Guidelines for the Application of Crossing Solutions at Roundabouts and Channelized Turn Lanes for Pedestrians with Vision Disabilities (2016)

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NCHRP 3-78b: Final Project Report April 2016 9 APPENDIX C: RISK MODEL DETAILS This appendix summarizes the risk modeling results for the combined data for TOPR-34 and NCHRP 3-78b. In order to create models to predict pedestrian risk rate, Stata was used to analyze data collected at roundabouts in states of Washington, Oregon, New York, Michigan, North Carolina, Maryland, Ohio, Wisconsin, and channelized turn lane locations in Colorado, North Carolina, Maryland and Arizona. 9.1 Methodology 9.1.1 Definition of Risk Models & Data Collection As part of accessibility audits of the intersections for the purpose of NCHRP 3-78b project and the FHWA TOPR34 project, the research team recruited blind subjects to participate in an indicator study which asked them to approach and stand at the crosswalk location at curb and identify when they would cross by raising their hand. During the study subjects were accompanied at all times by an orientation and mobility (O&M) specialist. After participant’s indication, the O&M specialist would rank the participant’s decision as estimated intervention, risky event, or safe event as described below: 1. Estimated Intervention – if the pedestrian had stepped into the roadway at the time the decision was made, the O&M specialist would have chosen to intervene by physically restraining the participant to avoid a collision with an approaching vehicle. 2. Risky Event – if the pedestrian had stepped into the roadway at the time the decision was made, the O&M specialist may have chosen to intervene, depending on driver reaction, pedestrian walking speed, or other considerations. 3. Safe Event – if the pedestrian had stepped into the roadway at the time the decision was made, the O&M specialist would not have chosen to intervene, and would have let the crossing proceed. Each subject completed approximately ten trials at each study location and 5 to 7 subjects were recruited for each location. Based on the count of trials that were ranked as estimated intervention or risky event, the terms intervention rates and intervention-risky rates were defined for each site as below: 𝐼𝑛𝑡𝑒𝑟𝑣𝑒𝑛𝑡𝑖𝑜𝑛 𝑅𝑎𝑡𝑒 = 𝐶𝑜𝑢𝑛𝑡 𝑜𝑓 𝐴𝑙𝑙 𝐼𝑛𝑡𝑒𝑟𝑣𝑒𝑛𝑡𝑖𝑜𝑛 𝐸𝑣𝑒𝑛𝑡𝑠 𝐴𝑐𝑟𝑜𝑠𝑠 𝐴𝑙𝑙 𝑆𝑢𝑏𝑗𝑒𝑐𝑡𝑠 𝑓𝑜𝑟 𝑂𝑛𝑒 𝑠𝑖𝑡𝑒 𝐶𝑜𝑢𝑛𝑡 𝑜𝑓 𝐴𝑙𝑙 𝑇𝑟𝑖𝑎𝑙𝑠 𝐴𝑐𝑟𝑜𝑠𝑠 𝐴𝑙𝑙 𝑆𝑢𝑏𝑗𝑒𝑐𝑡𝑠 𝑓𝑜𝑟 𝑂𝑛𝑒 𝑠𝑖𝑡𝑒 𝐼𝑛𝑡𝑒𝑟𝑣𝑒𝑛𝑡𝑖𝑜𝑛 – 𝑅isky R𝑎𝑡𝑒 = = 𝐶𝑜𝑢𝑛𝑡 𝑜𝑓 𝐴𝑙𝑙 𝐼𝑛𝑡𝑒𝑟𝑣𝑒𝑛𝑡𝑖𝑜𝑛 plus Risky 𝐸𝑣𝑒𝑛𝑡𝑠 𝐴𝑐𝑟𝑜𝑠𝑠 𝐴𝑙𝑙 𝑆𝑢𝑏𝑗𝑒𝑐𝑡𝑠 𝑓𝑜𝑟 𝑂𝑛𝑒 𝑠𝑖𝑡𝑒 𝐶𝑜𝑢𝑛𝑡 𝑜𝑓 𝐴𝑙𝑙 𝑇𝑟𝑖𝑎𝑙𝑠 𝐴𝑐𝑟𝑜𝑠𝑠 𝐴𝑙𝑙 𝑆𝑢𝑏𝑗𝑒𝑐𝑡𝑠 𝑓𝑜𝑟 𝑂𝑛𝑒 𝑠𝑖𝑡𝑒 In order to predict the rate of intervention and intervention-risky events, the research team collected many other performance measures that they hypothesized might contribute to higher risky and intervention situations for bind pedestrians. These variables are results of many hours of research study and observation of blind pedestrian crossing, and interviews with blind pedestrians. The variables are defined in Table 9-1. 125

