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

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B-1   Contents B-2 Chapter 1 Introduction B-8 Chapter 2 Procedure B-8 Step 1 Determine Potential Overlap of Individual Treatment Effects B-11 Step 2 Determine Magnitude of Individual Treatment Effects B-11 Step 3 Define the Applicability of Individual CMFs B-11 Step 4 Select and Apply an Appropriate Method to Estimate the Combined Effect B-12 Estimating the Standard Error of the Combined Safety Effect of Multiple Treatments B-12 Extension of Method to Estimate the Combined Safety Effect of Three or More Treatments B-13 Chapter 3 Example Applications of Procedure B-20 Chapter 4 Supporting Research B-20 Combination of Centerline and Shoulder Rumble Strip Installation B-28 Combination of Lane and Shoulder Widening B-32 Combination of Intersection Skew Angle and Sight Distance Improvements B-35 References A P P E N D I X B Procedure for Estimating the Combined Safety Effect of Two Treatments

B-2 Crash modification factors and functions (CMFs) provide users with an opportunity to quan- tify the safety performance of their decisions. In some cases, a transportation agency will apply multiple treatments to a location, such as signalizing a stop-controlled intersection, adding turn lanes, and reducing intersection skew. The preferred approach to estimate the combined safety effect of multiple treatments is to apply a single CMF that represents the combined treatments. In the absence of such a CMF, practitioners need to know how to apply CMFs that represent individual treatment effects to estimate the combined safety effect. These guidelines present a 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 target audience for these guidelines is those who develop and apply CMFs to quantify the safety performance of design decisions or contemplated safety treatments. These users may include highway designers, traffic engineers, transportation planners, and highway safety ana- lysts and researchers. The guidelines begin with an overview of methods to estimate the combined safety effect of multiple treatments. Continue reading for a background on the application of multiple CMFs or skip to Chapter 2 for the procedure on applying single-effect CMFs to estimate the combined safety effect of two treatments. Examples in Chapter 3 illustrate how users can apply CMFs to estimate the joint safety effect of two treatments. Chapter 2 discusses how to extend the method to estimate the combined safety effect of more than two treatments, but readers should note the lack of research to verify the accuracy of com- bining more than two individual CMFs. Methods to Estimate the Combined Safety Effect of Multiple Treatments Table B1 provides a summary of the following five methods for estimating the combined safety effect of multiple treatments. Note that not all methods combine individual CMFs. For example, the Dominant Effect for Overlapping Crash Types method applies CMFs separately to applicable crash types and severities, and then aggregates the results to estimate the combined effect. • Dominant Effect Method • Additive Effects Method • Multiplicative Method • Dominant Common Residuals Method • Dominant Effect for Overlapping Crash Types C H A P T E R   1 Introduction

