The data set considers each curve or curve series as an observation, and both directions are coded separately to account for differences in the directionality of traffic flow and other site characteristics. This data set provides the opportunity to consider multiple treatments at horizontal curves, both before and within the curve, for traffic signs as well as pavement markings and reflective delineators. Since this data set includes a variety of potential countermeasures, several are highly correlated and require further analysis to separate effects. Since extensive data are already avail- able, no additional data collection is required to use this database. Highway Safety Information System The Highway Safety Information System (HSIS) is a multistate database that contains high- quality crash, roadway inventory, and traffic volume data. Several HSIS member states maintain a safety improvement database, including California, Florida, North Carolina, Ohio, Washington, and the City of Charlotte. Three of those states (California, North Carolina, and Ohio) recently pro- vided their improvements databases for a feasibility test on establishing a multistate database for HSIS. These three databases include more than 14,700 safety improvements entries representing

38 Guidelines for the Development and Application of Crash Modification Factors nearly 5,800 different treatments. With the states’ permission, team members reviewed this data- base to search for locations where multiple treatments were implemented. State DOT Internal Research and Records Another opportunity to investigate potential interactions among combined treatments is to solicit input from State DOTs. The following opportunities were identified from a review of the literature. Colorado DOT. The Colorado DOT implemented multiple treatments on more than 100 projects, tracking the safety performance before treatment and documenting the opportunities for improvement. New York State DOT. There is a study from the NYSDOT on resurfacing where the safety impacts of resurfacing alone seemed to harm safety, but it enhanced safety when implemented with other safety improvements. Washington State DOT. WSDOT began installing rumble strips on undivided highways in 1999 as a countermeasure for roadway departure crashes. Installations on the shoulders were intended to reduce run-off-road crashes, while centerline rumble strips targeted reductions in cross-centerline crashes. WSDOT conducted an evaluation to estimate the effectiveness of the individual and combined treatments (Olson et al. 2013). Their report, Performance Analysis of Center line and Shoulder Rumble Strips Installed in Combination in Washington State, docu- ments the results of the analysis and provides CMFs for the combined treatment as well as CMFs for the individual treatment of shoulder rumble strips. An earlier report, Performance Analysis of Center line Rumble Strips in Washington State, produced CMFs for the individual treatment of centerline rumble strips (Olson et al. 2011). The results of these studies can be used to test exist- ing and proposed methods for combining CMFs. They can also be used to further explore the effects of sequential and simultaneous installation of treatments. The research team contacted these states and solicited input from several others to identify potential data sets for use in this study. In general, there is a lack of data, primarily treatment date and location, to support this specific research. In many cases, there are sufficient data to develop a CMF for one or both individual countermeasures or to develop a CMF for the com- bined countermeasure, but not enough data to develop CMFs for both individual countermea- sures and the combined countermeasure. Subtask 3.4 Develop Plan for Phase 2 The fourth subtask involved the development of a framework for Phase 2 based on the results of the first three subtasks. The essence of Task 3, Phase 2, is to define a recommended method (or methods) for estimating the combined treatment effect from individual CMFs and assess these methods through empirical investigation. A two-step process is proposed for conducting the assessment: • Step 1. Define ground truth. It is not enough to simply compare the results of various methods to each other. There is a need to first establish a baseline that can be used to compare the validity of the results. The baseline can be established through existing CMFs or by estimating new CMFs for combined treatments. • Step 2. Assess methods. The second step is to apply the proposed methods to estimate the combined treatment effect for various combinations of treatments based on existing indi- vidual CMFs. The estimates are then compared to the baseline (from Step 1) to assess the validity of the methods.

Findings and Applications 39   A detailed work plan is presented in this section to guide the efforts required to complete Phase 2. The following sections describe the proposed method to collect and assemble the required data, estimate the ground truth for specific combinations of treatments, assess the credibility of existing and proposed methods, and develop final guidelines for combining single-effect CMFs to estimate the joint effect of multiple treatments. Collecting and Assembling Data Subtask 3.3 identified potential data sources and previous studies that could be used to estab- lish the baseline CMFs for specific combinations of treatments or to identify existing CMFs for single treatments. An obvious starting point is the CMF Clearinghouse. As part of Phase 1, the research team queried the CMF Clearinghouse to identify CMFs for combinations of treatments and then queried again to identify CMFs for the individual related treatments. Table 7 presents the results, and the shaded cells represent treatment combinations with the highest potential for inclusion in this study. In this scenario, the proposed methods for combining CMFs could be assessed with the data in hand; however, the following potential issues were identified during the review of CMFs from the CMF Clearinghouse: • Applicability of CMFs. The CMFs for combination treatments may be generally applicable or may apply to specific crash types, crash severities, area types, roadway/intersection types, and other characteristics. The same is true for CMFs for individual treatments. While individual CMFs exist for many of the corresponding combination treatments, there are few cases when all the CMFs are directly applicable to the same scenario. • Quality of CMFs. The quality of existing CMFs is noted by the star rating in the CMF Clearinghouse. As one objective of this task is to rigorously evaluate various methods for combining CMFs, it is important to base the evaluation on high-quality CMFs. If the CMFs for either the combined or individual treatments are of poor quality, then they will not pro- vide a strong basis for the evaluation. As part of Phase 2, existing CMFs were further screened based on quality and applicability. In general, there are relatively few high-quality CMFs for combinations of treatments that also have corresponding high-quality and directly applicable CMFs for all the individual treatments. As such, it was necessary to assemble data to estimate new CMFs for establishing the ground truth and filling the gaps where individual CMFs do not currently exist for all treatments within a specific combination. Defining Ground Truth As discussed in Subtask 3.1, Known Issues, Assumption of Independence, it is often difficult to establish independence for two treatments. As such, it becomes necessary to quantify the likely degree of overlap between two or more treatments and account for this overlap when estimating their combined effects. The objective of this section is to describe evidence-based methods for quantifying the interaction of two or more treatments. This interaction is quanti- fied for selected CMF combinations, and the results are used to (1) develop alternative methods for estimating the combined effect from individual CMFs, and (2) assess the validity of existing methods for estimating the combined effect from individual CMFs. Assuming two potential treatments (Treatment P and Treatment Q), four categories of sites are defined by treatment type combination, as shown in Table 8. In this scenario, each treatment is a binary outcome (i.e., either present or not present). The four cells in the lower right quadrant of the table represent the attributes of a group of sites. Each of the four cells describes sites with a specified treatment level for each of the two treatments. For example, sites with level A1 cor- respond to sites that have treatment P at level A and treatment Q at level 1. If category A1 is the base condition (i.e., neither treatment present), then CMFs could be established for the other

40 Guidelines for the Development and Application of Crash Modification Factors Combined Treatment Combined Treatment ID Combined Treatment Star Rating Combined Treatment Applicability Individual Applicable CMFs Available? Individual CMF IDs (From Clearinghouse) Individual CMF Star Ratings Add additional signal and upgrade to 12- inch lenses 77 2 Urban, 4- legged, signalized Yes Signal head (1414) 12-inch lenses (1444) 3 2 Add centerline and move STOP bar to extended curb lines 73 0 General No -- -- Add centerline and move STOP bar to extended curb lines, double stop signs 73 0 General Partial Double stop signs (1661) 1 Add centerline and STOP bar, replace 24- inch with 30- inch stop signs 81 0 General Partial Larger stop signs (1677) 0 Convert STOP control (2-way) to signal control and install left-turn lane 66 0 General Yes Signal (1760) Left-turn lane (4648) 0 0 Flatten side slopes and remove the guardrail 72 2 General Partial Side slope (26) 5 Implement shoulder widening in conjunction with shoulder rumble strip installation on freeways 21 3 Principal arterial Other freeways and expressways Yes Shoulder widening (3653) Shoulder rumbles (121) 3 4 Implement signs and crossbucks at previously unprotected crossings 14 3 General No -- -- Improve horizontal and vertical alignments 66 0 General Yes Horizontal alignment (2826) Vertical alignment (720) 2 2 Table 7. Summary of existing CMFs for combined treatments.

Findings and Applications 41   (continued on next page) Improve signal visibility, including signal lens size upgrade, installation of new backplates, the addition of reflective tapes to existing backplates, and installation of additional signal heads 277 4 Urban, 4- legged, signalized Yes 12-inch lenses (1444) New backplates (1446) Reflective tape (1410) Signal head (1414) 2 0 4 3 Install a combination of chevron signs, curve warning signs, and/or sequential flashing beacons 102 3–4 4-lane, principal arterial Other freeways and expressways Yes Chevron signs (1898) Curve warning signs (1077) Flashing beacons (1089) 3 0 0 Install chevron signs, curve warning signs, and sequential flashing beacons 102 3 4-lane, principal arterial Other freeways and expressways Yes Chevron signs (1898) Curve warning signs (1077) Flashing beacons (1089) 3 0 0 Install chevron signs and curve warning signs 102 3 4-lane, principal arterial Other freeways and expressways Yes Chevron signs (1898) Curve warning signs (1077) 3 0 Install centerline and shoulder rumble strips 152 4 2-lane undivided Yes Centerline rumbles (2424) Shoulder rumbles (2421) 4 4 Install edgelines and centerlines at sites with higher incidences of crashes 2 3 Rural minor collector Yes Edgelines (4729) Centerlines (1209) 2 0 Install edgelines, centerlines, and post- mounted delineators 14 4 2+ lane undivided Yes Edgelines (83) Centerlines (87) Delineators (80) 3 3 3 Install paved shoulder and rumble strips 186 2 Principal arterial Other Yes Pave shoulder (2829) Shoulder rumbles (2832) 2 2 Combined Treatment Combined Treatment ID Combined Treatment Star Rating Combined Treatment Applicability Individual Applicable CMFs Available? Individual CMF IDs (From Clearinghouse) Individual CMF Star Ratings Table 7. (Continued).

42 Guidelines for the Development and Application of Crash Modification Factors Combined Treatment Combined Treatment ID Combined Treatment Star Rating Combined Treatment Applicability Individual Applicable CMFs Available? Individual CMF IDs (From Clearinghouse) Individual CMF Star Ratings Install raised pavement markers and transverse rumble strips on approach to horizontal curves 14 2 Rural, 2-lane curves No -- -- Install transverse rumble strips and raised pavement markers 1 2 Rural, 2-lane curves No -- -- Install transverse rumble strips, raised pavement markers, and transverse markings 1 1 Rural, 2-lane curves No -- -- Install signals and add channelization 66 0 General Yes Signal (1760) Left-turn lane (4648) 0 0 Install wider markings and both edgeline and centerline rumble strips with resurfacing 309 4 Rural, 2-lane, undivided Yes Wider markings (4737) Edgeline rumbles (3430) Centerline rumbles (3350) Resurfacing (2976) 4 4 5 4 Install wider markings and edgeline rumble strips with resurfacing 309 4 Rural principal arterial Other freeways and expressways with a median Partial Wider markings (4792) Edgeline rumbles (not available) Resurfacing (2976) 4 -- 4 Install wider markings and edgeline rumble strips with resurfacing 309 4 Urban principal arterial Other freeways and expressways with a median Partial Wider markings (not available) Edgeline rumbles (not available) Resurfacing (2976) -- -- 4 Install wider markings and shoulder rumble strips with resurfacing 309 4 Rural principal arterial Other freeways and expressways with a median Yes Wider markings (4792) Shoulder rumbles (3423) Resurfacing (2976) 4 4 4 Install wider markings and shoulder rumble strips with resurfacing 309 4 Urban principal arterial Other freeways and expressways with a median Partial Wider markings (not available) Shoulder rumbles (3422) Resurfacing (2976) -- 4 4 Table 7. (Continued).

Findings and Applications 43   Combined Treatment Combined Treatment ID Combined Treatment Star Rating Combined Treatment Applicability Individual Applicable CMFs Available? Individual CMF IDs (From Clearinghouse) Individual CMF Star Ratings Install wider markings with resurfacing 309 4 Rural principal arterial Other freeways and expressways with a median Yes Wider markings (4792) Resurfacing (2976) 4 4 Install wider markings with resurfacing 309 4 Urban principal arterial Other freeways and expressways with a median Partial Wider markings (not available) Resurfacing (2976) -- 4 Install additional travel lanes and a raised island 259 2 Urban and suburban vehicle/bicycle crashes Yes Lanes (4046) Raised median (4045) 2 2 Install additional travel lanes, a raised island, and a left-turn lane 259 2 Urban and suburban vehicle/bicycle crashes Yes Lanes (4046) Raised median (4045) Left-turn lane (4042) 2 2 2 Install a raised island and left-turn lane 259 2 Urban and suburban vehicle/bicycle crashes Yes Raised median (4045) Left-turn lane (4042) 2 2 Install lane narrowing through rumble strips and painted median at rural stop- controlled approaches 198 2 Intersection approach on rural, 2-lane, undivided roads Partial Rumble strips (not available) Painted median (1640) -- 0 Modify horizontal curve radius and length and provide spiral transitions 25 0 Rural, 2-lane Partial Curve radius (740) Curve length (not available) Spiral transition (not available) 0 -- -- Place edgeline and centerline markings 2 4 Rural, 2-lane Yes Edgelines (4729) Centerlines (1209) 2 0 Note: CMF Study ID from the CMF Clearinghouse. Table 7. (Continued). Level Treatment Q 1 (Not Present) 2 (Present) Treatment P A (Not Present) A1 A2 B (Present) B1 B2 Table 8. Study sites categorized by treatment type.

44 Guidelines for the Development and Application of Crash Modification Factors three categories, denoting the change in safety relative to the base condition. In this case, CMFs for A2, B1, and B2 would represent the effect of Treatment Q, Treatment P, and the combined effect of the two treatments, respectively. Table 8 is used to illustrate two treatments at two levels, but the concept can be expanded to three or more treatments and three or more levels per treatment. Before the methods are further defined, it is necessary to consider the timing of treatments (i.e., the distinction between treatments applied simultaneously and treatments applied sequen- tially). It is reasonable to argue that the eventual effect of sequential treatments will have approx- imately the same effect as the simultaneous application of the treatments given that the total effect of sequential treatments will come later. For example, paving the shoulder first and then adding a shoulder rumble strip the following year would have approximately the same effect in the second year as if they were implemented simultaneously. However, the timing of treatments has a more profound impact on the estimation of the associated CMFs, and therefore, on the desired format for this study. Sequential cases are more attractive for this study because the timing allows for the estimation of CMFs for both individual treatments as well as the combined treat- ment. Where treatments are applied simultaneously, there is still an opportunity to estimate the combined effect, but additional data or existing CMFs are required to estimate the individual treatment effects. It is also necessary to consider the “conditions” and “location” in the context of interaction effects. Conditions are defined by setting (road type or intersection type); crash type (severity, manner of collision); time (day/night); and traffic volume (if specified). All these attributes are used to describe the CMFs in Part D of the HSM. Location describes the portion of the road to which the treatment associated with a CMF is being applied (e.g., outside lane in one travel direction, curves on a two-lane highway with a radius of 400 to 500 feet, or one approach of a signalized intersection). The following two cases describe different levels of overlap among treatments based on the associated condition and location. • Case 1. If the CMFs are all defined for the same condition and the associated treatment is applied to the same location, then they are more likely to be highly related (i.e., likely to affect the same crashes). For example, two CMFs associated with treatments that target rear-end crashes resulting in injury during daytime hours on the northbound approach of a stop- controlled rural intersection are likely to have a high degree of overlap as they will affect the same crashes. • Case 2. If the CMFs are all defined for general conditions and non-specific locations (e.g., overall segments or overall intersection), then the degree to which they are related will be dif- ficult to quantify. For example, consider two CMFs that are both quantified in terms of their effect on total intersection crashes, and the associated treatments are applied to separate inter- section approaches. The effect of approach-specific treatment on total intersection crashes is an extrapolation of the treatment’s approach-specific effect that generalizes the unspecified conditions of the untreated intersection approaches. Several options are described in this section for quantifying the interaction among CMFs. The potential for successfully quantifying the interaction among CMFs using one of these options will be higher if the CMFs are defined for the same conditions and the same location (i.e., Case 1). A method is also described for estimating crash type or location-specific CMFs from more general CMFs (i.e., Case 2), but judgment-based methods for combining CMFs may also be useful when CMFs are defined for general conditions and non-specific locations. Engineering judgment would be used to determine whether each CMF is likely to affect specific conditions and whether these conditions overlap. Similarly, engineering judgment is used to determine whether the associated treatments interact when they are applied at relatively distant locations (e.g., an adjacent segment). The CMFs are more likely to interact when they have more

Findings and Applications 45   conditions in common or the treatment influences the same drivers at the same (or a nearby) location. While objective methods are desired for estimating the combined effect, there is likely a need for judgment-based methods in some situations. Case 1, Option 1—Treatments Applied Simultaneously with Existing CMFs. Option 1 applies to scenarios in which treatments are applied simultaneously. In this case, CMFs are available, and of sufficient quality and applicability, for the treatments in question. Specifically, CMFs are required for each of the following categories. • CMFP = change from A1 to B1 (i.e., apply treatment P to base condition) • CMFQ = change from A1 to A2 (i.e., apply treatment Q to base condition) • CMFPQ = change from A1 to B2 (i.e., apply treatment P and Q to base condition) When there is a single CMF available for each of the three prior categories, Equation 33 is used to estimate the interaction effect for combined treatments P and Q. Equation 33Interaction for combined treatments P and Q CMF CMF CMFPQ P Q( )= × When there are multiple CMFs available for any of the three prior categories, regression analysis would be used to quantify the interaction effect for combined treatments P and Q, using Equation 34 as the functional form and the existing CMFs as data points. Note that Equation 34 assumes a multiplicative interaction effect, and the interaction effect for combined treatments P and Q is quantified as exp(b3). Other functional forms may also be considered such as those presented in the identified approaches for combining CMFs (e.g., CMFPQ = β0 CMFPβ1 CMFQβ2). If the interaction effect is assumed to be additive, Equation 35 is used as the functional form, and the interaction effect for combined treatments P and Q is quantified as b5 (1 − CMFP) (1 − CMFQ). Equation 34CMF CMF CMF exp bPQ P Q 3( )= × × Equation 35CMF 1 CMF 1 CMF 1 b 1 CMF 1 CMFPQ P Q 5 P Q( ) ( ) ( )( )= + − + − + − − Case 1, Option 2—Treatments Applied Sequentially with Existing CMFs. Option 2 applies to scenarios in which treatments are applied sequentially. In these scenarios, CMFs are avail- able, and of sufficient quality and applicability, for the treatments in question. Specifically, CMFs are required for each of the following categories. Note that either CMFQ|P or CMFP|Q would be required depending on the sequence of treatments. • CMFP = change from A1 to B1 (i.e., apply treatment P to base condition) • CMFQ = change from A1 to A2 (i.e., apply treatment Q to base condition) • CMFQ|P = change from B1 to B2 (i.e., apply treatment Q at a site with treatment P) • CMFP|Q = change from A2 to B2 (i.e., apply treatment P at a site with treatment Q) When there is a single CMF available for these categories, either Equation 36 or Equation 37 is used to estimate the interaction effect of the added treatment. Equation 36Interaction for applying treatment Q to sites with P CMF CMFQ P Q= Equation 37Interaction for applying treatment P to sites with Q CMF CMFP Q P= When there are multiple CMFs available for any of these categories, regression analysis would be used to quantify the interaction effect. If a multiplicative interaction effect is assumed, Equa- tion 38 or Equation 39 is used as the functional form, and the existing CMFs are used as data points. The interaction effect of the added treatment is quantified as exp(b3).

46 Guidelines for the Development and Application of Crash Modification Factors Equation 38CMF CMF exp bQ P Q 3( )= × Equation 39CMF CMF exp bP Q P 3( )= × If an additive interaction effect is assumed, Equation 40 or Equation 41 is used as the func- tional form, and the existing CMFs are used as data points. The interaction effect of the added treatment is quantified as b5 (1 − CMFP) (1 − CMFQ). Equation 40CMF 1 CMF 1 CMF 1 b 1 CMF 1 CMF CMFQ P P Q 5 P Q P[ ]( ) ( ) ( )( )= + − + − + − − Equation 41CMF 1 CMF 1 CMF 1 b 1 CMF 1 CMF CMFP Q P Q 5 P Q Q[ ]( ) ( ) ( )( )= + − + − + − − Case 1, Option 3—Cross-Sectional Data and Regression Analysis. Option 3 applies when CMFs are not available, or not of sufficient quality and applicability, for all the treatments and the combined effect in question. For this option, it is necessary to identify sites with levels A1, A2, B1, and B2. Site-selection techniques are used to eliminate as many differences among sites as practical, resulting in a relatively homogeneous group of sites. The following site-selection techniques may be employed: • Propensity scores. Identify groups of sites with similar characteristics (with and without treatments P and Q). Detailed discussions of propensity score matching and its application in traffic safety research are available in papers by Rosenbaum and Rubin (1983) and Sasidharan and Donnell (2013). • Principal component analysis. Identify groups of sites with similar characteristics. Statistical techniques are used to control for remaining differences, and include the following: • Multivariable regression. Include independent variables in the model to account for changes among sites. • Instrumental variables. Develop instruments to control for potential endogeneity bias (i.e., treated sites tend to be high-crash locations). Three alternative cross-sectional model forms are presented below (Equation 42 and Equa- tion 43). Equation 42 is applicable when existing CMFs are not available (or not of sufficient quality or applicability) for any of the treatments or the combined effect in question. In this case, new CMFs are estimated for the individual treatments and the combined treatment effect. y exp b b x . . . b I b I b I I0 4 4 B B 2 2 B 3 2 Equation 42( )= + + + + + where y = crash frequency b0 = intercept “b4 x4 + . . .” = regression model variables as statistical control exp(bB IB) = implied CMF for treatment P exp(b2 I2) = implied CMF for treatment Q exp(b3 IB I2) = interaction effect for combined treatments P and Q exp(bB IB + b2 I2 + b3 IB I2) = implied CMF for combined treatments P and Q Equation 43 is applicable when CMFs are available (and of sufficient quality and applica- bility) for the individual treatments in question, but not for the combined effect. In this case, the interaction effect is quantified for combined treatments P and Q. This scenario assumes a

Findings and Applications 47   multiplicative interaction effect that can be used with existing CMFs to estimate the combined treatment effect. Equation 43y exp b b x . . . b I I CMF CMF0 4 4 3 B 2 P Q( )= + + + × × where CMFP = effect of a change from A1 to B1 (i.e., apply treatment P) CMFQ = effect of a change from A1 to A2 (i.e., apply treatment Q) Other terms as previously defined Equation 44 is applicable when CMFs are available (and of sufficient quality and applicability) for the individual treatments in question, but not for the combined effect. In this case, the inter- action effect is quantified for combined treatments P and Q. This scenario assumes an additive interaction effect that can be used with existing CMFs to estimate the combined treatment effect. Equation 44 y exp b b x . . . 1 CMF 1 CMF 1 b 1 CMF 1 CMF0 4 4 P Q 5 P Q[ ]( ) ( ) ( ) ( )( )= + + × + − + − + − − where b5 (1 − CMFP) (1 − CMFQ) = interaction effect for combined treatments P and Q Other terms as previously defined Since the interaction of treatment effects is central to Case 1, Option 3, the question of how interaction is to be built into the regression equation is particularly important. A model com- posed of single variable multiplicative factors is unsuitable as it cannot account for interaction. The preceding equations include the commonly used interaction term βX1X2 as a specific option, but this also may be unsuitable. The appropriate form is considered in Phase 2. Case 1, Option 4—Cross-Sectional Data and Pseudo Before-After. Option 4 applies when CMFs are available for some but not all the individual treatments. For this option, it is necessary to identify adjacent sites in cross-sectional data. Each site pair should have the same value for all variables of interest, except that they differ in treatment P, treatment Q, or both. The statistical techniques described in Option 3 would be used to control for the remaining differences. This approach will likely work best for segment sites as described by Bonneson and Pratt (2008). This option would proceed as follows: 1. Identify existing CMFs where possible 2. Identify sites required to compute remaining CMFs and interaction effects 3. Apply regression analysis (as described in Option 3) to compute remaining CMFs and quan- tify interaction effect a. If no existing CMFp, then CMFp is computed using sites that have a change from A1 to B1 (i.e., apply treatment P) b. If no existing CMFq, then CMFq is computed using sites that have a change from A1 to A2 (i.e., apply treatment Q) c. If no existing CMFpq, then CMFpq is computed using sites that have a change from A1 to B2 (i.e., apply treatment P and Q) d. If no existing CMFQ|P, then CMFQ|P is computed using sites that have treatment P and have a change from B1 to B2 (i.e., apply treatment Q) e. If no existing CMFP|Q, then CMFP|Q is computed using sites that have treatment Q and have a change from A2 to B2 (i.e., apply treatment P)

48 Guidelines for the Development and Application of Crash Modification Factors Case 2, Option 1—Estimating the Combined Effect when Interaction Is Unknown. The objective of this method is to estimate the combined effect of multiple treatments when the interaction is unknown or cannot be quantified. As discussed previously, this may be the case when the CMFs for individual treatments apply to more general conditions or the treatments are applied to different locations (e.g., different intersection approaches). The proposed approach focuses on two treatments, but the concepts extend to interactions of three or more treatments. The premise of this approach is to isolate a given treatment’s effect on crash distribution, as opposed to total crashes. Then, for multiple treatments, estimate the combined treatment effect on crashes in each distribution as the product of CMFs. The computed CMFs are applied to the appropriate crash distribution category, where the crash distribution used is that for the subject site. This approach will limit the double-counting of crashes when multiplying CMFs to just those crashes in each distribution category. Table 9 provides sample data for two treatments, including the CMFs for each crash category and the corresponding proportion of crashes in each category. The calculations below illustrate how a CMF for total crashes would be calculated using the traditional (multiplicative) approach as well as the proposed approach. Traditional Approach: CMFtotal, trt1 = 0.4 (0.3) + 1.0 (0.7) = 0.82 CMFtotal, trt2 = 0.5 (0.3) + 1.0 (0.7) = 0.85 CMFcombined = CMFtotal, trt1 × CMFtotal, trt2 = 0.82 × 0.85 = 0.70 Proposed Approach: CMFcombined, category 1 = 0.4 × 0.5 = 0.2 CMFcombined, category 2 = 1.0 × 1.0 = 1.0 CMFcombined = 0.2 (0.3) + 1.0 (0.7) = 0.76 The combined CMF for the proposed approach (0.76) is larger than that for the traditional approach (0.70), as expected. The proposed approach limits the effect of double-counting on a specific crash category. While the distribution used in the example above is for a generic “crash category,” the category could be defined by crash type (e.g., rear-end, angle), the number of vehicles in a crash (e.g., multiple vehicles, single-vehicle), or crash severity (e.g., fatal-or-injury, property-damage-only). The distribution could also be based on AADT if the treatment is for a specific travel direction. For segments, the distribution could be the proportion of AADT in the treated travel direction. The CMF value would be 1.0 for the untreated travel direction. For intersections, the distribution could be the proportion of entering AADT on the treated intersection approach(es). The CMF value would be 1.0 for the untreated intersection approaches. Assessing and Validating Methods Several existing methods were defined in Task 3.1 along with the associated strengths and limitations. The most common and promising existing methods were carried forward to Phase 2 Treatment CMF Crash Distribution Proportions Crash Category 1 Crash Category 2 Proportion of Total Crashes in Category 1 Proportion of Total Crashes in Category 2 Treatment 1 0.4 1.0 0.3 0.7 Treatment 2 0.5 1.0 Table 9. Sample data for estimating combined effects by crash proportion.

Findings and Applications 49   for further analysis. It is important to assess the validity of “common” methods to provide practitioners with evidence for either continuing along the current path or seeking an alterna- tive method. The assessment of promising methods will help to understand the magnitude of improvement that can be expected over current methods. This will provide practitioners with information to determine whether the level of effort to implement promising methods is worth the benefit (assuming there is a benefit) compared to their existing method. The quantitative assessment involves the application of existing methods to estimate the com- bined effect of multiple treatments based on individual CMFs. The results obtained from the existing methods are then compared to the ground truth established using methods in the pre- vious section. It will be apparent if existing and proposed methods are properly accounting for potential interaction effects among treatment combinations. The results were evaluated to identify potential regularities (e.g., magnitude of interaction effect) under different scenarios. Specifically, the results of the methods assessment can be sum- marized by facility type (e.g., tangents, curves, and intersections), crash type (e.g., total, fatal- and-injury, and run-off-road), and magnitude of treatment effect (e.g., small, medium, and large) to determine whether one or more methods perform better under different scenarios. It is expected that interaction effects will be greatest for combinations of treatments that target the same general crash types. Validation is appropriate if new methods are developed based on the data collected and assembled for this project. Validation will be possible if enough CMFs for combination treat- ments and the corresponding single-effect CMFs can be identified. The validation should be based on a separate data set, not including the information used to develop the new methods. If enough CMFs are available, then the sample will be randomly divided into two groups, one for development and one for validation. If relatively few CMFs are available for the development of new methods, then it will be necessary to use the entire data set for development. In this case, it will be necessary to validate new methods using the results of future research. If validation is not possible with the options described above, then the guidelines will demonstrate the applica- tion of the methods with direction for future validation. Subtask 3.5 Implement Plan for Phase 2 Selecting Combination Treatments In general, there are relatively few high-quality CMFs for combinations of treatments that also have corresponding high-quality and directly applicable CMFs for the associated individual treatments. As such, it was necessary to assemble data to estimate new CMFs for establishing the ground truth for specific combination treatments. The following three combination treatments were selected for detailed analysis based on the data reconnaissance in Subtask 3.3. • Combination of centerline and shoulder rumble strip installation on urban and rural, two- lane, undivided roads • Combination of lane and shoulder widening on rural, two-lane, undivided roads • Combination of intersection skew angle and sight distance improvements at three- and four- legged intersections with minor-road stop control For these three combination treatments, there were sufficient data available to estimate the CMF for the combined treatment effect and the CMF for all individual treatment effects. The CMFs developed for these three combination treatments are used as the primary means to assess the existing and proposed methods for estimating the combined effect of multiple treatments. Existing CMFs identified in Table 7 from the CMF Clearinghouse are used to supplement the assessment of existing methods but are not the primary focus due to issues with quality and applicability.

50 Guidelines for the Development and Application of Crash Modification Factors Data Collection The following sections describe the data collected and assembled for each of the three com- bination treatments. Combination of Centerline and Shoulder Rumble Strip Installation. The data for this safety evaluation came from the following two sources: • Washington State DOT (WSDOT) Rumble Strip Inventory. WSDOT provided the research team with their statewide rumble strip inventory. This data set provides the rumble strip type (e.g., centerline or shoulder), the location (e.g., route number and milepost), and the start and completion dates for all rumble strips installed on state-maintained roads since 1995. It also identifies where and when sections of rumble strips have been replaced or updated or new types of rumble strips have been added (e.g., shoulder rumble strips added to a section with existing centerline rumble strips). • Highway Safety Information System (HSIS). HSIS provides roadway, traffic, and crash data for select states, including Washington. The research team requested and obtained a total of 11 years (2002–2012) of roadway, traffic, and crash data from HSIS. The research team first processed the rumble strip inventory and separated the data into the following three categories: • Roadway sections with only centerline rumble strips (CLRS) • Roadway sections with only shoulder rumble strips (SRS) • Roadway sections with both CLRS and SRS (not necessarily installed at the same time) After this step, it was evident that most sections only had CLRS or both CLRS and SRS. Sections with SRS alone were rare, and the inventory included only eight miles of road with existing SRS. To estimate the individual safety effect of SRS, the research team identified sections of roadway where SRS were added to existing CLRS. With this study design, the “before” period is the time between the installation of CLRS and the installation of SRS (i.e., only CLRS were present and active). The “after” period is the time after SRS were installed (i.e., both CLRS and SRS were present and active). One key condition for this design is that the gap between the installation of CLRS and SRS (i.e., the “before” period) must be sufficient. Therefore, the team only selected roadway sections with at least one full calendar year between the installation of CLRS and SRS. The three conditions required to estimate CMFs for CLRS, SRS, and the combined treatment are sum- marized in Table 10. The research team requested 13 years (2000–2012) of specific crash, roadway, and traffic data from HSIS; however, roadway data for Washington were not available for 2000–2001. As such, the HSIS staff provided the requested variables for 11 years (2002–2012), and the research team completed the following four key steps to process the data files. Treatment Effect of Interest “Before” Condition “After” Condition Reference Group CMF for CLRS No rumble strip Only CLRS are present No rumble strip CMF for SRS Only CLRS are present Both SRS and CLRS are present; SRS installed 1+ years after CLRS Only CLRS are present CMF for the combined effect of CLRS and SRS No rumble strip Both CLRS and SRS are present No rumble strip Table 10. Summary of before and after conditions.

Findings and Applications 51   Step 1: Identify Short Segments and Merge into Longer Segments. In this step, the research team identified short roadway segments and examined the possibility of combining these seg- ments into longer segments for analysis. During this process, the team identified segments that are identical in terms of key cross-sectional characteristics but separated by a very short segment with a different cross-section. This is often the case when a bridge segment separates a longer segment into thirds, with the bridge segment sandwiched between two segments with identical cross-sectional features (e.g., number of lanes, lane width, shoulder width, and shoulder type). For these locations, the team examined the crash data to identify crashes coded as “bridge” (i.e., LOC_CHAR=3, 13). This analysis revealed that merging segments would not affect the final count of target crashes for this study. Ultimately, the research team combined these segments for analysis to avoid statistical issues related to short segment length. Figure 3 illustrates the segment merging process. In this example, segments 1 and 3 are identi- cal in terms of key cross-sectional features and separated by a short bridge (Segment 2). These three segments are merged to create one long segment. The newly combined segment would have the total length of the three combined segments and the cross-sectional characteristics of the two longer segments. The team developed computer codes to automate the process of sorting the data and merging those segments that could be combined. Step 2: Merge Rumble Strip Inventory with HSIS Data. In this step, the team used segment location information (i.e., route number and milepost) from the statewide rumble strip inven- tory to “tag” all HSIS road segments as either “treated” or “untreated.” In some cases, the rumble strip inventory and HSIS segments partially overlapped and required further processing to create appropriate analysis segments. Figure 4 is an illustration of the process. In addition to the treatment status (i.e., treated or untreated), the team assigned the treat- ment type for each treated segment (i.e., CLRS, SRS, or CLRS+SRS) using the information from the WSDOT rumble strip inventory. In this step, the team also performed visual verifications of rumble strip presence and types by using a combination of Google Earth’s Street View and WSDOT’s photo log (http://www.wsdot.wa.gov/mapsdata/tools/srweb.htm). Figure 5 shows a Segment 1 Length: 0.31 mile Number of lanes: 2 Lane width: 12 ft Shoulder width: 6 ft Segment 2 Length: 0.02 mile Number of lanes: 2 Lane width: 16 ft Shoulder width: 2 ft Segment 3 Length: 0.32 mile Number of lanes: 2 Lane width: 12 ft Shoulder width: 6 ft Merged segment Length: 0.36 mile Number of lanes: 2 Lane width: 12 ft Shoulder width: 6 ft Figure 3. Illustration of merging roadway segments.

52 Guidelines for the Development and Application of Crash Modification Factors Segment Segment Rumble Strip Segments HSIS Combined Segments Segment 1: Segment 2-1: Segment 2-2: Figure 4. Illustration of tagging roadway segments. Figure 5. Visual verification of rumble strip presence and type (segment with only CLRS shown).

Findings and Applications 53   screen capture from the WSDOT photo log. While the team did not confirm the treatment presence and type for all segments, they randomly checked and confirmed at least 20% of the segments. Due to the verified accuracy of the rumble strip inventory, it was determined that the treatment presence and type were relatively accurate for this analysis. Step 3: Select Treated Segments and Candidate Untreated Segments for Each Category. In this step, the team separated the data into the following five treatment status and type categories: 1. Treated segments with CLRS only 2. Treated segments with SRS only 3. Treated segments with both CLRS and SRS (where SRS were installed simultaneously or within one year of the CLRS) 4. Treated segments with both CLRS and SRS (where SRS were installed at least one full calendar year after CLRS) 5. Untreated segments As discussed in the previous section, the data set only has approximately eight miles of road- way where SRS are installed without CLRS. The number of crashes from this category would not be enough for any meaningful statistical analysis. As such, the team decided not to use segments with SRS only (Category 2 above) and removed them from the data set. The result of this step is four subsets of roadway segments with all geometric features and traffic characteristics from the HSIS database and the rumble strip presence and type from the WSDOT rumble strip inventory. The following is a summary of the total miles in each category. 1. Treated segments with CLRS only: 844 segments totaling 938.47 miles of roadway with CLRS only are used as the “treated” group for the safety evaluation of CLRS. Some of these segments are also used as the reference group for the safety evaluation of SRS (discussed below). 2. Treated segments with both CLRS and SRS (where SRS were installed simultaneously or within one year of the CLRS): 103 segments totaling 113.5 miles of roadway with both CLRS and SRS are used as the “treated” group for evaluating the combined safety effects of both CLRS and SRS. 3. Treated segments with both CLRS and SRS (where SRS were installed at least one full calendar year after CLRS): 42 segments totaling 40.39 miles of roadway with SRS installed at least one full calendar year after the installation of CLRS are used as the “treated” group for the safety evaluation of SRS. The reference group was selected from those segments with only CLRS (discussed above). 4. Untreated segments: Nearly 12,000 segments totaling 4,400 miles of roadway with no rumble strips are used for selecting the reference group for CLRS and CLRS+SRS treatments. The team employed propensity score matching to select reference sites that match the treatment sites in terms of general site characteristics. Step 4: Merge Crash Data with Roadway Data. The team screened HSIS crash data files for Washington State and matched the crashes to the segments selected in Step 3 using a com- bination of route number and milepost. Crash location type (i.e., loc_type) was used to exclude crashes that are coded as “intersection” or “intersection-related.” Crash counts were summa- rized by crash type and severity for each segment. Table 11 provides summary statistics for the Washington State data by treatment category, and Table 12 is a summary of the descriptive statistics for reference groups. Combination of Lane and Shoulder Widening. The data for this safety evaluation came from the HSIS database. Specifically, the team requested and obtained crash, roadway, traffic volume, and horizontal curve data for Illinois, Ohio, and Washington State. These three states

54 Guidelines for the Development and Application of Crash Modification Factors were selected for study because horizontal curve information is readily available in the HSIS database. Horizontal curve data supplement geometric characteristics and allow the research team to perform separate analyses for tangent and curve segments. HSIS staff provided three years of data for each state (2006–2008 for Illinois, 2008–2010 for Ohio, and 2010–2012 for Washington). Although the original goal was to obtain the most recent three years of data, the team determined that different study periods for different states are more appropriate because some states changed their crash reporting threshold. The change in report- ing threshold would affect the number of property-damage-only (PDO) crashes and the total number of crashes reported in the database. The following is a summary of changes in crash reporting thresholds. • Illinois increased the reporting threshold from $500 to $1,500 in 2009 (Illinois Department of Transportation 2013). • Ohio increased the reporting threshold from $400 to $1,000 in 2011 (Nujjetty et al. 2014). Variables CLRS SRS CLRS and SRS Number of treated segments 844 42 103 Total length, miles 938.47 40.39 113.5 Average segment length, miles 1.11 0.96 1.10 Total years of data 11 (2002– 2012) 7 (2006–2012) 11 (2002–2012) Segment-years in before period 5,840 54 502 Segment-years in after period 2,380 159 403 Minimum traffic volume, vehicles/day 597 1,738 1,668 Maximum traffic volume, vehicles/day 33,063 19,436 22,148 Average traffic volume, vehicles/day 5,278 6,718 7,689 Total crashes in before period 12,062 186 1,521 Total crashes in after period 4,429 408 1,078 Fatal-and-injury crashes in before period 5,337 70 652 Fatal-and-injury crashes in after period 1,759 172 433 ROR crashes in before period 5,439 61 516 ROR crashes in after period 1,764 109 285 Target crashes (ROR + head-on + sideswipe) in before period 5,018 68 572 Target crashes (ROR + head-on + sideswipe) in after period 1,642 122 319 Abbreviation: ROR, run-off-road. Table 11. Summary statistics for treated sites from Washington State rumble strip data set. Variables CLRS SRS CLRS and SRS Number of reference segments 513 91 83 Total length, miles 574.63 75.21 74.65 Average segment length, miles 1.12 0.83 0.90 Total years of data 11 (2002– 2012) 8 (2005–2012) 11 (2002–2012) Minimum traffic volume, vehicles/day 149 975 488 Maximum traffic volume, vehicles/day 38,279 19,189 23,294 Average traffic volume, vehicles/day 5,050 6,652 8,258 Total crashes 8,705 728 1,824 Fatal-and-injury 3,603 574 721 ROR crashes 3,222 557 528 Target crashes (ROR + head-on + sideswipe) 3,503 604 577 Table 12. Summary statistics for reference sites from Washington State rumble strip data set.

Findings and Applications 55   At the time of the data request, the most recent year of data available in the HSIS database was 2012. Therefore, 2006–2008 and 2008–2010 were the most recent three years of data in which the reporting threshold remained the same for Illinois and Ohio, respectively. More details on the data and data processing are provided in the following sections. Roadway Data. The team requested roadway, curve, and traffic data files for each state. The roadway files contain geometric and traffic characteristics of roadway segments; however, they do not contain information on horizontal curves. Therefore, the team obtained and merged curve files with the roadway files to define tangent and curve segments for separate analyses. The research team screened the data files and kept only rural, two-lane road segments. The data were further reduced by removing all segments shorter than 0.1 miles. Given current crash locating and reporting practices, these very short segments were removed because there are reasons to believe that crashes might not be reliably merged to these very short segments. The research team also examined and identified other relatively short segments (< 0.1 miles) that could be combined into longer ones for this study. The team followed a similar process to the previous combination treatment (centerline and shoulder rumble strips), which is discussed above in the section titled Step 1: Identify Short Segments and Merge into Longer Segments. The process is illustrated above in Figure 3. Crash Data. Crashes were merged with each roadway segment using the route identification numbers and mileposts. For each segment, the total number of crashes (all types and severity levels) and the number of crashes by type and severity were summarized. The following four crash types were included in the analysis: • Total crashes (all types and severity levels) • Fatal-and-injury crashes (all types) • Run-off-road crashes (all severity levels) • Target crashes (run-off-road, head-on, sideswipe same and opposite directions, all severity levels) Data Summary and Preliminary Examination. The research team generated a frequency table for the various lane width and shoulder width combinations to examine the available sample sizes. The team selected specific lane and shoulder width combinations based on the categories with the most abundant sample sizes for all three states. For tangents, these included segments with 11-ft or 12-ft lane widths, and 3-ft, 4-ft, or 8-ft shoulder widths. For curves, these included segments with 11-ft or 12-ft lane widths, and 2-ft, 4-ft, or 8-ft shoulder widths. For tangents, the following are the two combined treatments of interest, using a baseline cross-section of 11-ft lanes and 3-ft shoulders. This allowed the team to develop CMFs for increasing the lane width from 11-ft to 12-ft and for increasing the shoulder width from 3-ft to 4-ft and 3-ft to 8-ft. • 12-ft lanes and 4-ft shoulders compared to 11-ft lanes and 3-ft shoulders • 12-ft lanes and 8-ft shoulders compared to 11-ft lanes and 3-ft shoulders For curves, the following are the two combined treatments of interest, using a baseline cross- section of 11-ft lanes and 2-ft shoulders. This allowed the team to develop CMFs for increasing the lane width from 11-ft to 12-ft and for increasing the shoulder width from 2-ft to 4-ft and 2-ft to 8-ft. • 12-ft lanes and 4-ft shoulders compared to 11-ft lanes and 2-ft shoulders • 12-ft lanes and 8-ft shoulders compared to 11-ft lanes and 2-ft shoulders For each “treated” group (i.e., 12-ft lanes, 4-ft shoulders, and 8-ft shoulders), propensity score matching was performed to select similar sites from the pool of candidate “untreated” segments

56 Guidelines for the Development and Application of Crash Modification Factors (i.e., 11-ft lanes and 3-ft or 2-ft shoulders). Only the selected “untreated” segments with matched propensity scores were used with the “treated” segments for model estimation and CMF develop- ment. Data descriptions of lane–shoulder combinations for tangent and horizontal curve segments on rural, two-lane, undivided roads are presented separately under this section of the report. Table 13 and Table 14 summarize the final tangent and curve segment data sets used for model estimation and CMF development. Table 13 presents the key descriptive statistics for individual data sets from Illinois, Ohio, and Washington State, as well as the combined data from all three states. The horizontal curve data set presented in Table 14 only includes data from Ohio and Washington State because the Illinois curve data set is incomplete. Specifically, the Illinois HSIS curve data set contains only horizontal curves with radii equal to or less than 2291.83 feet (or 2.5-degree curves) (Council and Mohamedshah 2009). Combination of Intersection Skew Angle and Sight Distance Improvements. The data for this evaluation came from NCHRP Project 17-59: Safety Impacts of Intersection Sight Distance (ISD). The goal of NCHRP Project 17-59 was to determine the safety effects of ISD using a cross- sectional method, which includes consideration of intersection angle, among other intersection- related characteristics. The intersection angle was determined using a desktop approach, while the available ISD was measured through field visits. More details on the data and data processing are discussed in the following sections: • Field data collection • Desktop data collection • Treatment definitions Data Elements Illinois Ohio Washington Combined Number of segments All segments 4,213 1,225 1,312 6,750 11-ft lanes (all) 1,124 247 575 1,946 3-ft shoulders 269 127 210 606 4-ft shoulders 588 89 222 899 8-ft shoulders 267 31 143 441 12-ft lanes (all) 3,089 978 737 4,804 3-ft shoulders 957 240 122 1,319 4-ft shoulders 945 416 240 1,601 8-ft shoulders 1,187 322 375 1,884 AADT Mean 2,721 4,113 4,623 3,344 Max 12,667 19,700 23,765 23,765 Min 29 137 195 29 Segment length, miles Mean 0.37 0.86 0.38 0.47 Max 2.39 8.41 4.17 8.41 Min 0.1 0.1 0.1 0.1 Total crashes, crashes/three years Mean 1.02 4.9 1.04 1.73 Max 23 117 16 117 Min 0 0 0 0 Fatal-and-injury crashes, crashes/three years Mean 0.19 1.12 0.38 0.4 Max 6 26 8 26 Min 0 0 0 0 Run-off-road crashes, crashes/three years Mean 0.26 1.35 0.48 0.5 Max 9 32 8 32 Min 0 0 0 0 Target crashes, crashes/three years Mean 0.31 1.72 0.54 0.61 Max 12 34 9 34 Min 0 0 0 0 Table 13. Summary of lane width and shoulder width on tangents.

Findings and Applications 57   Field Data Collection. Intersections were visited during late spring, summer, and early fall (i.e., when the foliage is robust) in North Carolina, Ohio, and Washington State. Three inde- pendent data collection teams visited sites in each state. Sites were selected in corridors known to have both major- and minor-road AADTs without consideration of crash history. Before visiting the locations, the project team verified that traffic control devices at the major road were visible to the minor-road driver and the grade measured at the minor road is less than or equal to 3% grade. This minimized potential safety impacts of grade and limited sight distance to the minor-road stop control. Once verified, field teams collected the following information at each intersection location: • Available ISD (in feet) • Vertical gradient (in percentage) 100 ft, 250 ft, and 500 ft from the intersection on the major road approaches • Traffic volume verification Data Elements Ohio Washington Combined Number of segments All segments 357 1,300 1,657 11-ft lanes (all) 97 545 642 2-ft shoulders 48 193 241 4-ft shoulders 35 225 260 8-ft shoulders 14 127 141 12-ft lanes (all) 260 755 1,015 2-ft shoulders 61 146 207 4-ft shoulders 110 377 487 8-ft shoulders 89 232 321 AADT Mean 2,992 2.907 2,926 Max 10,920 25,220 25,220 Min 380 203 203 Segment length, miles Total 62.17 240.11 302.28 Mean 0.17 0.18 0.18 Max 0.56 1.26 1.26 Min 0.1 0.1 0.10 Curve radius, feet Mean 1,078 2,925 2,527 Max 1,910 50,000 50,000 Min 250 276 250 Total crashes, crashes/three years Total 437 702 1,139 Mean 1.22 0.54 0.69 Max 12 8 12 Min 0 0 0 Fatal-and-injury crashes, crashes/three years Total 107 264 373 Mean 0.31 0.20 0.23 Max 5 5 5 Min 0 0 0 Run-off-road crashes, crashes/three years Total 169 419 588 Mean 0.47 0.32 0.35 Max 5 7 7 Min 0 0 0 Target crashes, crashes/three years Total 205 446 651 Mean 0.57 0.34 0.39 Max 7 7 7 Min 0 0 0 Table 14. Summary of lane width and shoulder width on horizontal curves.

58 Guidelines for the Development and Application of Crash Modification Factors • Lane width • Shoulder width • Posted speed limit • Presence of turn lanes Since available ISD was determined by independent field teams, the project team developed a standardized method for obtaining available ISD. First, the intersection was broken into indi- vidual approach directions, which serve as the unit of analysis. In this case, a three-legged inter- section has two analysis units, as shown in Figure 6. As prescribed by AASHTO’s A Policy on Geometric Design of Highways and Streets (Green Book), the decision point (DP), or location of the driver’s eyes when stopped on the minor road, was measured as 14.5 feet from the edge of the major-road travel lane and 4 feet from the center of the minor-road approach. The driver’s eye height was assumed as 42 inches, as was the object height. The field team measured the available sight distance using a combination of a laser range- finder and metal target looking left and right from each DP. The rangefinder was mounted on top of a monopod and included a 4x magnification to remove the impacts of the data collec- tor’s vision capability. The target was a standard 14-inch by 14-inch slow-moving vehicle sign, providing a replicable object and sufficient density for bounce-back from the rangefinder. Two- person teams gathered the data where the first person moved the target along the major road away from the DP, stopping when they reached the point at which the full metal target just began to disappear from the view of the sighting person while looking through the rangefinder’s scope. This location became the critical point (CP) for that direction of view. The CP was identified as the limit of available ISD and was measured up to a practical limit of one-quarter mile (or 1,320 ft). If the available ISD exceeded this amount, the distance was noted to be 1,321 ft. Desktop Data Collection. The research team obtained crash and traffic volume data from the HSIS database for 2009 to 2011. The crash data included location, type, severity, the initial direc- tion of vehicles, sequence of events, light condition, weather condition, and vehicle type. These factors allowed the team to identify crashes by approach direction, separated by crash type and severity. Only crashes involving a vehicle on the major road and minor road were included since Figure 6. Location of decision point at a three-legged intersection.

Findings and Applications 59   crashes needed to be applied to a specific sightline. The following crash types were identified for analysis of individual and combined CMFs: • Total target crashes. Crashes involving a vehicle from the minor-road approach and from the major-road approach, associated with a directional analysis unit. The appropriate analysis unit is identified by the approaching direction of the major-road vehicle. • Fatal-and-injury target crashes. The subset of total target crashes involving at least one vehicle occupant with a fatality or injury (K, A, B, or C on the KABCO scale). • Right-angle crashes. The subset of total target crashes in which both vehicles on the major and minor roads were intending to move straight through the intersection. It is possible to have right-angle crashes on three-legged intersections, as some intersections had driveways. Additional characteristics of interest collected via desktop include the following: • Intersection angle (degrees) • Traffic volume (AADT) • Area type • Functional classification • Presence and direction of horizontal curvature • Number of intersection legs • Access density (points within 0.25 miles) • Quality of ISD The project team collected a quantitative measurement of skew angle for analysis. The data collection process showed that the intersection angle varies depending on the points selected on each leg of the intersection, particularly for legs with horizontal curves. Figure 7 illustrates this issue with Google Earth screenshots for an intersection with a two-lane major road approach. The radii of the circles represent four lengths explored (50, 75, 100, and 150 ft). As the figure shows, the measurements vary from 91 degrees to 72 degrees, based on the circle’s radius. With the center of the circle located at the intersection center, the research team selected 75 ft from the point of intersection for all intersection angle measurements. This distance most closely matches the angle experienced by the first few drivers in a queue and provides a consistent method across intersections. Treatment Definitions. A cross-sectional regression modeling approach is employed to estimate the CMFs for various categories of ISD and intersection angle. In essence, available ISD and intersection angles are observed for several intersections and crash frequency is compared across these intersections while controlling for other safety-related characteristics. Available ISD was considered in three levels for analysis, including the following: • 500 ft to 750 ft • 750 ft to 1,000 ft • 1,320 ft or more Figure 7. Intersection angle measurements.

60 Guidelines for the Development and Application of Crash Modification Factors There were too few observations with available ISD less than 500 ft and too few observations between 1,000 and 1,320 ft for further consideration. Intersection angle was considered in three levels for analysis, including the following: • 50 degrees to 75 degrees • 75 degrees to 85 degrees • 85 degrees to 90 degrees There were too few observations below 50 degrees for further consideration. The most com- mon condition observed was the highest available ISD category (1,320 feet) and the highest intersection angle (85 to 90 degrees). As such, the baseline condition is defined as sites with ISD greater than or equal to 1,320 feet and an intersection angle of 85 to 90 degrees. The team used propensity score matching to select similar sites with different available ISD and intersection angles. Note that while the available ISD and intersection angle differ for the comparison sites, the general characteristics such as traffic volume and posted speed are similar. The following provides a summary of the various available ISDs and intersection angle conditions considered for analysis: • Individual ISD effect. Available ISD of more than 1,320 ft compared to a baseline condition of 500 ft to 750 ft • Individual intersection angle effect. Intersection angle of 85 degrees to 90 degrees compared to a baseline condition of 50 degrees to 75 degrees • Combined treatment effect. Available ISD of more than 1,320 ft and intersection angle of 85 degrees to 90 degrees compared to baseline conditions for both Table 15 provides summary statistics for the North Carolina, Ohio, and Washington data used in the final analysis for CMF development. Crash totals are for three years, and AADT values are averages for the three-year period. Analysis The following sections describe the data analysis and results for each of the three combination treatments. Combination of Centerline and Shoulder Rumble Strip Installation. For this analysis, the team was able to employ a rigorous empirical Bayes before-after method to estimate CMFs for the individual treatment effects (i.e., CLRS only and SRS only) as well as the combined treatment effect (i.e., CLRS+SRS). As discussed previously, propensity score matching was employed to Variables of Interest Base ISD and Angle Base Angle and 500–750 ft ISD Base ISD and 50 to 75 Angle 500–750 ft ISD and 50 to 75 Angle Number of Intersections 233 154 145 46 Minimum Major AADT 815 3,256 3,173 1,293 Average Major AADT 35,755 44,299 28,911 27,386 Maximum Major AADT 96,459 114,000 78,000 87,100 Minimum Minor AADT 125 300 330 183 Average Minor AADT 3,908 4,327 3,112 3,374 Maximum Minor AADT 27,324 47,136 14,509 10,158 Total Crashes 46 74 55 11 Fatal-and-Injury Target Crashes 15 37 38 2 Right-Angle Crashes 16 36 40 10 Table 15. Summary of the data set.

Findings and Applications 61   identify a suitable reference group for each treatment category. The focus crash types for this analysis included the following: • Total crashes (all crash types and severities) • Fatal-and-injury crashes (all crash types) • Run-off-road crashes (all crash severities) • Target crashes (run-off-road + head-on + sideswipe) Tables 16 through 18 present the CMFs and standard errors for CLRS, SRS, and CLRS+SRS on urban and rural, two-lane, undivided roads. Each table presents the CMFs and standard errors for the four crash types of interest. This information defines the ground truth, which is used to assess existing methods in the next section. Combination of Lane and Shoulder Widening. For this analysis, the team employed a rigorous cross-sectional method to estimate CMFs for the individual and combined treatment effects. As discussed previously, the team used propensity score matching to match sites in the various treatment categories with sites in the baseline category. The focus crash types for this analysis included the following: • Total crashes (all crash types and severities) • Fatal-and-injury crashes (all crash types) • Run-off-road crashes (all crash severities) • Target crashes (run-off-road + head-on + sideswipe either direction) Table 19 through Table 23 present the CMFs and standard errors for various lane and shoulder combinations on rural, two-lane, undivided tangent sections. Each table presents the CMFs and standard errors for the four crash types of interest. This information defines the ground truth, which is used to assess existing methods in the next section. Again, the two combined treatments of interest for tangent sections are (1) 12-ft lanes and 4-ft shoulders compared to 11-ft lanes and 3-ft shoulders, and (2) 12-ft lanes and 8-ft shoulders compared to 11-ft lanes and 3-ft shoulders. Applicable Crash Type CMF Standard Error Total crashes 0.996 0.019 Fatal-and-injury crashes 1.047 0.031 Run-off-road crashes 0.935 0.028 Target crashes 0.912 0.026 Table 16. CMFs for CLRS only. Applicable Crash Type CMF Standard Error Total crashes 1.060 0.070 Fatal-and-injury crashes 1.301 0.111 Run-off-road crashes 0.818 0.099 Target crashes 0.844 0.098 Table 17. CMFs for SRS only. Applicable Crash Type CMF Standard Error Total crashes 0.906 0.042 Fatal-and-injury crashes 1.074 0.072 Run-off-road crashes 0.813 0.059 Target crashes 0.788 0.055 Table 18. CMFs for CLRS + SRS.

62 Guidelines for the Development and Application of Crash Modification Factors Applicable Crash Type CMF Standard Error Total crashes 0.994 0.063 Fatal-and-injury crashes 1.015 0.102 Run-off-road crashes 0.820 0.073 Target crashes 0.819 0.069 Table 19. CMFs for widening shoulder width to four feet on tangents. Applicable Crash Type CMF Standard Error Total crashes 0.892 0.068 Fatal-and-injury crashes 0.657 0.084 Run-off-road crashes 0.691 0.075 Target crashes 0.700 0.071 Table 20. CMFs for widening shoulder width to eight feet on tangents. Applicable Crash Type CMF Standard Error Total crashes 0.924 0.054 Fatal-and-injury crashes 0.796 0.076 Run-off-road crashes 0.734 0.061 Target crashes 0.744 0.057 Table 21. CMFs for widening lane width to 12 feet on tangents. Applicable Crash Type CMF Standard Error Total crashes 0.873 0.047 Fatal-and-injury crashes 0.827 0.073 Run-off-road crashes 0.702 0.055 Target crashes 0.689 0.050 Table 22. CMFs for combination of widening lane width to 12 feet and shoulder width to four feet on tangents. Applicable Crash Type CMF Standard Error Total crashes 0.850 0.047 Fatal-and-injury crashes 0.720 0.063 Run-off-road crashes 0.610 0.048 Target crashes 0.646 0.047 Table 23. CMFs for combination of widening lane width to 12 feet and shoulder width to eight feet on tangents.

Findings and Applications 63   Table 24 through Table 26 present the CMFs and standard errors for various lane and shoulder combinations on rural, two-lane, undivided horizontal curve sections. Each table presents the CMFs and standard errors for the four crash types of interest. This information defines the ground truth, which is used to assess existing methods in the next section. Again, the two combined treat- ments of interest for horizontal curve sections are (1) 12-ft lanes and 4-ft shoulders compared to 11-ft lanes and 2-ft shoulders, and (2) 12-ft lanes and 8-ft shoulders compared to 11-ft lanes and 2-ft shoulders. For the first combination (i.e., 12-ft lanes and 4-ft shoulders compared to the baseline), the research team determined that the results were unreliable due to small sample sizes and lack of statistical significance (i.e., not statistically significant at the 20% significance level). Specifi- cally, CMFs developed from model parameters that are not statistically significant would not help to assess the different methods and achieve the objective of this study. As such, the results are presented only for the second combination (i.e., 12-ft lanes and 8-ft shoulders compared to the baseline). Combination of Intersection Skew Angle and Sight Distance Improvements. For this analysis, the team employed a cross-sectional modeling approach to estimate CMFs for the individual treatment effects as well as the combined treatment effect. As discussed previously, the team used propensity score matching to match sites in the various treatment categories with sites in the baseline category. The focus crash types for this analysis included the following: • Total target crashes. Crashes involving a vehicle from the minor road approach and from the major road approach, associated with a directional analysis unit. The appropriate analysis unit is identified by the approaching direction of the major road vehicle. • Fatal-and-injury target crashes. Subset of total target crashes involving at least one vehicle occupant with a fatality or injury (K, A, B, or C on the KABCO scale). Applicable Crash Type CMF Standard Error Total crashes 0.810 0.137 Fatal-and- injury crashes 0.635 0.170 Run-off-road crashes 0.630 0.147 Target crashes 0.612 0.139 Table 24. CMFs for widening shoulder width to eight feet on curves. Applicable Crash Type CMF Standard Error Total crashes 0.884 0.140 Fatal-and-injury crashes 0.754 0.194 Run-off-road crashes 0.951 0.194 Target crashes 0.947 0.187 Table 25. CMFs for widening lane width to 12 feet on curves. Applicable Crash Type CMF Standard Error Total crashes 0.760 0.105 Fatal-and-injury crashes 0.659 0.144 Run-off-road crashes 0.551 0.105 Target crashes 0.575 0.105 Table 26. CMFs for combination of widening lane width to 12 feet and shoulder width to eight feet on curves.

64 Guidelines for the Development and Application of Crash Modification Factors • Right-angle crashes. Subset of total target crashes in which both vehicles on the major and minor roads were intending to move straight through the intersection. It is possible to have right-angle crashes on three-legged intersections, as some intersections had driveways. Table 27 through Table 29 present the CMFs and standard errors for available ISD, intersec- tion angle, and their combination at three- and four-legged intersections with minor road stop control. Each table presents the CMFs and standard errors for the three crash types of interest. This information defines the ground truth, which is used to assess existing methods in the next section. For these improvements, treatment effects were defined as the following: • Individual ISD effect. Available ISD of more than 1,320 ft compared to a baseline condition of 500 ft to 750 ft • Individual intersection angle effect. Intersection angle of 85 degrees to 90 degrees compared to a baseline condition of 50 degrees to 75 degrees • Combined treatment effect. Available ISD of more than 1,320 ft and intersection angle of 85 degrees to 90 degrees compared to baseline conditions for both Assessing and Validating Methods for Estimating the Combined Effect of Multiple Treatments The following three sections present the results of the methods assessment for each of the three combination treatments. These sections use the ground truth CMFs established in this research project as presented in the previous section (Analysis). The primary methods of interest include the following: • Multiplicative: CMFt = CMF1 × CMF2 • Multiplicative with Generalized Reduction: CMF 1 2 3 1 CMF CMFt 1 2( )( )= − − ×   Applicable Crash Type CMF Standard Error Target crashes 0.456 0.122 Fatal-and-injury target crashes 0.272 0.104 Right-angle crashes 0.265 0.116 Table 27. CMFs for increasing ISD to 1,320+ ft (from 500–750 ft). Applicable Crash Type CMF Standard Error Target crashes 0.414 0.119 Fatal-and-injury target crashes 0.211 0.082 Right-angle crashes 0.186 0.085 Table 28. CMFs for increasing intersection angle to 85–90 degrees (from 50–75 degrees). Applicable Crash Type CMF Standard Error Target crashes 0.469 0.219 Fatal-and-injury target crashes 0.823 0.769 Right-angle crashes 0.146 0.095 Table 29. CMFs for combination of increasing ISD to 1,320+ ft (from 500–750 ft) and intersection angle to 85–90 degrees (from 50–75 degrees).

Findings and Applications 65   • Multiplicative with Systematic Reduction: CMF CMF 1 1 CMF 2 t 1 2= × − −     • Dominant Effect: CMFt = CMF1 (largest effect) • Dominant Common Residuals: CMFt = (CMF1 × CMF2)CMF1 where CMFt = CMF for the combined treatments CMF1 = CMF for the most effective treatment CMF2 = CMF for the second most effective treatment For each method, the combined CMF estimated from the method is compared to the ground truth from the analysis section. Further, the methods are assessed based on the mean squared error (MSE), which is the squared difference of the estimated combined CMF and the ground truth. Lower MSE values are preferred, indicating a closer match between the estimated com- bined CMF and the ground truth. In addition, the methods are assessed for over- or underesti- mating the combined CMF compared to the ground truth. Combination of Centerline and Shoulder Rumble Strip Installation. Table 30 through Table 33 present the assessment results for total crashes, fatal-and-injury crashes, run-off-road crashes, and target crashes (run-off-road + head-on + sideswipe), respectively. Each table pres- ents four CMFs for each method: (1) CMF for CLRS only, (2) CMF for SRS only, (3) estimated CMF for CLRS + SRS based on existing method, and (4) ground truth CMF for CLRS and SRS. The final two columns of each table indicate the MSE and over- or underestimation, respectively. Again, lower MSEs are preferred. Table 34 presents a summary of the MSEs and the average MSE for each method from the previous four tables. Based on the CMFs for CLRS, SRS, and CLRS+SRS, the Dominant Effect method performs best for total, fatal-and-injury, and run-off-road crashes as well as overall (i.e., average MSE across all crash types). For target crashes, the Dominant Common Residuals method performs best. Table 35 presents a summary of the difference between the ground truth and estimated com- bined CMF from each method. The difference is always computed as the ground truth minus the estimate from the respective method. As such, positive values indicate that the method is over- estimating the combined effect and negative values indicate that the method is underestimating Method CMF1 CMF2 Combined CMF (By method) Combined CMF (Ground truth) MSE Over- or Under- Estimation Multiplicative = CMF1*CMF2 0.996 1.060 1.056 0.906 0.0224 Under Multiplicative with Generalized Reduction = 1 −(2/3*(1 −(CMF1*CMF2))) 0.996 1.060 1.037 0.906 0.0172 Under Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.996 1.060 1.026 0.906 0.0144 Under Dominant Effect = CMF1 (largest effect) 0.996 1.060 0.996 0.906 0.0081 Under Dominant Common Residuals 0.996 1.060 1.056 0.906 0.0224 Under = (CMF1*CMF2)CMF1 Table 30. Methods assessment for CLRS + SRS (total crashes).

66 Guidelines for the Development and Application of Crash Modification Factors Method CMF1 CMF2 Combined CMF (By method) Combined CMF (Ground truth) MSE Over- or Under- Estimation Multiplicative = CMF1*CMF2 1.047 1.301 1.362 1.074 0.0830 Over Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) 1.047 1.301 1.241 1.074 0.0280 Over Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 1.047 1.301 1.205 1.074 0.0170 Over Dominant Effect = CMF1 (largest effect) 1.047 1.301 1.047 1.074 0.0007 Under Dominant Common Residuals = (CMF1*CMF2)CMF1 1.047 1.301 1.382 1.074 0.0949 Over Table 31. Methods assessment for CLRS + SRS (fatal + injury crashes). Method CMF1 CMF2 Combined CMF (By method) Combined CMF (Ground truth) MSE Over- or Under- Estimation Multiplicative = CMF1*CMF2 0.818 0.935 0.765 0.813 0.0023 Over Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) 0.818 0.935 0.843 0.813 0.0009 Under Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.818 0.935 0.791 0.813 0.0005 Over Dominant Effect = CMF1 (largest effect) 0.818 0.935 0.818 0.813 0.0000 Under Dominant Common Residuals =(CMF1*CMF2)CMF1 0.818 0.935 0.803 0.813 0.0001 Over Table 32. Methods assessment for CLRS + SRS (run-off-road crashes). Method CMF1 CMF2 Combined CMF (By method) Combined CMF (Ground truth) MSE Over- or Under- Estimation Multiplicative = CMF1*CMF2 0.844 0.912 0.770 0.788 0.0003 Over Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) 0.844 0.912 0.846 0.788 0.0034 Under Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.844 0.912 0.807 0.788 0.0004 Under Dominant Effect = CMF1 (largest effect) 0.844 0.912 0.844 0.788 0.0031 Under Dominant Common Residuals =(CMF1*CMF2)CMF1 0.844 0.912 0.802 0.788 0.0002 Under Table 33. Methods assessment for CLRS + SRS (target crashes).

Findings and Applications 67   the combined effect. Based on the CMFs for CLRS, SRS, and CLRS+SRS, the Multiplicative with Generalized Reduction method consistently underestimates the combined effect (4 of 4). The Multiplicative with Systematic Reduction method, Dominant Effect method, and Domi- nant Common Residuals method also underestimate the combined effect for most crash types (3 of 4). The Multiplicative method appears most likely to overestimate the combined effect (2 of 4), which is a primary limitation associated with this method. The Dominant Effect method performs best (i.e., smallest difference without overestimating) for total, fatal-and-injury, and run-off-road crashes as well as overall (i.e., the average difference across all crash types). For target crashes, the Dominant Common Residuals method performs best. Combination of Lane and Shoulder Widening. Recall that the two scenarios for lane and shoulder width combinations for tangents are: • Combination 1. 12-ft lanes and 4-ft shoulders compared to 11-ft lanes and 3-ft shoulders • Combination 2. 12-ft lanes and 8-ft shoulders compared to 11-ft lanes and 3-ft shoulders The methods assessment is applied to each scenario, and the results are presented sepa- rately below. Tables 36 through 39 present the assessment results for lane and shoulder width Combination 1 (12-ft lanes and 4-ft shoulders compared to 11-ft lanes and 3-ft shoulders) for Method MSE Total Crashes MSE F and I Crashes MSE ROR Crashes MSE Target Crashes Average MSE Multiplicative = CMF1*CMF2 0.0224 0.0830 0.0023 0.0003 0.0270 Multiplicative with Generalized Reduction = 1- (2/3*(1−(CMF1*CMF2))) 0.0172 0.0280 0.0009 0.0034 0.0124 Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.0144 0.0170 0.0005 0.0004 0.0081 Dominant Effect = CMF1 (largest effect) 0.0081 0.0007 0.0000 0.0031 0.0030 Dominant Common Residuals = (CMF1*CMF2)CMF1 0.0224 0.0949 0.0001 0.0002 0.0294 Table 34. Summary of mean square error by method for CLRS + SRS. Method Difference Total Crashes Difference F and I Crashes Difference ROR Crashes Difference Target Crashes Average Difference Multiplicative = CMF1*CMF2 -0.150 -0.288 0.048 0.018 -0.093 Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) -0.131 -0.167 -0.030 -0.058 -0.097 Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) -0.120 -0.130 0.021 -0.019 -0.062 Dominant Effect = CMF1 (largest effect) -0.090 0.028 -0.005 -0.056 -0.031 Dominant Common Residuals =(CMF1*CMF2)CMF1 -0.150 -0.307 0.010 -0.014 -0.115 Table 35. Summary of differences by method for CLRS + SRS.

68 Guidelines for the Development and Application of Crash Modification Factors Method CMF 1 CMF 2 Combined CMF (By method) Combined CMF (Ground truth) MSE Over- or Under- Estimation Multiplicative = CMF1*CMF2 0.924 0.994 0.918 0.873 0.0021 Under Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) 0.924 0.994 0.946 0.873 0.0053 Under Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.924 0.994 0.921 0.873 0.0023 Under Dominant Effect = CMF1 (largest effect) 0.924 0.994 0.924 0.873 0.0026 Under Dominant Common Residuals =(CMF1*CMF2)CMF1 0.924 0.994 0.924 0.873 0.0027 Under Table 36. Methods assessment for lane and shoulder width combination 1 (total crashes on tangents). Method CMF 1 CMF 2 Combined CMF (By method) Combined CMF (Ground truth) MSE Over- or Under- Estimation Multiplicative = CMF1*CMF2 0.796 1.015 0.807 0.827 0.0004 Over Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) 0.796 1.015 0.872 0.827 0.0020 Under Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.796 1.015 0.801 0.827 0.0006 Over Dominant Effect = CMF1 (largest effect) 0.796 1.015 0.796 0.827 0.0010 Over Dominant Common Residuals =(CMF1*CMF2)CMF1 0.796 1.015 0.843 0.827 0.0003 Under Table 37. Methods assessment for lane and shoulder width combination 1 (fatal-and-injury crashes on tangents). Method CMF1 CMF 2 Combined CMF (By method) Combined CMF (Ground truth) MSE Over- or Under- Estimation Multiplicative = CMF1*CMF2 0.734 0.820 0.602 0.702 0.0101 Over Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) 0.734 0.820 0.734 0.702 0.0011 Under Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.734 0.820 0.668 0.702 0.0012 Over Dominant Effect = CMF1 (largest effect) 0.734 0.820 0.734 0.702 0.0010 Under Dominant Common Residuals =(CMF1*CMF2)CMF1 0.734 0.820 0.689 0.702 0.0002 Over Table 38. Methods assessment for lane and shoulder width combination 1 (run-off-road crashes on tangents).

Findings and Applications 69   total crashes, fatal-and-injury crashes, run-off-road crashes, and target crashes (run-off-road + head-on + sideswipe), respectively. Each table presents four CMFs for each method: (1) CMF for lane widening only (11 to 12 feet), (2) CMF for shoulder widening only (three to four feet), (3) estimated CMF for lane and shoulder widening based on existing method, and (4) ground truth CMF for lane and shoulder widening. The final two columns of each table indicate the MSE and over- or underestimation, respectively. Again, lower MSEs are preferred. Tables 40 through 43 present the assessment results for lane and shoulder width Combina- tion 2 (12-ft lanes and 8-ft shoulders compared to 11-ft lanes and 3-ft shoulders) for total crashes, fatal-and-injury crashes, run-off-road crashes, and target crashes (run-off-road + head-on + sideswipe), respectively. Each table presents four CMFs for each method: (1) CMF for lane widening only (11 to 12 feet), (2) CMF for shoulder widening only (three to eight feet), (3) estimated CMF for lane and shoulder widening based on existing method, and (4) ground truth CMF for lane and shoulder widening. The final two columns of each table indicate the MSE and over- or underestimation, respectively. Lower MSEs are preferred. Method CMF 1 CMF 2 Combined CMF (By method) Combined CMF (Ground truth) MSE Over- or Under- Estimation Multiplicative = CMF1*CMF2 0.744 0.819 0.609 0.689 0.0064 Over Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) 0.744 0.819 0.739 0.689 0.0025 Under Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.744 0.819 0.676 0.689 0.0002 Over Dominant Effect = CMF1 (largest effect) 0.744 0.819 0.744 0.689 0.0030 Under Dominant Common Residuals =(CMF1*CMF2)CMF1 0.744 0.819 0.692 0.689 0.0000 Under Table 39. Methods assessment for lane and shoulder width combination 1 (target crashes on tangents). Method CMF 1 CMF 2 Combined CMF (By method) Combined CMF (Ground truth) MSE Over- or Under- Estimation Multiplicative = CMF1*CMF2 0.892 0.924 0.824 0.850 0.0007 Over Multiplicative with Generalized Reduction = 1−(2/3*(1−CMF1*CMF2))) 0.892 0.924 0.883 0.850 0.0011 Under Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.892 0.924 0.858 0.850 0.0001 Under Dominant Effect = CMF1 (largest effect) 0.892 0.924 0.892 0.850 0.0018 Under Dominant Common Residuals =(CMF1*CMF2)CMF1 0.892 0.924 0.842 0.850 0.0001 Over Table 40. Methods assessment for lane and shoulder width combination 2 (total crashes on tangents).

70 Guidelines for the Development and Application of Crash Modification Factors Method CMF 1 CMF 2 Combined CMF (By method) Combined CMF (Ground truth) MSE Over- or Under- Estimation Multiplicative = CMF1*CMF2 0.657 0.796 0.523 0.720 0.0387 Over Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) 0.657 0.796 0.682 0.720 0.0014 Over Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.657 0.796 0.590 0.720 0.0168 Over Dominant Effect = CMF1 (largest effect) 0.657 0.796 0.657 0.720 0.0039 Over Dominant Common Residuals =(CMF1*CMF2)CMF1 0.657 0.796 0.653 0.720 0.0044 Over Table 41. Methods assessment for lane and shoulder width combination 2 (fatal-and-injury crashes on tangents). Method CMF 1 CMF 2 Combined CMF (By method) Combined CMF (Ground truth) MSE Over- or Under- Estimation Multiplicative = CMF1*CMF2 0.691 0.734 0.507 0.610 0.0106 Over Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) 0.691 0.734 0.671 0.610 0.0037 Under Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.691 0.734 0.599 0.610 0.0001 Over Dominant Effect = CMF1 (largest effect) 0.691 0.734 0.691 0.610 0.0065 Under Dominant Common Residuals =(CMF1*CMF2)CMF1 0.691 0.734 0.625 0.610 0.0002 Under Table 42. Methods assessment for lane and shoulder width combination 2 (run-off-road crashes on tangents). Method CMF 1 CMF 2 Combined CMF (By method) Combined CMF (Ground truth) MSE Over- or Under- Estimation Multiplicative = CMF1*CMF2 0.700 0.744 0.520 0.646 0.0158 Over Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) 0.700 0.744 0.680 0.646 0.0012 Under Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.700 0.744 0.610 0.646 0.0013 Over Dominant Effect = CMF1 (largest effect) 0.700 0.744 0.700 0.646 0.0029 Under Dominant Common Residuals =(CMF1*CMF2)CMF1 0.700 0.744 0.633 0.646 0.0002 Over Table 43. Methods assessment for lane and shoulder width combination 2 (target crashes on tangents).

Findings and Applications 71   For horizontal curve segments, the combination scenario presented in this study is 12-ft lanes and 8-ft shoulders compared to 11-ft lanes and 2-ft shoulders. Table 44 through Table 47 present the assessment results for total crashes, fatal-and-injury crashes, run-off-road crashes, and target crashes (run-off-road + head-on + sideswipe), respectively. Each table presents four CMFs for each method: (1) CMF for lane widening only (11 to 12 feet), (2) CMF for shoulder widening only (two to eight feet), (3) estimated CMF for lane and shoulder widening based on existing method, and (4) ground truth CMF for lane and shoulder widening. The final two columns of each table indicate the MSE and over- or underestimation, respectively. Lower MSEs are preferred. Table 48 and Table 49 summarize the MSEs and the average MSE for each method for lane and shoulder width Combination 1 and Combination 2, respectively, on tangents. Based on the CMFs for 12-ft lanes and 4-ft shoulders (Combination 1, Table 48), the Dominant Com- mon Residuals method performs best overall (i.e., average MSE across all crash types) and for all crash types except total crashes. For total crashes, the Multiplicative method performs best. Method CMF1 CMF 2 Combined CMF (By method) Combined CMF (Ground truth) MSE Over- or Under- Estimation Multiplicative = CMF1*CMF2 0.810 0.884 0.716 0.760 0.0019 Over Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) 0.810 0.884 0.811 0.760 0.0026 Under Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.810 0.884 0.763 0.760 0.0000 Under Dominant Effect = CMF1 (largest effect) 0.810 0.884 0.810 0.760 0.0025 Under Dominant Common Residuals =(CMF1*CMF2)CMF1 0.810 0.884 0.763 0.760 0.0000 Under Table 44. Methods assessment for 12-ft lane and 8-ft shoulder width combination (total crashes on curves). Method CMF1 CMF 2 Combined CMF (By method) Combined CMF (Ground truth) MSE Over- or Under- Estimation Multiplicative = CMF1*CMF2 0.635 0.754 0.479 0.659 0.0323 Over Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) 0.635 0.754 0.653 0.659 0.0000 Over Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.635 0.754 0.557 0.659 0.0103 Over Dominant Effect = CMF1 (largest effect) 0.635 0.754 0.635 0.659 0.0005 Over Dominant Common Residuals =(CMF1*CMF2)CMF1 0.635 0.754 0.626 0.659 0.0010 Over Table 45. Methods assessment for 12-ft lane and 8-ft shoulder width combination (fatal-and-injury crashes on curves).

72 Guidelines for the Development and Application of Crash Modification Factors Method CMF1 CMF 2 Combined CMF (By method) Combined CMF (Ground truth) MSE Over- or Under- Estimation Multiplicative = CMF1*CMF2 0.630 0.951 0.600 0.551 0.0024 Under Multiplicative with Generalized Reduction = 1−(2/3*(1−CMF1*CMF2)) 0.630 0.951 0.733 0.551 0.0333 Under Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.630 0.951 0.615 0.551 0.0041 Under Dominant Effect = CMF1 (largest effect) 0.630 0.951 0.630 0.551 0.0063 Under Dominant Common Residuals =(CMF1*CMF2)CMF1 0.630 0.951 0.724 0.551 0.0302 Under Table 46. Methods assessment for 12-ft lane and 8-ft shoulder width combination (run-off-road crashes on curves). Method CMF 1 CMF 2 Combined CMF Combined CMF MSE Over- or Under- Estimation (By method) (Ground truth) Multiplicative = CMF1*CMF2 0.612 0.947 0.579 0.575 0.0000 Under Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) 0.612 0.947 0.719 0.575 0.0208 Under Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.612 0.947 0.595 0.575 0.0004 Under Dominant Effect = CMF1 (largest effect) 0.612 0.947 0.612 0.575 0.0013 Under Dominant Common Residuals =(CMF1*CMF2)CMF1 0.612 0.947 0.716 0.575 0.0198 Under Table 47. Methods assessment for 12-ft lane and 8-ft shoulder width combination (target crashes on curves). Method MSE Total Crashes MSE F&I Crashes MSE ROR Crashes MSE Target Crashes Average MSE Multiplicative = CMF1*CMF2 0.0021 0.0004 0.0101 0.0064 0.0047 Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) 0.0053 0.0020 0.0011 0.0025 0.0027 Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.0023 0.0006 0.0012 0.0002 0.0011 Dominant Effect = CMF1 (largest effect) 0.0026 0.0010 0.0010 0.0030 0.0019 Dominant Common Residuals =(CMF1*CMF2)CMF1 0.0027 0.0003 0.0002 0.0000 0.0008 Table 48. Summary of mean square error by method for lane and shoulder width combination 1 (tangents).

Findings and Applications 73   Note, however, that some CMFs for total crashes are not statistically significant at the 95% con- fidence level. Based on the CMFs for 12-ft lanes and 8-ft shoulders (Combination 2, Table 49), the Dominant Common Residuals method performs best overall and for total and target crashes. The Multiplicative with Systematic Reduction method performs best for run-off-road crashes and equally as well as the Dominant Common Residuals method for total crashes. The Multipli- cative with Generalized Reduction method performs best for fatal-and-injury crashes. Table 50 summarizes the MSEs and average MSE for each method for the lane and shoulder width combination on horizontal curves. The Multiplicative with Systematic Reduction and Dominant Common Residuals methods perform best for total crashes. The Multiplicative with Generalized Reduction method performs best for fatal-and-injury crashes while the Multipli- cative method performs best for both run-off-road and target crashes. Overall, the Dominant Effect method results in the lowest average MSE across crash types. Table 51 and Table 52 present a summary of the difference between the ground truth and estimated combined CMF from each method for Combination 1 and Combination 2, respec- tively, on tangents. Method MSE Total Crashes MSE F&I Crashes MSE ROR Crashes MSE Target Crashes Average MSE Multiplicative = CMF1*CMF2 0.0007 0.0387 0.0106 0.0158 0.0165 Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) 0.0011 0.0014 0.0037 0.0012 0.0018 Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.0001 0.0168 0.0001 0.0013 0.0046 Dominant Effect = CMF1 (largest effect) 0.0018 0.0039 0.0065 0.0029 0.0038 Dominant Common Residuals =(CMF1*CMF2)CMF1 0.0001 0.0044 0.0002 0.0002 0.0012 Table 49. Summary of mean square error by method for lane and shoulder width combination 2 (tangents). Method MSE Total Crashes MSE F&I Crashes MSE ROR Crashes MSE Target Crashes Average MSE Multiplicative = CMF1*CMF2 0.0019 0.0323 0.0024 0.0000 0.0091 Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) 0.0026 0.0000 0.0333 0.0208 0.0142 Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.0000 0.0103 0.0041 0.0004 0.0037 Dominant Effect = CMF1 (largest effect) 0.0025 0.0005 0.0063 0.0013 0.0027 Dominant Common Residuals =(CMF1*CMF2)CMF1 0.0000 0.0010 0.0302 0.0198 0.0128 Table 50. Summary of mean square error by method for lane and shoulder width combination (curves).

74 Guidelines for the Development and Application of Crash Modification Factors Table 53 presents a summary of the difference between the ground truth and estimated com- bined CMF from each method for the lane-shoulder combination on horizontal curves. The dif- ference is always computed as the ground truth minus the estimate from the respective method. As such, positive values indicate that the method is overestimating the combined effect, and negative values indicate that the method is underestimating the combined effect. The Multi- plicative method overestimates the combined effect in most cases (9 of 12). The Multiplicative with Generalized Reduction and Dominant Effect methods underestimate the combined effect in most cases (10 of 12 and 9 of 12 respectively). The Multiplicative with Systematic Reduction and Dominant Common Residuals methods appear to split between overestimation and under- estimation. In this assessment, no single method consistently performs better than all others do; however, the Dominant Common Residuals method performs best in the most number of cases (5 of 12). Combination of Intersection Skew Angle and Sight Distance Improvements. Table 54 through Table 56 present the assessment results for total target crashes, fatal-and-injury target crashes, and right-angle crashes, respectively. Each table presents four CMFs for each method: (1) CMF for available ISD only, (2) CMF for intersection angle only, (3) estimated CMF for avail- able ISD and intersection angle based on existing method, and (4) ground truth CMF for available Method Difference Total Crashes Difference F&I Crashes Difference ROR Crashes Difference Target Crashes Average Difference Multiplicative = CMF1*CMF2 -0.046 0.019 0.100 0.080 0.039 Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) -0.073 -0.045 -0.032 -0.050 -0.050 Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) -0.048 0.025 0.034 0.013 0.006 Dominant Effect = CMF1 (largest effect) -0.051 0.031 -0.032 -0.054 -0.026 Dominant Common Residuals = (CMF1*CMF2)CMF1 -0.051 -0.017 0.013 -0.002 -0.014 Table 51. Summary of differences by method for lane and shoulder width combination 1 (tangents). Method Difference Total Crashes Difference F&I Crashes Difference ROR Crashes Difference Target Crashes Average Difference Multiplicative = CMF1*CMF2 0.026 0.197 0.103 0.126 0.113 Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) -0.032 0.038 -0.061 -0.034 -0.023 Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) -0.008 0.129 0.011 0.036 0.042 Dominant Effect = CMF1 (largest effect) -0.042 0.062 -0.081 -0.054 -0.029 Dominant Common Residuals =(CMF1*CMF2)CMF1 0.009 0.067 -0.015 0.013 0.018 Table 52. Summary of differences by method for lane and shoulder width combination 2 (tangents).

Findings and Applications 75   Method Difference Total Crashes Difference F&I Crashes Difference ROR Crashes Difference Target Crashes Average Difference Multiplicative = CMF1*CMF2 0.044 0.180 -0.049 -0.004 0.043 Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) -0.051 0.006 -0.182 -0.144 -0.093 Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) -0.003 0.101 -0.064 -0.020 0.003 Dominant Effect = CMF1 (largest effect) -0.050 0.023 -0.080 -0.036 -0.036 Dominant Common Residuals = (CMF1*CMF2)CMF1 -0.003 0.032 -0.174 -0.141 -0.071 Table 53. Summary of differences by method for lane and shoulder width combination (curves). Method CMF1 CMF2 Combined (By Method) Combined CMF (Ground truth) MSE Over- or Under- Estimation Multiplicative = CMF1*CMF2 0.414 0.456 0.189 0.469 0.0785 Over Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) 0.414 0.456 0.459 0.469 0.0001 Over Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.414 0.456 0.302 0.469 0.0280 Over Dominant Effect = CMF1 (largest effect) 0.414 0.456 0.414 0.469 0.0030 Over Dominant Common Residuals 0.414 0.456 0.501 0.469 0.0010 Under = (CMF1*CMF2)CMF1 Table 54. Methods assessment for ISD and intersection angle (total target crashes). Method CMF1 CMF2 Combined (By Method) Combined CMF (Ground truth) MSE Over- or Under- Estimation Multiplicative = CMF1*CMF2 0.211 0.272 0.057 0.823 0.5865 Over Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) 0.211 0.272 0.372 0.823 0.2040 Over Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.211 0.272 0.134 0.823 0.4746 Over Dominant Effect = CMF1 (largest effect) 0.211 0.272 0.211 0.823 0.3745 Over Dominant Common Residuals = (CMF1*CMF2)CMF1 0.211 0.272 0.547 0.823 0.0765 Over Table 55. Methods assessment for ISD and intersection angle (fatal-and-injury target crashes).

76 Guidelines for the Development and Application of Crash Modification Factors ISD and intersection angle. Note that CMF1 is always the smaller estimated individual CMF, and CMF2 is always the larger estimated individual CMF. The final two columns of each table indicate the MSE and over- or underestimation, respectively. Again, lower MSEs are preferred. Table 57 presents a summary of the MSEs and the average MSE for each method from the previous three tables. Based on the CMFs for available ISD, intersection angle, and their com- bination, the Multiplicative with Generalized Reduction method performs the best for total target crashes as well as overall. The Dominant Common Residuals method performs the best for fatal-and-injury crashes, and the Multiplicative with Systematic Reduction method performs the best for right-angle crashes. Table 58 presents a summary of the difference between the ground truth and estimated com- bined CMF from each method. The difference is always computed as the ground truth minus the estimate from the respective method. As such, positive values indicate that the method is over- estimating the combined effect and negative values indicate that the method is underestimating the combined effect. Based on the CMFs for available ISD, intersection angle, and their combi- nation, the Multiplicative method consistently overestimates the combined effect (3 of 3). The Multiplicative with Systematic Reduction method also consistently overestimates the combined Method CMF 1 CMF 2 Combined (By Method) Combined CMF (Ground truth) MSE Over- or Under- Estimation Multiplicative = CMF1*CMF2 0.186 0.265 0.049 0.146 0.0094 Over Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) 0.186 0.265 0.366 0.146 0.0484 Under Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.186 0.265 0.118 0.146 0.0008 Over Dominant Effect = CMF1 (largest effect) 0.186 0.265 0.186 0.146 0.0016 Under Dominant Common Residuals = (CMF1*CMF2)CMF1 0.186 0.265 0.571 0.146 0.1804 Under Table 56. Methods assessment for ISD and intersection angle (right-angle crashes). Method MSE Total Target Crashes MSE Fatal-and- Injury Target Crashes MSE Right- Angle Crashes Average MSE Multiplicative = CMF1*CMF2 0.0785 0.5865 0.0094 0.2248 Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) 0.0001 0.2040 0.0484 0.0842 Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.0280 0.4746 0.0008 0.1678 Dominant Effect = CMF1 (largest effect) 0.0030 0.3745 0.0016 0.1264 Dominant Common Residuals = (CMF1*CMF2)CMF1 0.0010 0.0765 0.1804 0.0860 Table 57. Summary of mean square error by method for available ISD and intersection angle.

Findings and Applications 77   effect (3 of 3). The Multiplicative with Generalized Reduction and Dominant Effect methods overestimate the combined effect for most crash types (2 of 3). The Dominant Common Residuals method underestimates the combined effect for most crash types (2 of 3). Overall, the Dominant Common Residuals method performs best without overestimating (i.e., the smallest average difference and only overestimates one crash type). The Dominant Common Residuals method also performs best for fatal-and-injury target crashes. The Multi- plicative with Generalized Reduction method performs best for total target crashes. The Multipli- cative with Systematic Reduction method performs best for right-angle crashes. Summary of Methods Assessment The previous section provides a discussion of the methods assessment by treatment. This section provides a summary of the methods assessment by facility type, crash type, the mag- nitude of treatment effect, and inclusion of CMFs greater than 1.0 to determine whether one or more methods perform better under different scenarios. Table 59 summarizes the average MSE by facility type, including tangents, curves, and intersections. One single method does not perform best under all scenarios. Specifically, the Dominant Common Residuals method performs best for tangents, the Dominant Effect method performs best for curves, and the Multiplicative with Generalized Reduction method performs best for intersections. Table 60 summarizes the average MSE by crash type, including total, fatal-and-injury, run- off-road, right-angle, and target. Again, it is apparent that one single method does not perform best under all scenarios. Specifically, the Dominant Common Residuals method performs best Method Difference, Total Target Crashes Difference, Fatal- and-Injury Target Crashes Difference, Right-Angle Crashes Average Difference Multiplicative = CMF1*CMF2 0.280 0.766 0.097 0.381 Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) 0.010 0.451 -0.220 0.080 Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.167 0.689 0.028 0.295 Dominant Effect = CMF1 (largest effect) Dominant Common Residuals = (CMF1*CMF2)CMF1 -0.032 0.276 -0.425 -0.060 0.055 0.612 -0.040 0.209 Table 58. Summary of differences by method for available ISD and intersection angle. Method Tangent Curve Intersection Multiplicative = CMF1*CMF2 0.0106 0.0092 0.2248 Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) 0.0023 0.0142 0.0842 Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.0028 0.0037 0.1678 Dominant Effect = CMF1 (largest effect) 0.0028 0.0027 0.1264 Dominant Common Residuals = (CMF1*CMF2)CMF1 0.0010 0.0128 0.0860 Table 59. Summary of average MSE by method by facility type.

78 Guidelines for the Development and Application of Crash Modification Factors for total and fatal-and-injury crashes. The Multiplicative with Systematic Reduction method performs best for run-off-road and right-angle crashes. Finally, the Dominant Effect method per- forms best for total and target crashes. Table 61 summarizes the average MSE by the magnitude of the individual treatment effects. The six categories that define the magnitude of individual treatment effects include small-small, small-medium, small-large, medium-medium, medium-large, and large-large. The magnitude of an individual treatment effect is defined as follows: • Small. Change in crashes is less than 10% (i.e., CMF between 0.90 and 1.10) • Medium. Change in crashes is 10% to 25% (i.e., CMF = 0.75–0.9 or 1.10–1.25) • Large. Change in crashes is greater than 25% (i.e., CMF < 0.75 or > 1.25) Again, it is apparent that one single method does not perform best under all scenarios. Spe- cifically, the Dominant Common Residuals method performs best for two of the six categories (small-medium and medium-medium) and performs almost equally as well for the medium- large and large-large categories. The Dominant Effect method performs best for two of the six categories (small-small and small-large). The Multiplicative with Generalized Reduction method performs best for two of the six categories (medium-large and large-large). The Multiplicative with Systematic Reduction method performs equally as well as the Dominant Common Residuals method for the medium-medium category. Table 63 summarizes the average MSE by the inclusion of CMFs greater than 1.0. In the discus- sion of existing methods for combining CMFs, it is noted that the Dominant Common Residuals Method Total Fatal-and-Injury Run-Off- Road Right-Angle Target Multiplicative = CMF1*CMF2 0.0068 0.1482 0.0064 0.0094 0.0202 Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) 0.0066 0.0471 0.0098 0.0484 0.0056 Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.0042 0.1039 0.0015 0.0008 0.0061 Dominant Effect = CMF1 (largest effect) Dominant Common Residuals = (CMF1*CMF2)CMF1 0.0063 0.0354 0.0077 0.1804 0.0042 0.0038 0.0761 0.0035 0.0016 0.0027 Table 60. Summary of average MSE by method by crash type. Method Small- Small Small- Medium Small- Large Medium- Medium Medium- Large Large- Large Multiplicative = CMF1*CMF2 0.0123 0.0009 0.0285 0.0019 0.0219 0.1402 Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) 0.0113 0.0019 0.0274 0.0026 0.0013 0.0515 Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.0084 0.0004 0.0072 0.0000 0.0071 0.1010 Dominant Effect = CMF1 (largest effect) 0.0054 0.0015 0.0025 0.0021 0.0777 Dominant Common Residuals = (CMF1*CMF2)CMF1 0.0126 0.0002 0.0483 0.0000 0.0014 0.0517 Table 61. Summary of average MSE by method by magnitude of treatment effect.

Findings and Applications 79   Table 62. Summary of average MSE by method by inclusion of CMFs > 1.0. Method 0 1 2 1 or 2 Multiplicative = CMF1*CMF2 0.0499 0.0114 0.0830 0.0353 Multiplicative with Generalized Reduction = 1−(2/3*(1−(CMF1*CMF2))) 0.0206 0.0096 0.0280 0.0157 Multiplicative with Systematic Reduction = CMF1*(1−(1−CMF2)/2) 0.0338 0.0075 0.0170 0.0107 Dominant Effect = CMF1 (largest effect) 0.0259 0.0046 0.0007 0.0033 Dominant Common Residuals = (CMF1*CMF2)CMF1 0.0198 0.0114 0.0949 0.0392 Scenario CMF1 SE(CMF1) CMF2 SE(CMF2) CMFt (By method) SE(CMFt) (By method) CMFt (Ground truth) SE(CMFt) (Ground truth) CLRS + SRS Total Crashes 1.060 0.070 0.996 0.019 1.056 0.069 0.906 0.042 CLRS + SRS Fatal-and-Injury Crashes 1.301 0.111 1.047 0.031 1.362 0.125 1.074 0.072 CLRS + SRS Run-Off-Road Crashes 0.818 0.099 0.935 0.028 0.765 0.094 0.813 0.059 CLRS + SRS Target Crashes 0.844 0.098 0.912 0.026 0.770 0.090 0.788 0.055 Lane and Shoulder Combo 1 Total Crashes on Tangents 0.924 0.054 0.994 0.063 0.918 0.084 0.873 0.047 Lane and Shoulder Combo 1 Fatal-and-Injury Crashes on Tangents 0.796 0.076 1.015 0.102 0.807 0.119 0.827 0.073 Lane and Shoulder Combo 1 Run-Off-Road Crashes on Tangents 0.734 0.061 0.820 0.073 0.602 0.072 0.702 0.055 Lane and Shoulder Combo 1 Target Crashes on Tangents 0.744 0.057 0.819 0.069 0.609 0.072 0.689 0.050 Lane and Shoulder Combo 2 Total Crashes on Tangents 0.892 0.068 0.924 0.054 0.824 0.081 0.850 0.047 Lane and Shoulder Combo 2 Fatal-and-Injury Crashes on Tangents 0.657 0.084 0.796 0.076 0.523 0.084 0.720 0.063 Lane and Shoulder Combo 2 Run-Off-Road Crashes on Tangents 0.691 0.075 0.734 0.061 0.507 0.071 0.610 0.048 Lane and Shoulder Combo 2 Target Crashes on Tangents 0.700 0.071 0.744 0.057 0.520 0.072 0.646 0.047 Lane and Shoulder Total Crashes on Curves 0.810 0.137 0.884 0.140 0.716 0.167 0.760 0.105 Lane and Shoulder Fatal-and-Injury Crashes on Curves 0.635 0.170 0.754 0.194 0.479 0.180 0.659 0.144 Lane and Shoulder Run-Off-Road Crashes on Curves 0.630 0.147 0.951 0.194 0.600 0.185 0.551 0.105 Lane and Shoulder Target Crashes on Curves 0.612 0.139 0.947 0.187 0.579 0.178 0.575 0.105 ISD and Intersection Angle Total Target Crashes 0.414 0.119 0.456 0.122 0.189 0.075 0.469 0.219 ISD and Intersection Angle Fatal-and-Injury Target Crashes 0.211 0.082 0.272 0.104 0.057 0.033 0.823 0.769 ISD and Intersection Angle Right-Angle Crashes 0.186 0.085 0.265 0.116 0.049 0.033 0.146 0.095 Table 63. Summary of method assessment for estimating the standard error of the combined effect.

80 Guidelines for the Development and Application of Crash Modification Factors method is not appropriate when combining CMFs greater than 1.0 because the product of the individual CMFs is then raised to a power greater than 1.0, which intensifies rather than dampens the combined effect. The following are the four specific cases listed in the table. • 0: Both CMFs are less than 1.0 • 1: One of the CMFs is greater than 1.0 • 2: Both CMFs are greater than 1.0 • 1 or 2: One or both CMFs are greater than 1.0 (the above two categories combined) Again, it is apparent that one single method does not perform best under all scenarios; how- ever, there are clear choices for the two general scenarios. Specifically, the Dominant Common Residuals method performs best when both CMFs are less than 1.0. The Dominant Effect method performs best when one or more CMFs are greater than 1.0. The following are observations from the comparisons of methods with respect to facility type, crash type, the magnitude of individual treatment effects, and inclusion of CMFs greater than 1.0. • As shown in Tables 59 through 62, the Multiplicative method never performs best, and it performs particularly poorly when both treatment effects are large. • For scenarios where there is a typical target crash type (e.g., run-off-road crashes on curves), and the treatments address the same type of crash, the Dominant Effect method appears to be the most appropriate. In these cases, the Dominant Effect method will only consider the benefit of the most effective treatment. For example, consider a scenario where both the lane and shoulder width are widened on horizontal curves to target run-off-road crashes. If the CMF for lane widening from 11 to 12 feet is 0.95, and the CMF for shoulder widening from 2 to 8 feet is 0.63, then the combined effect is assumed to be 0.63. • For scenarios where the treatment targets a few select crash types (e.g., head-on, sideswipe, and run-off-road crashes on tangents), and the treatments could address one or more of these crash types, the Dominant Common Residuals method appears to be the most appropriate. In these cases, the Dominant Common Residuals method gives credit to the expected safety benefit of additional treatments, but discounts additional benefits based on the benefit of the most effective treatment. For example, consider a scenario where both the lane and shoulder width are widened on tangents to target head-on, sideswipe, and run-off-road crashes. If the CMF for lane widening from 11 to 12 feet is 0.74, and the CMF for shoulder widening from 3 to 8 feet is 0.70, then the combined effect is computed as 0.63 [i.e., (0.70×0.74)0.70]. • At locations where any variety of treatments could be applied to address any number of contributing factors (e.g., rear-end, right-angle, and turning crashes at intersections), the Dominant Common Residuals method may be most appropriate. While the Multiplicative with Generalized Reduction method performed best for intersections (Table 59), the Domi- nant Common Residuals methods performed almost as well and performed best for total crashes (Table 60). For example, consider a scenario where both ISD and intersection angle are improved to address all crashes between a vehicle on the major road and one on the minor road. If the CMF for improving ISD is 0.46, and the CMF for improving intersection angle is 0.41, then the combined effect is computed as 0.50 [i.e., (0.41×0.46)0.41]. • For scenarios where both treatments have small effects, there is relatively little difference between the methods, but the Dominant Effect method performs best. • For scenarios where one treatment has a small effect and the other has a large effect, the Domi- nant Effect method performs best. Note that the Dominant Common Residuals method does not perform well in this case (i.e., the large difference in the treatment effects). • For all other scenarios (small-medium, medium-medium, medium-large, and large-large), the Dominant Common Residuals method appears to be the most appropriate. While the Multiplicative with Generalized Reduction method performs best when both treatment effects are large, the Dominant Common Residuals method is a close second.

Findings and Applications 81   • For scenarios where both CMFs are less than 1.0, the Dominant Common Residuals method performs best. • For scenarios where one or more CMFs are greater than 1.0, the Dominant Effect method performs best. If a single method is desired for all scenarios, the Dominant Common Residuals method appears to be most suitable if both CMFs are less than 1.0. This is based on a comparison of the estimated and actual combined CMF for the 19 combination treatment scenarios tested in this study. Specifically, the Dominant Common Residuals method performs best for 8 of 19 scenarios. The Multiplicative with Systematic Reduction method performs best for 4 of 19 scenarios. The Multiplicative, Multiplicative with Generalized Reduction, and Dominant Effect methods per- formed best in 3 of 19 scenarios. Note that two methods performed equally well in two scenarios, so the above numbers do not total 19. Assessing and Validating Methods for Estimating the Standard Error of the Combined Effect This section presents the results of the method assessment for estimating the standard error of the combined effect. The method assessment is based on 19 scenarios, comparing the estimated combined effect and standard error from the multiplicative method with ground truth CMFs and standard errors established in this research project. The preceding Analysis section presents the individual and combined ground truth CMFs and standard errors for the following three treatments. • Combination of centerline and shoulder rumble strip installation • Combination of lane and shoulder widening • Combination of intersection skew angle and sight distance improvements. The following equation presents the primary method of interest to estimate the standard error of the combined effect. Again, this relates to the Multiplicative method and does not apply to other methods. SE CMF CMF Var CMF CMF Var CMF CMFt n n t Equation 45. . .12 1 2 2( )( ) ( )( ) ( ) ( )= + × × + − where SE(CMFt) = standard error of the combined treatment effect Var(CMFn) = variance of the nth CMF (i.e., SE(CMFn)2) CMFt = CMF for the combined treatments CMF1 = CMF for the most effective treatment CMF2 = CMF for the second most effective treatment CMFn = CMF for the nth most effective treatment Table 63 presents 19 scenarios, including the individual CMFs and associated standard errors, estimated combined treatment effect from the Multiplicative method (CMFt) and associated standard error, and ground truth of the combined treatment effect and associated standard error. For each scenario, the estimated standard error of the combined effect is compared to the ground truth. In addition, the methods are assessed with respect to overestimating or underes- timating the standard error of the combined effect compared to the ground truth. As evident when comparing the last two columns of Table 63, the proposed method over- estimates the standard error of the combined effect in 16 of 19 scenarios. For the last three scenarios, the proposed method underestimates the standard error of the combined effect. It should be noted that the sample size was relatively small for estimating the combined effect in the last three scenarios, inflating the ground truth standard error of the combined effect.

82 Guidelines for the Development and Application of Crash Modification Factors Additionally, the Multiplicative method severely overestimates the combined treatment effect in these three scenarios. From the equation above, it is apparent that overestimating the combined treatment effect results in underestimating the standard error of the combined treatment effect. The Multiplicative method and associated standard error assume the single-effect CMFs represent independent random variables. As such, the proposed method provides a reasonable upper bound on the estimate of the standard error of the combined effect; however, it does not explicitly recognize correlation among the CMF values. If the correlation is not zero, then the true standard error will be smaller than the estimated standard error from the proposed method. Assessment of methods to estimate the combined treatment effect (Table 59 through Table 62) shows that there is a correlation among the individual CMFs. This is supported by the results in Table 63 where the proposed method overestimates the standard error in nearly all scenarios. Beyond a simple comparison of the estimated and ground truth values for the combined effect and associated standard error, it is important to understand how decisions may change using the estimated values as opposed to the ground truth. Table 64 presents the 95% confidence limits and related decisions based on the estimates and ground truth. Note that the estimates are based on CMFs from the Multiplicative method and the associated standard errors. The decision is different in 6 of the 19 scenarios. For four of the scenarios, the decision based on estimated values would be that no effect occurs (i.e., not significant), while the decision based on ground truth would be that a safety benefit is achieved (i.e., significant decrease). In one case, the deci- sion based on estimated values would be that a safety disbenefit occurs (i.e., significant increase), while the decision based on ground truth would be that no effect occurs (i.e., not significant). In another case, the decision based on estimated values would be that a safety benefit is achieved (i.e., significant decrease) while the decision based on ground truth would be that no effect occurs (i.e., not significant). Exploring Magnitude and Structure of Interaction Effects for Combination Treatments Before developing guidelines on combining multiple CMFs to estimate the combined effect of multiple treatments, there is a need to explore the magnitude and structure of potential inter- action effects among various roadway characteristics and treatments categories. This has been recently shown by Wu and Lord (2016), who found that the traditional method for combining CMFs resulting from regression models can result in biased CMFs if the considered variables are not independent. They found that the resulting bias is significantly correlated with the degree of dependence of the considered variables. Additionally, they found that while the coefficients for variables of interest may be over- or underestimated, other variables included in the analysis may compensate by being over- or underestimated as well. This section explores potential interactions for combined treatments using the following safety data sets: • Rural, two-lane, four-legged intersections with stop control on the minor road approach • Isolated horizontal curves on rural, two-lane highways The first data set is a subset of the data collected for NCHRP Project 17-59: Safety Impacts of Intersection Sight Distance. The second data set was collected for NCHRP Project 03-106: Traffic Control Device Guidelines for Curves. Table 65 and Table 66 present correlation matrices for the variables collected in the data sets. Each correlation matrix has an associated key to define the variables included. The correlation matrices indicate the degree of association among variables included. A value of 1.00 indicates

Findings and Applications 83   that two variables are perfectly correlated, while a value of 0.00 indicates no correlation between the variables. The direction of the correlation characterizes the relationship between the vari- ables; however, the strength of correlation for 1.00 and –1.00 is the same. Note that the matrices only include explanatory variables and exclude dependent variables. Most variables are less than 50% associated with each other, while some variables are more than 50% correlated. Correlations 50% to 74% are indicated by underlined italics, while correla- tions 75% to 99% are indicated by underlined bold. There is no single definition of correlation that defines when two variables are highly correlated; however, many researchers begin to note correlation when the coefficient is between 0.50 and 0.60 (positive or negative). Scenario 95% Confidence Limits (By method) Decision (By method) 95% Confidence Limits (Ground truth) Decision (Ground truth) CLRS + SRS Total Crashes 0.92 1.19 Not significant 0.82 0.99 Significant decrease CLRS + SRS Fatal-and-Injury Crashes 1.12 1.61 Significant increase 0.93 1.22 Not significant CLRS + SRS Run-Off-Road Crashes 0.58 0.95 Significant decrease 0.70 0.93 Significant decrease CLRS + SRS Target Crashes 0.59 0.95 Significant decrease 0.68 0.90 Significant decrease Lane and Shoulder Combo 1 Total Crashes on Tangents 0.75 1.08 Not significant 0.78 0.97 Significant decrease Lane and Shoulder Combo 1 Fatal-and-Injury Crashes on Tangents 0.57 1.04 Not significant 0.68 0.97 Significant decrease Lane and Shoulder Combo 1 Run-Off-Road Crashes on Tangents 0.46 0.74 Significant decrease 0.59 0.81 Significant decrease Lane and Shoulder Combo 1 Target Crashes on Tangents 0.47 0.75 Significant decrease 0.59 0.79 Significant decrease Lane and Shoulder Combo 2 Total Crashes on Tangents 0.66 0.98 Significant decrease 0.76 0.94 Significant decrease Lane and Shoulder Combo 2 Fatal-and-Injury Crashes on Tangents 0.36 0.69 Significant decrease 0.60 0.84 Significant decrease Lane and Shoulder Combo 2 Run-Off-Road Crashes on Tangents 0.37 0.65 Significant decrease 0.52 0.70 Significant decrease Lane and Shoulder Combo 2 Target Crashes on Tangents 0.38 0.66 Significant decrease 0.55 0.74 Significant decrease Lane and Shoulder Total Crashes on Curves 0.39 1.04 Not significant 0.55 0.97 Significant decrease Lane and Shoulder Fatal-and-Injury Crashes on Curves 0.13 0.83 Significant decrease 0.38 0.94 Significant decrease Lane and Shoulder Run-Off-Road Crashes on Curves 0.24 0.96 Significant decrease 0.35 0.76 Significant decrease Lane and Shoulder Target Crashes on Curves 0.23 0.93 Significant decrease 0.37 0.78 Significant decrease ISD and Intersection Angle Total Target Crashes 0.04 0.34 Significant decrease 0.04 0.90 Significant decrease ISD and Intersection Angle Fatal-and-Injury Target Crashes 0 0.12 Significant decrease 0 2.33 Not significant ISD and Intersection Angle Right-Angle Crashes 0 0.11 Significant decrease 0 0.33 Significant decrease Table 64. The difference in decisions comparing estimated and ground truth CMFs and standard errors of the combined effect.

A B C D E F G H I J K L M N O P Q R S T A 1.00 B 0.47 1.00 C 0.00 0.04 1.00 D 0.49 0.37 0.03 1.00 E 0.24 0.38 0.09 0.09 1.00 F 0.32 0.48 -0.31 0.34 0.17 1.00 G 0.32 0.50 -0.20 0.32 0.31 0.93 1.00 H -0.17 0.07 -0.01 -0.05 0.13 0.21 0.20 1.00 I -0.23 0.13 -0.03 -0.12 0.24 0.13 0.22 0.80 1.00 J 0.34 -0.02 -0.19 0.23 -0.30 0.29 0.17 -0.06 -0.16 1.00 K -0.03 0.17 -0.26 -0.16 0.01 0.31 0.21 0.16 0.00 -0.06 1.00 L -0.13 0.09 -0.21 -0.16 0.15 0.27 0.23 0.14 0.05 -0.12 0.89 1.00 M 0.35 0.04 -0.14 0.22 -0.34 0.34 0.22 -0.05 -0.12 0.89 0.04 -0.07 1.00 N -0.34 -0.10 0.01 -0.22 0.19 -0.17 -0.07 -0.06 0.04 -0.62 0.17 0.32 -0.64 1.00 O 0.41 0.04 -0.17 0.24 -0.32 0.32 0.18 -0.04 -0.16 0.95 0.05 -0.07 0.93 -0.66 1.00 P -0.41 -0.04 0.17 -0.24 0.32 -0.32 -0.18 0.04 0.16 -0.95 -0.05 0.07 -0.93 0.66 -1.00 1.00 Q -0.14 -0.19 0.16 0.01 -0.14 -0.39 -0.39 -0.14 -0.08 -0.17 -0.38 -0.45 -0.14 -0.05 -0.14 0.14 1.00 R -0.13 -0.13 0.22 0.04 -0.04 -0.32 -0.23 0.00 0.13 -0.17 -0.41 -0.40 -0.15 -0.25 -0.20 0.20 0.24 1.00 S -0.30 -0.21 0.21 -0.17 0.03 -0.45 -0.29 -0.01 0.18 -0.27 -0.30 -0.23 -0.24 -0.05 -0.31 0.31 0.10 0.64 1.00 T 0.23 0.22 -0.36 0.12 0.05 0.30 0.17 0.00 -0.17 0.17 0.37 0.25 0.11 0.19 0.15 -0.15 -0.16 -0.67 -0.63 1.00 Key A: Major-road AADT B: Minor-road AADT C: Posted speed limit D: Lane width E: Presence of stop line F: Presence of advance intersection warning sign G: Distance from intersection to advance intersection warning sign H: Presence of advance STOP AHEAD sign I: Distance from intersection to advance STOP AHEAD sign J: Presence of edgeline extension K: Presence of speed advisory sign L: Level of speed reduction from posted speed limit to advisory speed M: Average annual temperature N: Total annual snowfall O: Indicator for North Carolina P: Indicator for Ohio Q: Intersection angle R: Available ISD S: Indicator for flat terrain (base condition rolling or mountainous) T: Grade 500 ft before intersection on a major road Table 65. Example 1 intersection database.

Findings and Applications 85   Characteristics that are strongly related make it difficult to discern the individual effects when the two characteristics are considered jointly. Example 1, in Table 65, shows that the correlation coefficient between the presence of an edgeline extension and the indicator for North Carolina is 0.95. This is because nearly all sites in North Carolina had edgeline extensions and no sites in Ohio had edgeline extensions. In a cross-sectional analysis, the inclusion of both variables would lead to a collinearity problem (i.e., both variables explain the same information). This presents an issue when there is interest in understanding the individual effect of the edgeline extension. In this case, the variable indicating the presence of edgeline extension will not characterize the treatment effect insomuch as characterize any observed differences between the two states. Similarly, the state indicators are highly related to several variables that characterize the differ- ence between states, including mean temperature, total snowfall, and the presence of edgeline extensions. Table 66 (Example 2) shows correlated treatments that may be considered together in a safety analysis of horizontal curves. For example, the presence of an advance turn warning sign is highly correlated with the advisory speed and/or the reduction in speed from the posted speed limit to the advisory speed. Due to the high level of correlation, resulting CMFs will have a potential overlap in treatment effects. For example, if a practitioner is considering an advance turn warning sign and the installation of an advisory speed sign, there is a potential overlap in the individual CMFs (i.e., both CMFs are explaining the same effect). The correlation matrix also indicates that several treatments are correlated with the degree of curvature, including total curve angle, advisory speed, speed reduction, and the presence of a turn warning sign. A B C D E F G H I J K L M N O P A 1.00 B -0.28 C 0.07 -0.36 1.00 D -0.28 0.31 E 0.01 -0.07 0.01 -0.19 1.00 F -0.14 -0.03 0.06 0.20 1.00 G 0.31 -0.08 -0.13 -0.29 0.08 -0.10 1.00 H 0.22 -0.01 -0.03 -0.01 0.16 0.24 -0.10 1.00 I 0.26 -0.28 0.11 -0.24 0.19 0.02 0.06 0.25 1.00 J 0.24 -0.65 0.25 -0.54 0.35 0.10 0.16 0.14 0.36 1.00 K -0.25 -0.26 0.05 -0.02 -0.14 -0.08 -0.31 -0.92 1.00 L 0.38 -0.39 0.15 -0.32 0.15 0.02 0.14 0.17 0.22 0.32 -0.28 1.00 M -0.36 -0.20 -0.22 -0.03 -0.21 -0.12 -0.35 -0.78 0.73 -0.63 1.00 N 0.10 0.09 -0.04 -0.04 -0.01 -0.05 -0.14 -0.17 0.16 0.13 0.09 1.00 O -0.19 -0.26 -0.01 0.04 0.00 0.02 -0.20 -0.42 0.44 -0.23 0.42 -0.22 1.00 P 0.07 1.00 0.56 0.67 0.64 0.00 0.47 0.26 -0.03 1.00 0.09 0.49 0.54 0.18 0.25 0.13 -0.04 0.00 0.03 0.10 -0.05 -0.17 0.17 0.00 0.09 -0.10 -0.07 1.00 Key A: AADT B: Degree of curvature C: Horizontal curve length D: Total horizontal curve angle E: Posted speed limit F: Presence of reflective delineators G: Presence of reflective pavement markers H: Lane width I: Shoulder width J: Advisory speed K: Speed reduction L: Presence of advance horizontal curve warning sign M: Presence of advance turn warning sign N: Presence of chevrons O: Presence of large reflective arrow P: Presence of both chevrons and large reflective arrow Table 66. Example 2 horizontal curve database.

86 Guidelines for the Development and Application of Crash Modification Factors An example of this is evident in a safety effectiveness evaluation conducted under FHWA’s Development of Crash Modification Factors project (Himes et al. 2017). The treatment of inter- est for the evaluation was edgeline rumble stripes on horizontal curves. The results indicated no significant reduction in total crashes or target crashes in Ohio but indicated significant reduc- tions in Kentucky. Upon further investigation, the Ohio Department of Transportation noted that they had completed a system-wide upgrade of horizontal curve warning devices (both in-curve and before curves) at approximately the same time as the installation of the edgeline rumble stripes. In this case, the two treatments targeted the same types of crashes. A reference group (i.e., similar sites without edgeline rumble stripes) was employed to control for other changes over time, including the system-wide sign upgrades. However, there was a similar reduction in crashes for both the treatment and reference groups (i.e., sites with and without edgeline rumble stripes). As such, the researchers concluded that the system-wide sign upgrades were beneficial and the edgeline rumble stripes provided no additional safety benefit at the curve locations beyond the benefit from the sign upgrades. CMFs for Combined Safety Effects of Treatment Combinations The research project associated with these guidelines resulted in 19 new CMFs that represent the combined safety effect of the following treatment combinations: • Combination of centerline and shoulder rumble strip installation • Combination of lane and shoulder widening • Combination of intersection skew angle and sight distance improvements The following subsections present the new CMFs for future use by practitioners. The documen- tation of the research effort to develop these CMFs is presented in Appendix B, Section B.4. Combination of Centerline and Shoulder Rumble Strip Installation. This treatment rep- resents the combined installation of centerline and shoulder rumble strips on urban and rural two-lane, undivided roads. Table 67 presents the CMFs and associated standard errors for the combined effect of installing centerline and shoulder rumble strips on urban and rural two-lane, undivided roads. Combination of Lane and Shoulder Widening. This treatment represents the combined widening of lane and shoulder width on rural two-lane, undivided roads. Table 68 and Table 69 present the CMFs and associated standard errors for two combinations of widening lane and Applicable Crash Type CMF Standard Error Total crashes (all crash types and severities) 0.906 0.042 Fatal-and-injury crashes (all crash types) 1.074 0.072 Run-off-road crashes (all crash severities) 0.813 0.059 Target crashes (run-off-road + head-on + sideswipe) 0.788 0.055 Table 67. CMFs for installing centerline and shoulder rumble strips. Applicable Crash Type CMF Standard Error Total crashes (all crash types and severities) 0.873 0.047 Fatal and injury crashes (all crash types) 0.827 0.073 Run-off-road crashes (all crash severities) 0.702 0.055 Target crashes (run-off-road + head-on + sideswipe) 0.689 0.050 Table 68. CMFs for widening lane width from 11 feet to 12 feet and shoulder width from three feet to four feet on tangents.

Findings and Applications 87   shoulder width on rural two-lane, undivided tangent sections. The following are the two com- bined treatments of interest for tangent sections. Both reflect a baseline condition of 11-ft lanes and 3-ft shoulders. • 12-ft lanes and 4-ft shoulders compared to 11-ft lanes and 3-ft shoulders • 12-ft lanes and 8-ft shoulders compared to 11-ft lanes and 3-ft shoulders Table 70 presents the CMFs and associated standard errors for the combination of widening lane and shoulder width on rural two-lane, undivided horizontal curve sections. The combined treatment of interest for horizontal curve sections is a cross-section with 12-ft lanes and 8-ft shoulders compared to a cross-section with 11-ft lanes and 2-ft shoulders. Combination of Intersection Skew Angle and Sight Distance Improvements. This treat- ment represents the combined improvement of intersection skew angle and ISD at three- and four-legged intersections with minor road stop control. The following are the focus crash types for this analysis. • Total target crashes. Crashes involving a vehicle from the minor-road approach and from the major-road approach, associated with a directional analysis unit. The appropriate analysis unit is identified by the approaching direction of the major-road vehicle. • Fatal-and-injury target crashes. The subset of total target crashes involving at least one vehicle occupant with a fatality or injury (K, A, B, or C on the KABCO scale). • Right-angle crashes. The subset of total target crashes in which both vehicles on the major and minor roads were intending to move straight through the intersection. It is possible to have right-angle crashes on three-legged intersections, as some intersections had driveways. Table 71 presents the CMFs and associated standard errors for the combination of improv- ing available ISD and intersection angle. The following are the defined improvements for this analysis: • Individual ISD effect: Available ISD of more than 1,320 feet compared to a baseline condition of 500 feet to 750 feet. • Individual intersection angle effect: Intersection angle of 85 degrees to 90 degrees compared to a baseline condition of 50 degrees to 75 degrees. • Combined treatment effect: Available ISD of more than 1,320 feet and intersection angle of 85 degrees to 90 degrees compared to baseline conditions for both. Applicable Crash Type CMF Standard Error Total crashes (all crash types and severities) 0.850 0.047 Fatal-and-injury crashes (all crash types) 0.720 0.063 Run-off-road crashes (all crash severities) 0.610 0.048 Target crashes (run-off-road + head-on + sideswipe) 0.646 0.047 Table 69. CMFs for widening lane width from 11 feet to 12 feet and shoulder width from three feet to eight feet on tangents. Applicable Crash Type CMF Standard Error Total crashes (all crash types and severities) 0.760 0.105 Fatal-and-injury crashes (all crash types) 0.659 0.144 Run-off-road crashes (all crash severities) 0.551 0.105 Target crashes (run-off-road + head-on + sideswipe) 0.575 0.105 Table 70. CMFs for widening lane width from 11 feet to 12 feet and shoulder width from two feet to eight feet on curves.

88 Guidelines for the Development and Application of Crash Modification Factors Guidelines on Combining Two CMFs to Estimate a Combined Treatment Effect Before estimating the combined safety effect of multiple treatments, the analyst must decide if it is necessary and appropriate to implement multiple treatments. If the treatments target dif- ferent safety issues and crash types, then it may be necessary to implement both treatments, and the analyst can proceed with the following guidelines to consider the combined effect. If multiple treatments target the same safety issues and crash types, then there is likely overlap among the treatment effects, and one treatment may be sufficient. Several of the results support this state- ment, particularly where the Dominant Effect method performs best. The study by Himes et al. (2017) provides further support where edgeline rumble stripes provided no additional safety benefit at curve locations beyond the benefit from a system-wide upgrade of horizontal curve warning devices. Figure 8 is a flowchart to guide the decision process for selecting the most appropriate method to estimate the combined effect of multiple treatments. The decision process is based on three key factors: potential overlap of individual treatment effects, the magnitude of individual treat- ment effects, and the applicability of the individual CMFs. A separate guidelines document in Appendix B provides a more detailed description of the process, including examples to illustrate how to navigate the decision process and then how to apply the methods. Note that Appendix B presents the recommended method to estimate the combined safety effect of two treatments at the same location. While the guidelines can be used to estimate the effects of more than two treatments, this study was unable to assess the accuracy of methods to combine more than two individual CMFs. The study required data from multiple projects in the same jurisdiction where each treatment was applied individually and in combination, and data fitting these criteria were not available for combinations of three or more treatments. Documenting Projects for Future Validation of Recommended Methods Several of the methods in the previous section rely on existing information to quantify the interaction among multiple treatments. When this information is unavailable, incomplete, or insufficient to reliably identify the individual and/or combined treatment effects, then it is neces- sary to conduct new research to obtain the required information. In some cases, proper docu- mentation of completed research studies could help prevent the need for additional research to obtain the same information. The remainder of this section presents instructions for docu- menting individual projects for future validation of methods to estimate the combined effect of multiple treatments. The following are critical details for quantifying the interaction among treatments and esti- mating the combined treatment effect. For further guidelines on documenting CMFs in general, refer to NCHRP’s Recommended Protocols for Developing Crash Modification Factors (Carter et al. 2012). Applicable Crash Type CMF Standard Error Target crashes 0.469 0.219 Fatal-and-injury target crashes 0.823 0.769 Right-angle crashes 0.146 0.095 Table 71. CMFs for increasing intersection sight distance to 1,320+ feet and intersection angle to 85–90 degrees.

Findings and Applications 89   Determine Potential Overlap of Individual Treatment Effects Case A: Zero overlap Case B: Some overlap Case C: Complete overlap Case D: Enhancing effects Case E: Counteracting effects Determine Magnitude of Individual Treatment Effects Small (< 10% change) Medium (10% - 25% change) Large (> 25% change) Define Applicability of Individual CMFs To what crash types and severities do the individual CMFs apply? Same Crash Type and Severity Proceed to Table 72 Different Crash Type and Severity Proceed to Table 73 The CMFs must be applied separately because they apply to different crash types and/or severities. Figure 8. Flowchart for selecting appropriate method. Overlap Magnitude Method Case A Case D Not applicable Additive effects with maximum reduction of 100% (i.e., CMF = 0) Case B Small-Small Dominant effect Small-Medium Dominant common residuals (if CMFs < 1.0); Dominant effect otherwise Small-Large Dominant effect Medium-Medium Dominant common residuals (if CMFs < 1.0); Dominant effect otherwise Medium-Large Dominant common residuals (if CMFs < 1.0); Dominant effect otherwise Large-Large Dominant common residuals (if CMFs < 1.0); Dominant effect otherwise Case C Not applicable Dominant effect Case E Not applicable Multiplicative Table 72. Method selection for same crash type and severity.

90 Guidelines for the Development and Application of Crash Modification Factors • Specific treatment(s). Describe the treatment(s) for which the CMF was developed. The description should be detailed enough to identify the original (baseline) condition and convey exactly what was implemented at the study sites. The treatment description should identify the exact location to which the treatment was applied. For example, was it applied to both directions of a segment or only the outside lane in one travel direction? Was it applied to all approaches or only one approach of a signalized intersection? • CMFs or CMFunctions. Present the effects of the individual and/or combined treatments. When listing CMFunctions, clearly label all terms in the function. • Standard error. Present the standard error of the mean value of CMF. • Applicable crash conditions. Describe the crash type and severity to which each CMF applies. • Applicable roadway conditions. Describe roadway conditions to which each CMF applies. Examples include the facility type (e.g., rural, two-lane, undivided segments or urban, multi- lane, four-legged, signalized intersections), state/municipality, traffic volume, and speed limit. Task 4 Recommended Procedures for Calibrating and Formulating Future CMFs That Identify Key Influential Site Characteristics Overview of Task and Products Task 4 involved the development of procedures for researchers for deriving future CMFs and CMFunctions, with a focus on CMFunctions. Task 4 was conducted in two phases: Phase 1 in which potential procedures are identified, and Phase 2 in which recommendations were developed for procedures to create future CMFs and CMFunctions. The description below is organized to summarize the efforts for each of several subtasks. The procedures produced from Task 4 are presented in two groups. The first group is spe- cifically targeted at researchers and consists of Appendix C, which presents the procedures for developing CMFunctions and four case studies to demonstrate the procedures. Overlap Method Case A Case D Modified Additive Effects with Maximum Reduction of 100% (i.e., CMF = 0) Assuming no overlap among treatment effects, one would expect the full benefit of each treatment. 1. Apply the CMF for the first treatment to the expected crashes for the applicable crash type/severity at the location of interest. 2. Apply the CMF for the second treatment to the expected crashes for the applicable crash type/severity at the location of interest. 3. Sum the expected reductions in crashes to estimate the net benefit. 4. Check that the expected reduction does not exceed the total number of expected crashes. If so, the expected reduction is equal to the total number of expected crashes. Case B Case E Dominant Effect for Overlapping Crash Types Assuming some overlap among the treatment effects, one would expect the full benefit of the most effective treatment and some additional benefit from the second treatment. 1. Apply the CMF for the most effective treatment to the expected crashes for the applicable crash type/severity at the location of interest. 2. Apply the CMF for the second treatment to the expected crashes for the applicable crash type/severity at the location of interest, excluding crashes associated with the most effective treatment. 3. Sum the expected reductions in crashes to estimate the net benefit. 4. Check that the expected reduction does not exceed the total number of expected crashes. If so, the expected reduction is equal to the total number of expected crashes. Case C Dominant Effect Assuming complete overlap among the treatment effects, one would expect the full benefit of only the most effective treatment. (This is a simplified version of Case B.) Apply the CMF for the most effective treatment to the expected crashes for the applicable crash type/severity at the location of interest. Table 73. Method selection for different crash type and severity.

Findings and Applications 91   The second group provides complementary discussion in two appendixes. These appendixes make the case that researchers and highway safety institutions that influence the conduct of research should engage, where practical, in randomized trials or at least in an approach that is close to achieving this desideratum. This would overcome some of the key issues with observa- tional studies that are illuminated in the first segment. These appendixes are: • Appendix F—Enhancing Future CMF Research • Appendix G—Developing Consensus in Research About the Safety Effect of Manipulations Subtask 4.1 Literature Review The first subtask assembled information considered helpful in providing researchers in the future with recommended procedures for developing CMFunctions. The focus was necessarily on developing CMFunctions since it is well recognized that for CMFs to be estimated for applica- tion with a minimum of variance, they must be made a function of circumstances. The literature review was based on the road safety literature as well as literature from other fields of science such as medicine and epidemiology. This task was complemented by the review for Task 2, which identified treatments for which CMFs may be expected to be variable depending on the application circumstance. That review also identified treatments that hold the potential for developing CMFunctions either through a meta- analysis of before-after evaluations or from cross-sectional studies. From that review, a candidate list of treatments in each category emerged for exploration in Phase 2. The literature review sought information on several aspects, including • Identifying treatments for which CMFs may vary with application circumstance (i.e., for which CMFunctions may be required), with further guidelines on – Whether continuous functions may be desired – Whether CMFs can be specified by variable category, i.e., CMF variability is determined through categorical analysis – Which CMFunctions can be derived from before-after evaluations and which ones need to be derived from cross-sectional studies • Identifying independent variables or categories that may be of interest for developing each CMFunction • Assessing and recommending methods for developing CMFunctions, based on a review of road safety literature and literature in other areas of study Literature pertinent to these aspects was categorized as follows: Category 1 Meta-Analysis of Treatment Effects Estimated from Sites Within a Study or Different Studies, or Both The review revealed that the general approach taken to quantifying heterogeneous effects, as CMFunctions would seek to do, is meta-regression. Although most of this literature is focused on developing meta-regression models from the results from multiple studies, it was assumed that, in principle, the same approach could be used for multiple estimates of effect for groups of similar entities within the same study. For example, road segments may be grouped by traffic volume, and estimates for each group could be treated as a single estimate. Category 2 Estimating CMFunctions from the Regression Analysis that Relates Crashes to Treatment-Related Factors It was concluded that there are considerable challenges in developing CMFunctions from cross- sectional regression analysis of crashes and that these challenges need to be well documented in

92 Guidelines for the Development and Application of Crash Modification Factors the guidelines, as well as how they can be mitigated. It was recognized that there is some research suggesting that, despite these challenges, it is possible to explore the development of CMFunctions with this approach, especially where this is a necessity and where corroboration with before-after results and intuitive reasoning is possible. This recognition prompted and supported the decision to pursue the development and demonstration of procedures for this approach to developing CMFunctions. Subtask 4.2 Develop Framework for Alternate Procedures This subtask developed a general framework for the part of the guidelines focusing on identi- fying key issues to be addressed in pursuing two approaches. • Regression models that relate crashes to CMF-related variables to develop CMFs and CMFunctions from coefficient estimates • Models that relate CMF point estimates to the application circumstance to develop CMFunctions The framework for alternative procedures evolved through what was learned from the litera- ture review and Tasks 2 and 3. The framework included a list of relevant topics and methodolo- gies to be covered in the Task 4 procedures to be developed in Phase 2. The topics covered are listed in the description of the Phase 2 effort. Subtask 4.3 Identify Potential Data Sources for Phase 2 This subtask focused on the identification of potential data that would facilitate the investiga- tion of a short list of treatments for demonstrating the procedures. It was thought that the list of potential treatments for investigation that emerged from Task 2, Subtask 2.3, would suffice for this purpose, since that Subtask presented a list of potential data sets, including a general description and applicability to this study. Subtask 4.4 Develop Plan for Phase 2 This subtask explored and described the proposed method to collect and assemble the required observational data, demonstrate the proposed methods, and develop final guidelines. Items addressed included: 1. Final identification of treatments to be investigated and influential factors 2. Collection and assembly of data 3. Issues to be explored in demonstrating methods for the two approaches to be pursued 4. Development and documentation of guidelines The plan was for the documentation of the recommended procedures to include: • Procedures for developing an experimental plan that will capture key factors influencing CMF value among sites • Procedures for developing CMFunctions from cross-sectional regression analysis, including guidelines for addressing the issues in inferring causality from these studies • Procedures for developing CMFunctions (e.g., meta-regression, weighted regression) from CMFs and assessing fit, including summary guidelines for better developing site and study- level estimates of the CMF and its variance • Procedures for quantifying the CMF standard error when computed as a function After consultation with the project panel, it was decided to also develop and document com- plementary guidelines on approaches and institutional requirements for engaging, where practi- cal, in randomized trials, or at least with an approach that is close to achieving this desideratum,

Findings and Applications 93   to overcome some of the key issues with observational studies that are illuminated in the rec- ommended procedures. This guidance was designed for institutions; namely, state and local transportation agencies (at present) or other transportation service providers. Subtask 4.5 Implement Plan for Phase 2 The four specific items identified in the work plan were executed in developing procedures for researchers as well as the procedures for institutions that influence the conduct of research. These procedures dealt with many issues in the statistical analysis of data to develop CMFunctions. Two general methods for CMFunction development were recommended and procedures were developed for these: (1) meta-regression of the site or study-level CMF estimates and (2) cross- sectional regression modeling. Below is a description of the thought processes and decisions made while producing the final deliverables. Items (1) and (2) Final Identification of Treatments to Be Investigated and Influential Factors and Collection and Assembly of Data The two items were combined since an important consideration in the final identification of treatments to be investigated was the availability of suitable data sets for the intended purposes. After careful consideration and investigation of the suitability of various treatment data sets, it was decided that each of the two methods to be demonstrated could be explored in case studies for two treatments as follows: Case Studies for Meta-Regression of Site or Study-Level CMF Estimates Case Study 1: Simultaneous application of shoulder rumble strips and centerline rumble strips on rural two-lane roads. The treatment selected for this case study was the simultaneous application of shoulder rumble strips and centerline rumble strips on rural two-lane roads. The data set used originated with an empirical Bayes before-after study analysis conducted under the FHWA Development of Crash Modification Factors (DCMFs) evaluation study. All site types are rural two-lane roadways and data from Pennsylvania, Missouri, and Kentucky are included. While the original analysis evaluated several crash types, including total crashes, it was decided to focus the case study on run-off-road crashes since this was the predominant target crash type, for which a CMFunction would be of most interest. In developing a CMFunction, only those variables that are shared among the three states and that are suspected to influence the value of the CMF were considered. These are: • AADT before treatment • The empirical Bayes expected crashes per year before treatment • Average shoulder width Case Study 2: Conversion of Conventional Intersections to Roundabouts. The treatment selected for this case study was the conversion of conventional signalized intersections to round- abouts. The data set used originated from several research efforts that each conducted an empiri- cal Bayes before-after study and estimated a CMF for each converted site and groups of sites. The case study focused on total crashes. In developing a CMFunction, only those variables that are shared across the data and that are suspected to influence the value of the CMF were considered. These are: • Entering AADT • The empirical Bayes expected crashes per year before treatment • Area type (urban vs. rural) • Number of circulating lanes • Number of entering legs

94 Guidelines for the Development and Application of Crash Modification Factors The data came from the three sources listed below. Some of the sites were used for both Source 1 and Source 2 and were only included once in this analysis. • Source 1—NCHRP Report 572: Roundabouts in the United States (Rodegerdts et al. 2007) • Source 2—NCHRP Report 705: Evaluation of Safety Strategies at Signalized Intersections (Srinivasan et al. 2011) • Source 3—Evaluating Performance and Making Best Use of Passing Relief Lanes (Bagdade et al. 2012) Case Studies for Cross-sectional Regression Modeling Case Study 3: Safety Effects of Flattening a Horizontal Curve. The data acquired included roadway geometry, including horizontal curvature data, traffic volume, and crash data for 2008 to 2012 from Washington State. All sites are rural two-lane roads. Case Study 4: Safety Effects of Left- and Right-Turn Lanes on Major Roads at Three-Legged Stop-Controlled Intersections. The data set used for the illustration consisted of 3,543 three- legged stop-controlled intersections on rural two-lane roadways. These data were used for an FHWA study that looked to validate and recalibrate the crash prediction models for inter- sections in the HSM two-lane rural road chapter. These data included sites from California, Minnesota, and Georgia. Item (3) Issues to be Explored in Demonstrating Methods for the Two Approaches to be Pursued In selecting issues to be explored it was recognized that not all the identified issues were pertinent or could be explored in a specific case study. In the end, the following key issues were explored: • Meta-regression – Selection of candidate influencing variables – Accounting for interactions among candidate variables – Different CMFunctions for different subgroups of data (e.g., grouped by jurisdiction) – Tools for exploring the appropriate functional form of the model – Whether fixed or random-effects models are appropriate – Procedures for creating subgroups of sites using important variables – Selection of the most robust CMFunctions from among several candidates • CMFunctions from cross-sectional data – Selection of candidate influencing variables – Accounting for interactions among candidate variables – Functional form for effects of independent variables – Tools for assessing the model fit and choosing among, or amalgamating information from, competing models – Including estimates from previous studies in the estimation methodology through Full Bayes methods Item (4) Development and Documentation of Guidelines During this task, it was determined that the procedures to be provided would be intentionally not detailed enough to be seen as prescriptive since that level of information is more effectively provided in sources dedicated to that purpose. Rather, the guidelines would introduce and discuss topics and methods relevant to successful CMFunction development with some limited illus- tration through examples and case studies. Through this, some level of prescriptive direction is

Findings and Applications 95   provided in conjunction with the case studies, with extensive and appropriate cross-referencing. In sum, the plan then was for the case studies to complement the procedural guidelines by: • Illustrating a heuristic methodology a future researcher may follow to derive a CMFunction. • Illuminating some of the considerable issues and challenges that may be encountered in the process and, in so doing, address what it may take for future researchers to resolve them. This included developing content for the complementary discussion that focused on key issues and challenges. • Illustrating the considerable data requirements for estimating a robust CMFunction so that future research planning will endeavor to assemble appropriate data sets. Following team discussions, the following topics were identified for which guidance would be provided based on information available from both published and unpublished literature sources. Guidance for Developing CMFunctions from Cross-Sectional Regression Models • Bias due to aggregation, averaging, or incompleteness in data • Functional form for effects of independent variables • Model structure—application of hierarchical modeling • Tools for assessing the model fit and choosing among, or amalgamating information from, competing models • Including estimates from previous studies in the estimation methodology through full Bayes methods • Addressing multicollinearity among explanatory variables • Addressing endogeneity • Modeling interactions, especially for estimating effects of combination treatments • Estimating precision of CMFs from CMFunctions derived • Corroboration of results • Database requirements Guidance for Developing CMFunctions from Models That Relate CMF Point Estimates to Application Circumstance • Conducting systematic reviews • Application circumstances and key influential factors to collect information on, grouped by treatment and location types • Conducting meta-regression – Exploratory analysis and identification of outliers – Selection of model form – Validation – Examples of meta-regression in road safety • Fixed versus random-effects models • Selection of estimation method • Guidelines for creating subgroups • Estimating precision of CMFs from CMFunctions derived • Improving site and study-level estimates of CMFs Complementary Guidance Focusing on Key Issues in CMF Development • Enhancing future CMF research (Appendix F) – Why look for alternative ways to get CMFs? – Designing observational studies

96 Guidelines for the Development and Application of Crash Modification Factors – What is the best way to predict? – Integration of research and practice • Developing consensus in research about the safety effect of manipulations (Appendix G) – Part I. Review of past research about the safety effect of pavement marking retroreflectivity ◾ Prior expectations ◾ When to stop modeling ◾ Can one get the CMF of PMR from models based on cross-sectional data? ◾ The quality of retroreflectivity data ◾ Should only statistically significant results be considered? ◾ Choices, assumptions, and uncertainties ◾ Consistency in regression coefficients ◾ Lessons of past research – Part II. Ways to determine the effect of a cause ◾ Laboratory experiments ◾ Randomized experiments ◾ Observational before-after and cross-sectional studies