NCHRP 3-78b: Final Project Report April 2016 Table 9-1: Variables of Interest in Risk Modeling Variable Description Value CTL Channelized Turn Lane Channelized Turn Lane=1, otherwise=0 RBTN Roundabout entry Roundabout entry=1, otherwise=0 RBTX Roundabout exit Roundabout exit =1, otherwise=0 NOISE Noise level experienced at the study location High=1, Low=0 SIGHT_D Whether the pedestrian sight distance was provided or not Sight distance provide=1, otherwise=0 LU Lane Utilization Unbalanced=1, balanced=0, OL_DEC Overlapping decision Points between yielding to pedestrian and finding gap in cross traffic Two decisions overlap=1, otherwise=0 XSPED_AVE Average pedestrian speed at crosswalk (>= 10mph) Continuous variable N2 Number of lanes Single lane =0, more than one lane=1 YR Average driver yield rate to pedestrians Continuous variable YUR Average yield utilization rate by blind pedestrians Continuous variable RDS Approach fastest path radius Continuous variable INT Intervention rates Continuous variable INTR Total of intervention and risky events rate Continuous variable Stata was used to analyze the data collected in order to create a model to predict the likelihood of intervention or intervention-risky crossings at an intersection by a blind pedestrian. Since the dependent variables are continuous and the independent variables are a combination of binary and continuous variables, multivariable linear regression models were generated. 9.2 Results 9.2.1 Descriptive Statistics The descriptive statistics for the variables are shown in Table 9-2. In total, 52 observations are gathered and included in the dataset, 40 roundabouts locations (entry and exit) and 12 channelized turn lane locations. Table 9-2 Descriptive Statistics for Risk Modeling Variables Variables N Ave St. Dev Min Max Dependent Variables INT 52 0.048 0.052 0 0.217 INTR 52 0.170 0.126 0 0.6 Binary Independent Variables CTL 52 0.231 0.425 0 1 RBTN 52 0.385 0.491 0 1 RBTX 52 0.385 0.491 0 1 NOISE 52 0.308 0.466 0 1 SIGHT_D 52 0.327 0.474 0 1 LU 52 0.212 0.412 0 1 PL_DEC 52 0.423 0.499 0 1 N2 52 0.635 0.486 0 1 Continues Independent variables XSPD_AVE 52 19.38 4.92 0 30.5 YR 52 0.59 0.29 0 1 YUR 52 0.623 0.246 0.14 1 RDS 52 241 216 50 1000 126

NCHRP 3-78b: Final Project Report April 2016 Across the study locations, the data shows that the average intervention rate is 0.05 and the average intervention-risky rate is 0.17. This suggests that, on average, blind participants made “bad” crossing decisions which may have resulted in an intervention about 5% of the time. The chance that a blind participant would make either a risky or dangerous (intervention) crossing decision at an intersection is about 17% among all locations. The results show that 31% of the study locations are associated with high noise levels (NOISE=0.308). Also, 33% of the locations were associated with not providing enough pedestrian sight distance (SIGHT_D = 0.327). On average, 21% of the multi-lane roundabouts suffer from imbalanced lane utilization either at entry or exit. Forty-two percent of the crosswalks are located at the point where drivers would be likely to be also looking for a gap in crossing traffic and, therefore, the locations have overlapping decision points. The average speed across all crossings observed at the crosswalk locations was 19 mph and the average observed yielding rate to pedestrians (blind and sighted), across all crossings was 59%. 9.2.2 Correlation A summarized version of the Pearson correlation table showing the correlation between the intervention rate and intervention-risky rate for all sites and the explanatory variables is shown in Table 9-3. Correlation coefficients are provided with the significance level indicated by superscripted asterisks. Since RBTN, RBTX, and CTL all together represent the whole sample size and CTL can be described as the combination of RBTN and RBTX, the variable CTL was eliminated from the rest of the analysis. The following variables show a significant positive correlation (p<0.01) with dependent variable INT; NOISE, SIGHT_D, OL_DEC, XSPD_AVE, RDS, RBTN. The variable N2, RBTX and YR show a significant (p<0.05, and p< 0.1 respectively) negative correlation with dependent variable INT. The following variables show a significant positive correlation (p<0.01) with dependent variable INTR; NOISE, SIGHT_D, OL_DEC, XSPD_AVE, RDS. The variables RBTN and YR are positively correlated with p<0.05. No significant correlation was found for LU (lane utilization) and YUR (yield utilization rate) in relation to either INT or INTR and therefore these variables are eliminated from modeling considerations in the next steps. 127

NCHRP 3-78b: Final Project Report April 2016 Table 9-3 Correlation Table for Variables n=52 INT INTR N2 NOISE SIGHT_D LU OL_DEC YR XSPD_AVE YUR RDS RBTN RBTX INT 1 INTR 0.8142** 1 N2 0.2082 0.2892* 1 NOISE 0.6949** 0.5765** 0.1597 1 SIGHT_D 0.4294** 0.4088** 0.018 0.3348** 1 LU -0.1908 -0.089 0.393** -0.0392 -0.2606+ 1 OL_DEC 0.398** 0.3936** 0.0031 0.5255** 0.3989** - 0.0623 1 YR -0.2587+ -0.334* 0.2816* -0.2609+ -0.2142 0.1128 -0.3305* 1 XSPD_AVE 0.3975** 0.3628** 0.2257 0.3098* 0.1563 - 0.2299 0.2516+ -0.3279* 1 YUR 0.1374 0.0975 0.4474** 0.0478 -0.1702 -0.15 -0.1171 0.3911** 0.2816* 1 RDS 0.4556** 0.4855** 0.3893** 0.4373** 0.1196 0.2063 0.251 -0.3067* 0.2892* 0.0344 1 RBTN 0.4632** 0.3137* 0.3536* 0.415** 0.2074 - 0.0223 0.1231 -0.2361 0.3522* 0.284* 0.4405** 1 RBTX -0.3148* -0.149 0.2715+ -0.3558* -0.3824** 0.268+ -0.277 0.4084** -0.1822 0.2358 -0.2238 -0.63 1 **p<0.005, *p<0.05, +p<0.10 INT Intervention rates INTR Total of intervention and risky events rate N2 Number of lanes NOISE Noise level experienced at the study location SIGHT_D Whether the pedestrian sight distance was provided or not LU Lane Utilization OL_DEC Overlapping decision Points between yielding to pedestrian and finding gap in cross traffic XSPED_AVE Average pedestrian speed at crosswalk (>= 10mph) YR Average driver yield rate to pedestrians YUR Average yield utilization rate by blind pedestrians RDS Approach fastest path radius RBTN Roundabout entry RBTX Roundabout exit 128

NCHRP 3-78b: Final Project Report April 2016 The correlation table revealed significant intercorrelation between independent variables. For example, XSPD_AVE (speed) and RDS (radius) are strongly correlated, which is expected since geometric design of the roundabout or CTL (radius) is proven to be one of the factors that control speed. Therefore, RDS is also excluded from consideration for model development. The variables listed below have a significant intercorrelation with each other: • NOISE: SIGHT_D, OL_DEC, YR, XSPD_AVE, RDS, RBTX, RBTN • SIGHT_D: NOISE, LU, OL_DEC, RBTX, RBTN • LU: SIGHT_D, RBTN • OL_DEC: NOISE, SIGHT_D, YR, XSPD_AVE, RBTN • YR: N2, NOISE, OL_DEC, XSPD_AVE, RDS, RBTX, RBTN • XSPD_AVE: NOISE, OL_DEC, YR, RDS, RBTN, RBTX, YUR • YUR: N2, YR, XSPD_AVE, RBTN • RDS: N2, NOISE, XSP_AVE, YR • RBTN: NOISE SIGHT_D, LU, OL_DEC, YR, YUR • RBTX: N2, NOISE, XSPD_AVE, YUR, RDS The significant intercorrelations between the independent variables were used as cues to manually select these variables for model development. 9.3 Model Development Intervention and intervention-risky rates are continuous variables that are constrained to be between 0% and 100%, making them suitable for use in multivariable linear regression modeling. Regression diagnostics were applied to the dependent and explanatory variables to verify that the data met the assumptions of linear regression. The form of the multivariable linear regression model for yielding rate is: Y=a + b1X1 + b2X2 + b3X3 (…) Where: Y is the value of the dependent variable, what is being predicted or explained; a is the constant or intercept; b1 is the slope for X1, the first independent variable that is explaining the variance in Y; b2 is the slope for X2, the second independent variable that is explaining the variance in Y; b3 is the slope for X3, the third independent variable that is explaining the variance in Y; and b4 and onwards are the slopes for additional independent variables that explain the variance in Y. Based on this equation, if the values of all variables except one independent variable (Xi) are kept constant, one unit increase in the value of Xi will increase the value of the response variable Y by the slope of Xi. The R2 statistic is generally used in regression models to describe how much variability of the data is explained by the model. For multivariable linear regression models, the variability of the model can be evaluated by the adjusted R2 statistic, which is an adjustment of the R2 based on the number of observations and predictors in the model. Higher adjusted R2 is an indicator of a better fit of the model to the data and the proportion of the data that can be explained by the model. 129

NCHRP 3-78b: Final Project Report April 2016 The models were developed using a manual selection process informed by the results of the correlation analysis. Significantly associated independent variables were not included in the same model. 9.3.1 Model Selection Process Since the independent variables show a significant intercorrelation, the team decided to start with single variable models and include other variables on the basis of non-existent co-linearity and improving the adjusted-R2. The single variable models are based on NOISE, XSPD_AVE and YR. The following are the single variable models for dependent variables INT and INTR. 130

NCHRP 3-78b: Final Project Report April 2016 Table 9-4 Single Variable Models for Intervention and Intervention-Risky Models Single Variable Intervention Models Single Variable Intervention-Risky Models Model 1a Coefficient Std. Err. t P>|t| [95% Conf. Interval.] NOISE 0.0773 0.0113 6.83 0 0.0546 0.1000 Constant 0.0241 0.0063 3.84 0 0.0115 0.0367 Prob>F 0 R2 0.4829 Adj. R2 0.4725 Model 1b Coefficient Std. Err. t P>|t| [95% Conf. Interval.] NOISE 0.1561 0.0313 4.99 0 0.0932 0.2189 Constant 0.1216 0.0174 7.01 0 0.0868 0.1565 Prob>F 0 R2 0.3323 Adj. R2 0.319 Model 2a Coefficient Std. Err. t P>|t| [95% Conf. Interval.] YR -0.0469 0.0248 -1.89 0.064 -0.0967 0.0028 Constant 0.0756 0.0162 4.66 0 0.0430 0.1082 Prob>F 0.064 R2 0.0669 Adj. R2 0.0483 Model 2b Coefficient Std. Err. t P>|t| [95% Conf. Interval.] YR -0.1474 0.0589 -2.5 0.016 -0.2656 -0.0292 Constant 0.2568 0.0386 6.66 0 0.1793 0.3342 Prob>F 0.0155 R2 0.1115 Adj. R2 0.0938 Model 3a Coefficient Std. Err. t P>|t| [95% Conf. Interval.] XSPD_AVE 0.0042 0.0014 3.06 0.004 0.0014 0.0069 Constant -0.0333 0.0273 -1.22 0.229 -0.0882 0.0216 Prob>F 0.0035 R2 0.158 Adj. R2 0.1412 Model 3b Coefficient Std. Err. t P>|t| [95% Conf. Interval.] XSPD_AVE 0.0093 0.0034 2.75 0.008 0.0025 0.0161 Constant -0.0106 0.0675 -0.2 0.875 -0.1463 0.1250 Prob>F 0.0082 R2 0.1316 Adj. R2 0.1143 131