Procedure for Estimating the Combined Safety Effect of Two Treatments B-3   Method Summary of Method Dominant Effect Additive Effects Multiplicative Dominant Common Residuals Dominant Effect for Overlapping Crash Types The dominant effect method applies the CMF for only the most effective treatment (i.e., lowest CMF value). This method is a simplified and conservative 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. The additive effects method assumes that CMFs are independent, and estimates the combined effect by adding the individual effects as follows: CMFt = 1 − [(1 − CMF1) + (1 − CMF2) + ⋯ + (1 − CMFn)] (1) 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 are added or if the estimated crash reductions are relatively large for just a few treatments. Another limitation is that it may not be appropriate if the treatment effects are not independent (i.e., when there are overlapping effects). Readers should note that this method adds the effects, not the CMFs themselves. The multiplicative method assumes that CMFs are independent, and estimates the combined effect by multiplying the individual CMFs as follows: CMFt = CMF1 ∗ CMF2 ∗ … ∗ CMFn (2) All terms as defined previously. This is the most common method at this time and is identified in the Highway Safety Manual (AASHTO, 2010). The primary limitation of this method is that the combined effect may be underestimated or overestimated if the treatment effects are not independent. This method, proposed by Elvik (2009), is like the multiplicative 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: CMFt = (CMF1 ∗ CMF2 ∗ … ∗ CMFn) (5) All terms as defined previously. 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 when the individual CMFs are greater than 1.0, particularly the most effective treatment. In these cases, the combined CMFs are raised to a power greater than 1.0, which intensifies the effect rather than dampening. As such, this method is not appropriate for CMFs greater than 1.0. 1 This method applies the CMF for only the most effective treatment (i.e., lowest CMF value) where there is overlap among the treatment effects. Otherwise, the CMFs are applied separately to the target crashes. In a standard CMF application, the estimated number of crashes without treatment, Nwo, is multiplied by a CMF to estimate the number of crashes with treatment, Nw. If Nwo consists of multiple crash types (e.g., A + B + C), then each crash type can be multiplied by the CMF separately: Nw = Nwo × CMF Nw = (A + B + C) × CMF Nw = A × CMF + B × CMF + C × CMF Consider the combined effect of two treatments, with one more effective than the other. CMF1 is associated with the more effective treatment and applies to crash types A and B. CMF2 is associated with the less effective treatment and applies to crash types B and C. Therefore, the applicable crashes for the two treatments are as follows. Nwo,1 = A + B Nwo,2 = B + C CMF1 is applied to Nwo,1 (A+B) to estimate the crashes with treatment one (Nw,1). CMF2 is applied to Nwo,2 (B+C) to estimate the crashes with treatment two (Nw,2). Nw,1 = Nwo,1 × CMF1 = (A + B) × CMF1 = A × CMF1 + B × CMF1 Nw,2 = Nwo,2 × CMF2 = (B + C) × CMF2 = B × CMF2 + C × CMF2 Following this logic, Nw,1 and Nw,2 could be combined to estimate Nw; however, there is an overlap in addressing crash type B. This method accounts for overlap by using only the most effective CMF for any overlapping crash types. In this case, the estimated crashes with both treatments, Nw, is computed as follows, omitting B × CMF2. Nw = A × CMF1 + B × CMF1 + C × CMF2 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. Table B1. Summary of existing methods for estimating combined effects.

B-4 Guidelines for the Development and Application of Crash Modification Factors Background on the Application of Multiple CMFs The key factors to consider when applying multiple CMFs include • Selection of appropriate CMFs • Application of CMFs by type and severity • Bounds of combined treatment effect • Overlapping effects among individual treatments • Magnitude of individual treatment effects Selecting an Appropriate CMF The CMF selection process involves several considerations including availability of CMFs, applicability of available CMFs, and quality of applicable CMFs. The key to selecting an appro- priate CMF is to identify the CMF that best matches the scenario at hand. The following is an overview of CMF availability, applicability, and quality. Readers can refer to the CMF Clearing- house for more information (www.cmfclearinghouse.org). The CMF Clearinghouse is a web- based database of CMFs that includes supporting documentation to help users identify, select, and apply appropriate CMFs. Availability of CMFs. The Highway Safety Manual (HSM; AASHTO 2010) and CMF Clearinghouse (FHWA 2016) are the two primary sources of CMFs. Applicability of CMFs. CMFs are applicable to specific crash types, severities, and roadway conditions. It is important for the user to identify the applicable crash types, severities, and road- way conditions of each CMF, and only use CMFs for the conditions to which they apply. Several variables define the applicability of a CMF including treatment type, roadway type, area type, segment or intersection geometry, segment or intersection traffic control, traffic volume, and state from which the CMF was developed. The HSM and CMF Clearinghouse provide informa- tion to help users decide which CMFs are most applicable to a given situation. Quality of CMFs. If multiple applicable CMFs exist for a given treatment, then the quality or standard error can be used to differentiate the results. The CMF Clearinghouse provides quality ratings for CMFs which may be used for this purpose. In the absence of a quality rating, users may compare CMFs by their standard error where a smaller standard error indicates a greater level of certainty for a CMF estimate. Applying CMFs by Type and Severity CMFs apply to specific crash types and severities. It is often useful to estimate the change in crashes by crash type and severity, but this should only be done when there are CMFs available for the specific crash types and severities in question. It is inappropriate to apply a CMF for a specific crash type and severity to another crash type and severity. For example, consider a CMF for installing a traffic signal at a two-way stop-controlled intersection. If the CMF applies to the net effect (all crash types and severities combined), then it is inappropriate to apply the CMF to estimate the individual effect on angle and rear-end crashes because the individual effects are not likely equivalent to the net effect of the treatment. In this example, a traffic signal may reduce angle crashes and increase rear-end crashes. