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Safety Evaluation of Permanent Raised Pavement Markers (2004)

Chapter: Chapter 4 - Safety Impact Analysis of PRPM Installations

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Suggested Citation:"Chapter 4 - Safety Impact Analysis of PRPM Installations." National Academies of Sciences, Engineering, and Medicine. 2004. Safety Evaluation of Permanent Raised Pavement Markers. Washington, DC: The National Academies Press. doi: 10.17226/13724.
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Suggested Citation:"Chapter 4 - Safety Impact Analysis of PRPM Installations." National Academies of Sciences, Engineering, and Medicine. 2004. Safety Evaluation of Permanent Raised Pavement Markers. Washington, DC: The National Academies Press. doi: 10.17226/13724.
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Suggested Citation:"Chapter 4 - Safety Impact Analysis of PRPM Installations." National Academies of Sciences, Engineering, and Medicine. 2004. Safety Evaluation of Permanent Raised Pavement Markers. Washington, DC: The National Academies Press. doi: 10.17226/13724.
×
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Suggested Citation:"Chapter 4 - Safety Impact Analysis of PRPM Installations." National Academies of Sciences, Engineering, and Medicine. 2004. Safety Evaluation of Permanent Raised Pavement Markers. Washington, DC: The National Academies Press. doi: 10.17226/13724.
×
Page 36
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Suggested Citation:"Chapter 4 - Safety Impact Analysis of PRPM Installations." National Academies of Sciences, Engineering, and Medicine. 2004. Safety Evaluation of Permanent Raised Pavement Markers. Washington, DC: The National Academies Press. doi: 10.17226/13724.
×
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Suggested Citation:"Chapter 4 - Safety Impact Analysis of PRPM Installations." National Academies of Sciences, Engineering, and Medicine. 2004. Safety Evaluation of Permanent Raised Pavement Markers. Washington, DC: The National Academies Press. doi: 10.17226/13724.
×
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Suggested Citation:"Chapter 4 - Safety Impact Analysis of PRPM Installations." National Academies of Sciences, Engineering, and Medicine. 2004. Safety Evaluation of Permanent Raised Pavement Markers. Washington, DC: The National Academies Press. doi: 10.17226/13724.
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33 CHAPTER 4 SAFETY IMPACT ANALYSIS OF PRPM INSTALLATIONS Two sets of analyses were undertaken to investigate the safety impact of snowplowable PRPMs on non-intersection- related crashes. First, composite analyses based on the empir- ical Bayes before-and-after procedure were used to assess the overall impact of PRPMs on different crash types. The same procedure was also applied to a sample of adjacent nontreat- ment sites to assess whether there were any spillover (i.e., crash migration) effects associated with PRPM implementa- tion for two-lane roadways in Pennsylvania. Second, a dis- aggregate analysis, applying univariate analysis and multi- variate regression techniques, was performed on the results of the nighttime composite analysis for individual sites. The disaggregate analysis aimed to determine the circumstances under which PRPMs were beneficial to safety. The results of these analyses were used to support the development of PRPM implementation guidelines. This chapter first describes the two methodologies (com- posite and disaggregate) used to evaluate the safety perfor- mance of PRPMs. It then presents the results of these analy- ses for two-lane roadways, four-lane freeways, and four-lane divided expressways, respectively. A more in-depth discus- sion of the results is presented in Chapter 5. Appendix A con- tains tables with the individual safety performance functions and annual factors developed during the analysis. 