Crash Modification Factors in the Highway Safety Manual: A Review (2023)

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23   Development of CMFunctions for Select Treatments 5.1 Background A key limitation of the HSM and the CMF Clearinghouse is the limited information regarding the variability in CMFs by application circumstances. It is difficult to think of any CMF of which it can categorically be said that the CMF would be constant from application to application. There are numerous examples in the recent and not­so­recent literature that suggest that CMFs do vary by application circumstances, such as traffic volume and roadway curvature (e.g., Srinivasan et al. 2009; Bahar et al. 2004). Three recent before–after empirical Bayes (EB) studies indicate that the estimated safety benefits of treatments are larger when targeted high­accident locations are evaluated than when the evaluation is based on blanket installations (Bahar et al. 2004; Lyon and Persaud 2008; Persaud et al. 2009). If the safety effect is indeed larger when a treatment is applied at sites with a high level of target crashes, then the CMF derived from such application circum­ stances may overestimate the effects of changes in a feature in a design application when the HSM predictive methodology is being used. There was much discussion about this point for the HSM1 when the task force realized that several CMF values for the same roadway characteristic were different from Part C to Part D. Ultimately, it was decided to avoid practitioner confusion and make the CMFs in Parts C and D the same and even add new CMFs to Part C from Part D. In developing the CMFunctions, the project team identified treatments for which the original data were available. In the case of EB before–after studies, the project team was looking for infor­ mation about individual treatment sites that were used in the evaluation, including the observed number of crashes in the after period, the EB expected number of crashes in the after period had the treatment not been implemented, and the variance of the expected number of crashes in the after period. For cross­sectional studies, the project was looking for the data that were used in estimating the CMFs. This chapter provides an overview of the findings; detailed results, including the recom­ mended CMFunctions, are documented in Appendices E, F, G, and H. Also included in this chapter is one example of a CMFunction that was estimated to illustrate how practitioners can use these CMFunctions. 5.2 Treatments for CMFunction Development The project team used methods discussed in NCHRP Project 17­63 (Carter et al. 2022) to develop CMFunctions for the following treatments: • Improving curve delineation on rural two-lane undivided roads. The data for this treat­ ment were obtained from a study conducted by Srinivasan et al. (2009), who used data from Washington State and Connecticut. Only the Connecticut data were available for estimating C H A P T E R 5

24 Crash Modification Factors in the Highway Safety Manual: A Review the CMFunctions. The original evaluation used an EB before–after method. The following variables were identified as candidates for CMFunction development: curve radius, annual average daily traffic (AADT), roadside hazard rating, curve length, number of signs within a curve, number of signs on curve approaches, posted speed limit, suggested speed limit, and the EB estimate of the expected crashes before treatment. • Shoulder and median width on rural multilane roads. The data for this treatment were based on a study conducted by Stamatiadis et al. (2009) that used cross­sectional models to estimate CMFs with data from California, Kentucky, and Minnesota. The intent of the effort to develop CMFunctions was to extend the models developed by Stamatiadis et al. (2009) to determine whether the safety effects of shoulder width and median width depend on other site characteristics. • Adding a two-way left-turn lane (TWLTL) to a two-lane road. The data for this treatment were based on a study conducted by Persaud et al. (2008). The original evaluation used the EB before–after method to estimate CMFs based on data from Arkansas, California, Illinois, and North Carolina. The following variables were identified as candidate variables in the evalua­ tion: area type (rural vs. urban), average shoulder width, AADT, and the EB estimate of the expected crashes before treatment. • Conversion of two-way stop-control to all-way stop control at four-leg intersections. The data for this exercise were obtained from a study conducted by Simpson and Hummer (2010) with information from North Carolina. The original evaluation used an EB before– after method. The following variables were identified as candidate variables for CMFunction development: major and minor road AADT, posted speed limits, presence of flashing beacons, and the EB estimate of the expected crashes before treatment. 5.3 Methodologies for Estimating CMFunctions The following three methods for estimating CMFunctions were investigated: meta­regression, the generalized linear model (GLM) method, and cross­sectional regression. Following is a brief overview of these methods. 5.3.1 Meta-regression The intent is to develop models to relate CMF point estimates to application circumstances to quantify the sources of systematic variation of effect for the expected CMF value. Depending on the context, meta­regression may be applied with site­level data or study­level data. In this case, site­level data were used, that is, a CMF was estimated for each site or group of similar sites and then used as an observation in the modeling. In this effort, this approach was used in estimating CMFs derived from EB before–after studies. In this effort, due to large variation in effect at indi­ vidual sites (attributable in large part to the randomness of crash counts), ranges of the variables of interest were used to bin sites together and then first calculate more stable estimates of effect for each bin. This was an iterative process and involved examining the number of crashes and sites within each bin as well as the stability and precision of CMFs estimated for each bin. 5.3.2 GLM Method As with the meta­regression method, in this effort, the GLM method was used in estimating CMFs derived from EB before–after studies. The GLM approach for estimating CMFunctions was initially developed by Srinivasan and Lan (2016, 2020). In this approach, the CMF from a study (or a site or group of sites) is approximated by the observed crash count in the after period divided by the expected crash frequency in the absence of the treatment. The observed crash