NCHRP 3-78b: Final Project Report April 2016 Table 9-4 shows the single variable models for intervention and intervention-risky predictions. Based on Table 9-4, the model with NOISE variable as the predictor has the highest R2 and adjusted R2 (0.48, 0.47 respectively for intervention and 0.33, 0.31 respectively for intervention-risky) among the rest of the models. The model with YR (yield rate) has the lowest R2 and adjusted R2 (0.06, 0.05 respectively for intervention model and 0.11, 0.09 respectively for the intervention-risk model). It seems that variable NOISE is a better predictor of the dependent variables for both intervention and intervention-risky models. Therefore more models with additional variables (two-variable, three-variable and four-variable models) are developed. Several other models with YR and XSPD_AVE variables are also developed and presented in Table 9-5. Table 9-5 shows the models that include NOISE have higher adjusted R2 compared to the rest of the models. The model with the highest adjusted R2 is Model 12 with variables NOISE, XPSD_AVE, SIGHT_D and RBTX (adjusted R2 = 0.54). However, XSPD_AVE and RBTX are not statistically significant at p<0.10. The next best models are models 10 and 13 with adjusted R2 = 0.53. Model 10 includes NOISE (p<0.005), XSPD_AVE (p<0.10) and SIGHT_D (p<0.005) and all variables are statically significant. Model 13 includes NOISE, XSPD_AVE, SIGHT_D, N2 and RBTX and neither N2, nor RBTX are statistically significant at p<0.10. Therefore the final suggested model for predicting intervention rates is Model 10 as shown in Table 9-6. It is important to note that the limitation of the model is that it should be used for speeds greater than 10 mph. Table 9-7 shows all the intervention-risky models developed by combining various variables in the models. Similar to the intervention models, the intervention-risky models that include NOISE as one of the independent variables have higher adjusted R2 than the rest of the models. Models 10b and 13b both have adjusted R2 of 0.38 and 0.53, respectively. However, Model 10b is consistent with the final proposed model for intervention rate and include variables NOISE (p<0.005) , XSPD_AVE(p=0.11) and SIGHT_D (p<0.10). Model 13b includes NOISE, XSPD_AVE, SIGHT_D, N2 and RBTX, however, XSPD_AVE, N2 and RBTX are not statistically significant in this model. Therefore, the final proposed model for intervention-risky prediction is model 10b as shown in Table 9-8. It is important to note that the limitation of the model is that it should be used for speeds greater than 10 mph. 132

NCHRP 3-78b: Final Project Report April 2016 Table 9-5 Intervention Models INT= NOISE YR XSPD_AVE SIGHT_D OLDEC N2 RBTX Constant Prob>F R2 Adj. R2 Model 1a 0.0773** 0.0241 0 0.483 0.473 Model 2a -0.0469+ 0.0756 0.064 0.067 0.048 Model 3a 0.0042** -0.0333 0.0035 0.158 0.141 Model 4a 0.0746** 0.0047 0.0229 0 0.484 0.463 Model 5a 0.069** 0.0243* 0.0187 0 0.527 0.507 Model 6a 0.0703** 0.0021+ -0.0149 0 0.52 0.5 Model 7a 0.0749** -0.0151 0.0337 0 0.489 0.469 Model 8a 0.0678** 0.0234* 0.0234* 0.0252 0 0.529 0.5 Model 9a 0.0651** 0.002+ 0.0243** -0.0049 -0.0175 0 0.56 0.523 Model 10a 0.0629** 0.002+ 0.023** -0.0177 0 0.559 0.531 Model 11a 0.062** 0.0018+ 0.0235* 0.0081 -0.0196 0 0.564 0.527 Model 12a 0.0575** 0.0016 0.022+ 0.0162 -0.0142 0 0.577 0.541 Model 13a 0.0574** 0.0016 0.0223+ 0.0042 0.0149 -0.0155 0 0.578 0.532 Model 14a 0.0024+ 0.0362* 0.0048+ 0.0314 -0.0262 0.0001 0.381 0.328 Model 15a 0.0036* 0.0412** -0.0347 0.0002 0.296 0.268 Model 16a 0.0033* 0.0331* -0.0309 0.0008 0.253 0.222 Model 17a -0.0317 0.0429** 0.0526 0.0028 0.214 0.181 + p<0.10, *p<0.05, **p<0.005 Table 9-6 Final Intervention Model INT= Coefficient Std. Err. t P>|t| [95% Conf. Interval.] NOISE 0.0629 0.0118 5.34 0 0.0393 0.0866 XSPD_AVE* 0.0020 0.0011 1.87 0.067 -0.0001 0.0041 SIGHT_D 0.0230 0.0112 2.06 0.044 0.0006 0.0455 Constant -0.0177 0.0204 -0.86 0.392 -0.0588 0.0234 Prob>F 0.00 R-squared 0.558 *Model Limitation: XSPD_AVE >=10 mph Adj. R-Squared 0.531 133

NCHRP 3-78b: Final Project Report April 2016 Table 9-7 Intervention-Risky Models INT= NOISE YR XSPD_AVE SIGHT_D OLDEC N2 RBTX Constant Prob>F R2 Adj. R2 Model 1b 0.0773** 0.0241 0.0000 0.4829 0.4725 Model 2b -0.0469 0.0756 0.0640 0.0669 0.0483 Model 3b 0.0042* -0.0333 0.0035 0.1580 0.1412 Model 4b 0.0746** 0.0047 0.0229 0.0000 0.4844 0.4633 Model 5b 0.0690** 0.0243* 0.0187 0.0000 0.5265 0.5071 Model 6b 0.0703** 0.0021+ -0.0149 0.0000 0.5196 0.5000 Model 7b 0.0749** -0.0151 0.0337 0.0000 0.4893 0.4685 Model 8b 0.0678** 0.0234 0.0234+ 0.0252 0.0000 0.5291 0.4997 Model 9b 0.0651** 0.0020 0.0243 -0.0049+ -0.0175 0.0000 0.5602 0.5228 Model 10b 0.0629** 0.0020+ 0.0230+ -0.0177 0.0000 0.5588 0.5312 Model 11b 0.0620** 0.0018* 0.0235 0.0081 -0.0196 0.0000 0.5642 0.5271 Model 12b 0.0575** 0.0016+ 0.0220 0.0162 -0.0143 0.0000 0.5769 0.5409 Model 13b 0.0574** 0.0016* 0.0223 0.0042 0.0149 -0.0155 0.0000 0.5782 0.5323 Model 14b 0.0024+ 0.0362* 0.0048 0.0314 -0.0262 0.0001 0.3809 0.3283 Model 15b 0.0036* 0.0412+ -0.0347 0.0002 0.2963 0.2676 Model 16b 0.0033* 0.0331* -0.0309 0.0008 0.2528 0.2223 Model 17b -0.0317* 0.0429** 0.0526 0.0028 0.2135 0.1814 + p<0.1, *p<0.05, **p<0.005 Table 9-8 Final Proposed Intervention-Risky Model INTR= Coefficient Std. Err. t P>|t| [95% Conf. Interval.] NOISE 0.1191 0.0329 3.62 0.001 0.0529 0.1853 XSPD_AVE* 0.0049 0.0030 1.64 0.108 -0.0011 0.0109 SIGHT_D 0.0617 0.0312 1.98 0.054 -0.0010 0.1245 Constant 0.0183 0.0572 0.32 0.751 -0.0967 0.1332 Prob>F 0 R-squared 0.4174 *Model Limitation: XSPD_AVE >=10 mph Adj. R-Squared 0.381 134

NCHRP 3-78b: Final Project Report April 2016 9.4 Summary Multivariable linear regression models were generated to predict the rate that blind pedestrians may make bad crossing decisions that result in intervention events and intervention and risky events. Two separate models were generated to predict the intervention rates (associated with dangerous crossing decisions) and total of intervention and risky crossing decisions. Both of these models include noise level at the crosswalk (0 or low levels of noise and 1 for high levels of noise), average speed of the vehicle at the crosswalk (continuous variable for values greater than 10 mph) and sight distance (0 if pedestrian sight distance is provided and 1 if it is not provided). Figure 9-1 plots the predicted intervention rates vs. the field observed intervention rates. Figure 9-2 shows the predicted intervention-Risky rates vs. the field observed intervention-risky rates. Figure 9-1 Plot of Predicted Intervention Rates vs. Observed Intervention Rates Predicted Vs. Observed Intervention Rates Intervention Rate 45 Degree Line 0.25 0.2 Adj. R2 = 0.53 0.15 0.1 0.05 0 0.00 0.05 0.10 0.15 0.20 0.25 Field Observed Intervention Rates M od el P re di ct ed In te rv en tio n Ra te s 135

NCHRP 3-78b: Final Project Report April 2016 Predicted Vs. Observed Intervention-Risky Rates Intervention-Risky Rate 45 Degree Line 0.7 0.6 Adj. R2= 0.38 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 Field Observed Intervention Rates M od el P re di ct ed In te rv en tio n Ra te s Figure 9-2 Plot of Predicted Intervention-Risky Rates vs. Observed Intervention-Risky Rates 136