4.1 COMPOSITE ANALYSIS METHODOLOGY An empirical Bayes before-and-after procedure (39) is presented in this section. The procedure was used to account for RTM while normalizing, where possible, for differences between the before periods and after periods. Overcoming these differences, as described in Section 2.2, is key to achieving a statistically defensible analysis. The empirical Bayes procedure accommodates temporal differences between before and after periods, such as traffic volumes, weather, traffic reporting practices, driving demographics, and vehicle technology. The steps followed by the empirical Bayes approach are as follows: • Step 1: Calibrate SPFs for total nonintersection crashes using data from the reference groups without PRPMs, as described in Chapter 3. The calibration of SPFs applies negative binomial generalized linear modeling. SPFs for disaggregate crash types were obtained by applying a multiplier to the SPF for total crashes. This multiplier is the ratio for the reference group and consists of the number of crashes of a specific type divided by the total number of crashes. To account for the effect of trends in safety not related to traffic volumes, annual factors were estimated using a procedure documented by Harwood et al. (40). The resulting SPFs, multipliers (α f), and annual factors are presented in Appendix A. • Step 2: Determine SPF predictions for each year in the before and after period at each PRPM location [i.e., E(K1) … E(Kn − 1), E(Kn + 1) … E(KY)], where n is the PRPM implementation year. • Step 3: Determine Cy , the ratio of the SPF estimate for Year y relative to Year 1 (4-1) • Step 4: Determine Cb and Ca , the sum of the ratios dur- ing the before period and the after period, respectively: (4-2) (4-3) • Step 5: Calculate Kˆ 1, the expected nonintersection crash frequency for the base year, Year 1: (4-4) Where Xb = Number of recorded nonintersection crashes dur- ing the before period and k = Constant for a given model. k is estimated from the SPF calibration process with the use of a maximum likelihood procedure. In the calibra- tion process, a negative binomial distributed ˆK X kk E K C b b 1 1 = + ( ) + C Ca y n Y = + ∑ 1 C Cb y n = −∑ 1 1 C E K E Ky y = ( ) ( )1

error structure is assumed, with k being the dis- persion parameter of this distribution. • Step 6: Calculate the total expected number of noninter- section crashes (B) and its variance [VAR(B)] during the after period that would have occurred if PRPMs were not implemented: B = Kˆ 1 × Ca (4-5) (4-6) • Step 7: Determine for each site its index of effectiveness (θsite) and it variance VAR(θsite): (4-7) (4-8) Where A = Total crash count during the after period. • Step 8: Determine the composite index of effectiveness (θ) and it variance VAR(θ) for all sites combined: (4-9) (4-10) Where ∑A = Sum of all crashes over the after period for all PRPM locations, ∑B = Sum of the expected number of crashes (B) for all PRPM locations, and ∑VAR(B) = Sum of the variances of the expected number of crashes, VAR(B). The standard error (s.e.) of θ is given by (4-11) The percent change in the number of crashes is equal to 100(1 − θ); thus, θ = 0.7 denotes a 30-percent reduction in crashes. The standard error (s.e.) indicates the accuracy of the index of effectiveness. An approximate 95-percent con- fidence interval can be determined by adding and subtracting twice the value of the standard error (2 × s.e.) from the value s.e. VAR( ) ( )θ θ= VAR VAR VAR θ θ( ) ( ) ( )( ) ( )( ) ( )( ) ( )( )= + + ∑ ∑ ∑ ∑ ∑ 2 2 2 2 1 1 A B B B B θ = ( ) + ( )( )( ) ∑ ∑ ∑ ∑ A B B B1 2VAR VAR VAR VAR site siteθ θ( ) = + ( )( ) + ( )( ) 2 2 2 2 1 1 A B B B B θsite 2VAR= ( ) + ( )( ) A B B B1 VAR B B CC k E K a b ( ) = + + ( )1 34 of θ. Thus, if θ equals 0.7 and the standard error is 0.12, then the confidence interval ranges from 0.46 to 0.94. This confi- dence interval indicates a significant positive effect. To summarize, if the confidence interval contains the value 1, then no significant effect has been observed. If θ is less than the value 1 and the upper value of the confidence inter- val is less than the value 1, then the treatment has had a sig- nificant positive effect on safety (i.e., a reduction in crashes). Conversely, if θ is greater than 1 and the lower value of the confidence interval is greater than 1, then the treatment had a significant negative effect on safety (i.e., an increase in crashes). 4.2 DISAGGREGATE ANALYSIS METHODOLOGY Disaggregate analysis performed on nighttime crashes included both univariate exploratory analysis and formal multivariate modeling. The univariate exploratory analysis was used to identify and isolate factors that might be asso- ciated with the variation in the safety impact of PRPM installations. The results of the exploratory analysis were used to guide the multivariate modeling in an attempt to relate the safety impact of PRPMs to variables found in the initial univariate analysis. These two analyses are described below. 4.2.1 Univariate Exploratory Analysis Using two-dimensional plots and spreadsheets sorted on variables of interest, the relationship between various factors and the calculated index of effectiveness (θ) for each site was explored by visual inspection for differences in effects that might relate to different levels of a variable in the statistical analysis. For the purpose of this study, a site is a homoge- neous segment of road represented by a set of attributes (shoul- der width, type, lane width, AADT, terrain, guide rails, hor- izontal alignment, etc.). 4.2.2 Multivariate Modeling of the Index of Effectiveness (θ) The results of the nighttime crash composite analysis for all states were combined to develop a model to estimate the index of effectiveness (i.e., the safety effect of PRPMs) using traffic volumes, site characteristics (e.g., surface width, shoulder widths, illumination, and other delin- eators), and PRPM characteristics (e.g., spacing) as explanatory variables. The model form is a linear model with a gamma error distribution for θ (39). The model was of the general form: θsite = α + b1x1 + b2 x2 + b3 x3 + … bn xn (4-12)

Where α = Calibrated intercept and b1, b2, … bn = Estimated effects on θ of factors or variables x1, x2, … xn. With this model form, categorical variables were desirable to ascertain conditions that favor PRPM installation. Thus, for variables such as degree of curvature and AADT, ranges had to be assigned an ordinal value. This assignment of ordi- nal values was an iterative process considering the number of crashes in a range, the variation in crashes per mile-year within and among ranges, and the observations from the uni- variate exploratory analysis. Stepwise linear regression was performed using the SAS™ statistical analysis software package (41), estimates of θ, and values of factors for individual sites. Statistically nonsignificant variables at the 90-percent degree of confi- dence were eliminated. The absence of a variable in the final model does not imply that the variable does not affect the safety impact of PRPM because a statistically nonsignificant effect could result from correlation with other variables, a lack of variation in the data, or a sample that is too small. In addition, the generally small size of the composite safety effects of PRPMs strongly indicates that one is unlikely to detect many factors that affect the safety effect of PRPMs. 4.3 RESULTS OF ANALYSES FOR TWO-LANE ROADWAYS 4.3.1 Composite Analysis Table 4-1 shows the results of the composite safety evalu- ation of snowplowable PRPMs on nonintersection segments of two-lane roadways. Statistically significant results (at the 95-percent confidence level) are shown in bold. Key findings are as follows: • Illinois shows significant increases in total crashes (9.1 percent), daytime crashes (17.9 percent), wet weather crashes (15.5 percent), and dry weather crashes (8.7 per- cent) after the nonselective implementation of PRPMs. • New Jersey shows a significant decrease in head-on crashes (19.6 percent) after the nonselective implemen- tation of PRPMs. • New York shows a significant decrease in total crashes (9.5 percent), nighttime crashes (13 percent), wet weather crashes (20 percent), and wet weather nighttime crashes (23.9 percent) after the selective implementation of PRPMs (at sites selected on the basis of wet-night crash history). • Pennsylvania shows significant increases in head-on crashes (37.2 percent) and guidance-related crashes (19.7 percent) after the selective implementation of PRPMs (at sites selected on the basis of overall night- time crash experience). 35 4.3.2 Univariate Disaggregate Analysis In the univariate disaggregate analysis, key findings are as follows: • The safety benefits of PRPMs on nighttime crashes increases as traffic volumes increase, decreases as degree of curvature increases, and decreases as roadway width and shoulder width decrease. • There is a correlation between traffic volumes and road- way design parameters (e.g., roadway width and shoul- der width) that could mask safety effects and that neces- sitates the more formal multivariate modeling described in the next section. 4.3.3 Multivariate Modeling of the Index of Effectiveness (θsite) Table 4-2 shows the results of the multivariate modeling of θsite. The model includes variables relating to AADT and degree of curvature only. These variables are significant at a 95-percent confidence level. Other variables relating to PRPM design (e.g., spacing), other delineation measures (e.g., chevrons), and roadway geometry (e.g., lane widths and shoulder widths) were also considered, but were found not to improve the model significantly. The sample size for the modeling for two-lane roadways consisted of 925 miles. It was necessary to group data for modeling because seg- ments tended to be short. This tendency to be short resulted in considerable variations in individual values of θ, models with nonsignificant parameter estimates, and a poor overall fit when ungrouped data were used. The data used for modeling were combined when sites shared a set of characteristics (e.g., all urban, no curvature, AADT < 20,000). The data were fur- ther grouped by segment lengths, the count of nighttime col- lisions in the after period, and the expected after period colli- sions without PRPM over all sites. Using these groupings, a θ value was obtained. The model was estimated with the char- acteristics of each group as individual data points, with weights applied for the total length of the segments in a group. To facilitate the grouping, ranges for variables such as degree of curvature and AADT had to be assigned an ordinal value. This was accomplished with the use of an iterative process to determine the best ranges by considering the num- ber of crashes within a range, the variation in crashes per mile-year within and among ranges, and the observations from the univariate analysis. The degree of curvature variable is the degree of curve in degrees per 100 ft and is calculated as (18,000/3.14 × radius), where radius is the radius of the curve in feet. Roadways with a degree of curvature less than 3.5 include gentle curves as well as roadway tangent sections (i.e., where the degree of curvature equals 0). Table 4-3 shows the accident modifica- tion factors (AMFs) derived from the respective models in Table 4-2. An AMF, like the index of effectiveness, is an index of how much crash experience is expected to change

following the implementation of a measure such as PRPMs. The AMF is the ratio between the number of crashes per unit of time expected after a measure is implemented and the number of crashes per unit of time estimated if the imple- mentation does not take place. An AMF less than 1 would indicate a positive safety effect (i.e., a reduction in crashes), while an AMF greater than 1 would indicate a negative safety 36 effect (i.e., an increase in crashes). For example, according to Table 4-2, at AADTs ranging between 15,000 and 20,000 on a roadway with a degree of curvature less than 3.5, the AMF is 0.757 (1.1573 − 0.4004), which translates into a 24.3-percent [100(1 − 0.757)] reduction. The results of the multivariate modeling of the index of effectiveness confirm the observations from the univariate Illinois New Jersey New York Pennsylvania (Nonselective) (Nonselective) (Selective) (Selective) # Sites = 5347 # Miles = 460.53 # Sites = 779 # Miles = 173.98 # Sites = 226 # Miles = 81.75 # Sites = 5383 # Miles = 266.94 Obs1 θ % Obs θ % Obs θ % Obs θ % Crash Type Exp2 s.e. Ch3 Exp s.e. Ch Exp s.e. Ch Exp s.e. Ch 1133 1.091 3508 1.032 1121 0.905 1244 0.980Total 1038 0.035 9.1 3399 0.027 3.2 1238 0.034 -9.5 1270 0.030 -2.0 292 1.071 1219 0.955 424 1.020 231 1.017Fatal and injury 272 0.065 7.1 1275 0.038 -4.5 415 0.057 2.0 227 0.068 1.7 592 1.179 2338 1.047 672 1.003 739 0.963Daytime 502 0.051 17.9 2232 0.034 4.7 669 0.048 0.3 767 0.038 -3.7 167 1.080 861 0.976 293 1.074 133 0.978Daytime fatal and injury 155 0.086 8.0 882 0.044 -2.4 272 0.072 7.4 136 0.086 -2.2 541 1.001 1148 0.991 449 0.873 505 1.039Nighttime 540 0.045 0.1 1158 0.040 -0.9 514 0.052 -12.7 486 0.048 3.9 156 1.106 350 0.899 131 1.000 98 1.074Nighttime fatal and injury 141 0.091 10.6 389 0.058 -10.1 131 0.097 0.0 91 0.110 7.4 773 1.087 2601 1.05 764 1.047 798 0.978Dry 711 0.041 8.7 2476 0.032 5.0 729 0.048 4.7 816 0.037 -2.2 Wet 284 1.155 15.5 876 0.972 -2.8 333 0.798 -20.2 440 1.047 4.7 246 0.072 900 0.045 417 0.05 420 0.053 28 0.859 180 0.804 120 1.372Head-on -33 0.163 -14.1 224 0.068 -19.6 Sample size too small 87 0.127 37.2 Sample size too small Sample size too small Sample size too small Sample size too small Sample size too small Sample size too small Sample size too small Sample size too small 140 0.761Wet-night 183 0.075 -23.9 397 1.018 279 1.197Guidance 390 0.053 1.8 Sample size too small 233 0.074 19.7 1 Obs = Observed crash frequency. 2 Exp = Expected crash frequency. 3 Ch = change. *A site is a homogeneous segment of road represented by a set of attributes (shoulder width, type, lane width, AADT, terrain, guide rails, horizontal alignment, etc.). Statistically significant results (at 95% confidence level) are shown in bold. TABLE 4-1 Results of safety evaluation of two-lane roadways (nonintersection crashes) with snowplowable PRPMs (selective and nonselective implementation)*

analysis that, generally, PRPMs are more effective on higher- volume roadways (possibly a reflection of the higher design standards of these highways) and on roadways with more gen- tle curvature. For example, at AADTs ranging between 15,000 and 20,000 on a roadway with a degree of curvature less than 3.5, a decrease in nighttime crashes of 24.3 percent follow- ing PRPM installation can be estimated from the model as noted above. At lower AADTs and sharper curvature, PRPMs can in fact be associated with an increase in crashes. For exam- ple, for PRPMs installed on roadways with AADTs between 5,000 and 15,000, an increase in nighttime crashes of 26 per- cent can be estimated from the model. That PRPMs are more effective on roadways with more gentle curvature (i.e., where the degree of curvature is less than 3.5) is contrary to a belief held by many. One possible explanation is that PRPMs may promote an increase in operating speeds and that the speed increase is a greater safety concern on a sharper curve. 4.3.4 Spillover Analysis The same before-and-after evaluation methodology used for PRPM locations was applied to a sample of road seg- ments found immediately surrounding the treated road seg- ments to examine possible migration and spillover effects. As discussed in Chapter 2, if a significant spillover effect were found, it would have been necessary to consider this effect in assessing the net effect of PRPM installations. Pennsylvania two-lane roadways were selected for the spillover study because their PRPMs were installed selec- tively, and the state DOT had the required data to support a spillover analysis study. New York, despite its selective pol- icy for PRPM installation, did not have sufficient data for a spillover analysis. In New Jersey, spillover analysis could 37 not be undertaken for two-lane facilities and for four-lane freeways and expressways because of the nonselective imple- mentation policies. The nonselective policies resulted in too small samples of potential spillover sites. Using data for Pennsylvania two-lane roadways, several nonoverlapping locations within 2 miles of a given PRPM installation were identified. The results of the spillover analy- sis are shown in Table 4-4. According to the results of the statistical analysis for the sample of two-lane roadways in the state of Pennsylvania, there were no significant spillover effects to adjacent roadways to those roadways where snowplowable PRPM were installed. 4.4 RESULTS OF ANALYSIS FOR FOUR-LANE FREEWAYS 4.4.1 Composite Analysis Table 4-5 shows the results of the composite safety evalua- tion of PRPMs on four-lane freeways. Statistically significant results (at 95-percent confidence level) are shown in bold. As mentioned in Chapter 3, the widespread implementa- tion of PRPMs on four-lane freeways and expressways dur- ing 1999 meant that Wisconsin DOT could only provide Model Parameters Applicable Condition Estimate Standard Error p-value Constant AADT ≤ 5000 Degree of curvature ≤ 3.5 1.1573 0.0260 < 0.001 AADT 2 5000 < AADT ≤ 15000 -0.1700 0.0395 0.003 AADT 3 15000 < AADT ≤ 20000 -0.4004 0.0607 < 0.001 Degree of curvature Degree of curvature > 3.5 0.2736 0.0824 0.011 TABLE 4-2 Index of effectiveness model for two-lane roadways (nighttime crashes) AADT (veh/day) AMF when DOC ≤ 3.5 AMF when DOC > 3.5 0–5000 1.16 1.43 5001–15000 0.99 1.26 15001–20000 0.76 1.03 DOC = Degree of curvature. Pennsylvania Two-Lane Spillover Sites # Sites1 = 5227 # Miles = 306.55 Obs2 θ Crash Type Exp3 s.e. % Ch4 1447 1.048 Total 1381 0.030 4.8 2 Obs = Observed crash frequency. 3 Exp = Expected crash frequency. 4 Ch = change. 1 A site is a homogeneous segment of road represented by a set of attributes (shoulder width, type, lane width, AADT, terrain, guide rails, horizontal alignment, etc.). TABLE 4-3 AMFs (nighttime crashes) derived from Table 4-2 TABLE 4-4 Results of spillover analysis: two-lane roadways in Pennsylvania (total crashes)

comparison group data (i.e., roadways without PRPMs) for a total of 43 miles of four-lane freeway. Additional crash data (total and fatal and injury) were collected for urban Interstate highways without PRPMs in Milwaukee County as an alter- native comparison group. Both comparison groups were used for composite analyses, and the results were compared. The methodology that was applied to estimate the annual factors for the two comparison groups is as follows: • Comparison Group 1: 43 miles of four-lane free- ways. The crash data for the 43 miles of freeway were used to derive a ratio between the crash counts for 2000 and the average annual crash counts for 1994 to 1998 (before period). This ratio was used as a multiplier to determine an annual calibration factor for the year 38 2000 (after period) crashes. This data preparation was undertaken for all crash types (see Appendix A, Table A-10). • Comparison Group 2: Milwaukee County. The urban Interstate highways without PRPMs in Milwaukee County were all illuminated and had a lower posted speed limit (45 mph or 72 km/h) when compared with four- lane freeways (55 mph or 86 km/h) on which PRPMs were installed. The crash data showed an increase in 2000 (after period) of 27 percent for total crashes and 16 percent for fatal and injury crashes when compared with the same crash types for 1994 to 1998 (before period). Thus, for the composite analysis, these per- centages were applied for crash types accordingly (see Appendix A, Table A-10). TABLE 4-5 Results of safety evaluation of four-lane freeways (nonselective implementation) with snowplowable PRPMs Missouri Freeway New York Freeway Pennsylvania Freeway # Sites1 = 1327 # Miles = 1441.80 # Sites = 64 # Miles = 36.49 # Sites = 1629 # Miles = 778.93 Obs2 θ % Obs θ % Obs θ % Crash Type Exp3 s.e.4 Ch5 Exp s.e. Ch Exp s.e. Ch 9195 0.979 335 1.031 3640 0.943Total 9394 0.012 -2.1 324 0.074 3.1 3860 0.019 -5.7 2720 0.946 91 1.179 501 1.000Fatal and Injury 2876 0.021 -5.4 77 0.141 17.9 501 0.047 0.0 5955 0.979 177 1.046 2155 0.935Daytime 6080 0.015 -2.1 169 0.100 4.6 2305 0.024 -6.5 1801 0.938 55 1.195 293 1.023Daytime Fatal and Injury 1919 0.026 -6.2 46 0.183 19.5 286 0.062 2.3 3240 0.991 158 0.900 1485 0.960Nighttime 3269 0.020 -0.9 175 0.090 -10.0 1547 0.028 -4.0 919 0.975 36 0.951 208 0.988Nighttime Fatal and Injury 942 0.035 -2.5 38 0.171 -4.9 211 0.070 -1.2 6343 1.046 167 0.997 2228 0.956Dry 6066 0.016 4.6 167 0.100 -0.3 2329 0.024 -4.4 Wet 2852 0.872 -12.8 161 0.974 -2.6 1404 0.946 -5.4 3270 0.019 165 0.096 1484 0.027 3870 0.897 834 0.986Guidance-related 4315 0.017 -10.3 Sample too small 845 0.038 -1.4 2 Obs = Observed crash frequency. 3 Exp = Expected crash frequency. 5 Ch = change. 1 A site is a homogeneous segment of road represented by a set of attributes (shoulder width, type, lane width, AADT, terrain, guide rails, horizontal alignment, etc.). 4 Statistically significant results (at 95% confidence level) are shown in bold.