Development of CMFunctions for Select Treatments 25 count is then used as the dependent variable, with the expected crashes as an offset in a count model that includes characteristics of application circumstances as independent variables. As in the case of meta­regression, this approach can be used with individual sites, group of sites, or at the study level. In this effort, this approach was used with data from individual sites. 5.3.3 Cross-Sectional Regression This approach was used with the data from Stamatiadis et al. (2009) that had used cross­ sectional models to estimate the CMF. In this effort, nonlinear mixed regression models were used to estimate CMFunctions. This methodology allows for complex model forms in which estimated parameters can themselves be a function of a higher­order model. A negative binomial error distribution was assumed in estimating the models. 5.4 Overview of Results Following is an overview of the results based on the estimated CMFunctions for each treatment. 5.4.1 Improving Curve Delineation on Rural Two-Lane Undivided Roads Appendix E provides the details of the CMFunctions, which were estimated by using the GLM approach for lane departure, crashes in dark conditions, and lane departure crashes in dark conditions. Overall, the CMFs were lower with higher levels of AADT, indicating that curve delineation was more effective when traffic volume levels were higher. Under low levels of AADT or expected crashes per mile (before treatment), or both, CMFs greater than 1.0 may be possible, which implies that for low­traffic or low­crash sites, the addition of curve delineation may increase crashes. The data available did not include lane or shoulder widths, so the impact of those variables on the predicted CMFs could not be explored. Curve radius was available, but no effects on the predicted CMFs could be determined for this data set. The following CMFunction was used to estimate the effect of improving curve delineation on lane departure crashes: CMF = e3.1178(AADT)−0.3850 To use this CMF for a particular site, the practitioner needs to input the AADT at the site before the treatment was applied. 5.4.2 Shoulder and Median Width on Rural Multilane Roads Appendix F provides the details of the CMFunctions. Following is a brief overview of the findings: • For single­vehicle and total crashes on divided roadways, the CMF for shoulder width decreased as AADT increased and increased if the right shoulder was paved. • For multivehicle crashes on divided roadways, the CMF for shoulder width was seen to be higher if the right shoulder was paved, and the CMF for median width was higher if a median barrier was present. • For single­vehicle and total crashes on undivided roadways, there was some indication that the CMF for shoulder width decreased as AADT increased, but this was based on a more­ complicated model formulation and may be an overfit to the data.

26 Crash Modification Factors in the Highway Safety Manual: A Review • For multivehicle crashes on undivided roadways, the CMF for shoulder width was found to increase as AADT increased. • The CMFs estimated for shoulder width and median width imply the same change in crash frequencies for a unit change in the variable—for example, that a change in median width from 2 ft to 8 ft has the same effect on crashes as a change from 8 ft to 14 ft. 5.4.3 Adding a TWLTL to a Two-Lane Road Appendix G provides the details of the CMFunctions. The GLM approach was determined to be unsuccessful for this data set. The meta­regression approach found some success for linear models using the AADT before the treatment as the predictor variable. These models generally found that the CMF was lower at higher levels of AADT, thus indicating that a TWLTL may be more effective when traffic volume levels are higher. However, for all the models, none of the parameters were statistically significant and the goodness of fit as measured by the R2 value was low. Hence, the conclusions from this effort were not considered definitive. 5.4.4 Conversion of Two-Way Stop-Control to All-Way Stop Control at Four-Leg Intersections Appendix H provides the details of the CMFunctions, which were developed by using the GLM approach for total and injury (including fatalities) crashes. For both types of severity, the CMFunctions indicated that the CMF decreases with an increasing crash rate (before treatment) and increases with an increasing AADT (sum of major and minor road AADT). This implies that converting two­way to all­way stop­controlled intersections would be more effective at high­crash intersections and intersections with higher AADT.