The composite analyses for the two comparison groups for Wisconsin showed conflicting results with respect to safety impact of PRPMs for all crash types. Therefore, the research team concluded that these data did not provide the required integrity to continue into further disaggregate analyses. Key findings from the analysis included the following: • Missouri shows significant reductions in fatal and injury crashes (5.4 percent), daytime fatal and injury crashes (6.2 percent), wet weather crashes (12.8 percent), and guidance-related crashes (10.3 percent) after the non- selective implementation of PRPMs. • Pennsylvania shows significant reductions in total crashes (5.7 percent), daytime crashes (6.5 percent), and wet weather crashes (5.4 percent) after the nonselective implementation of PRPMs. 4.4.2 Univariate Disaggregate Analysis As described previously, the univariate disaggregate analy- sis assists in the selection of variables to be considered in the subsequent multivariate analysis. Results from this analysis show that the safety benefit of PRPMs on nighttime crashes increases as traffic volumes increase and is greater on urban than on rural freeways. 4.4.3 Multivariate Modeling of the Index of Effectiveness (θsite) The results of the modeling for freeways are shown in Table 4-6. The AMFs derived from this model are shown in 39 Table 4-7. The AADT variable is the only significant vari- able. This variable was grouped for reasons explained earlier using the method outlined. The model confirms the findings of the univariate analysis that the safety benefits of PRPMs on freeways increase with increasing traffic volumes. According to this model, PRPMs may only be effective in reducing nighttime crashes where the AADT exceeds 20,000 veh/day. Since higher volumes are more likely to be found in urban areas, the underlying reason for the increasing effect with increasing AADT may relate to factors other than or in addition to AADT that may be peculiar to urban areas. Data were not available to isolate the effects of such factors. The research team studied the different design elements for potential relationships with the safety effect of PRPMs. Apparently because of little variation in the design attributes (e.g., lane widths and shoulder widths) of the freeway seg- ments, as shown in Tables 3-13 and 3-14, it was not statisti- cally feasible to include these attributes as variables in the multivariate models. The same applied to PRPM installation details, such as spacing. 4.5 RESULTS OF THE COMPOSITE ANALYSIS FOR FOUR-LANE DIVIDED EXPRESSWAYS The research team concluded that, because of the data con- straints and intrinsic difficulties encountered in Wisconsin and Pennsylvania for the data collected for the four-lane divided expressways, any further analysis would not result in any reliable findings. Thus, four-lane divided expressways could not be analyzed under this research project. Model Parameters Applicable Condition Estimate Standard Error p-value Constant AADT ≤ 20000 1.131 0.136 < 0.001 AADT 2 20,000 < AADT ≤ 60,000 -0.193 0.160 0.249 AADT 3 AADT > 60,000 -0.458 0.192 0.033 AADT (veh/day) AMF ≤ 20000 1.13 20001–60000 0.94 > 60000 0.67 TABLE 4-6 Index of effectiveness model for four-lane freeways (snowplowable PRPMs) TABLE 4-7 AMFs (nighttime crashes) derived from Table 4-6

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TRB’s National Cooperative Highway Research Program (NCHRP) Report 518: Safety Evaluation of Permanent Raised Pavement Markers examines the safety performance of snowplowable permanent raised pavement markers on two-lane roadways and four-lane freeways.

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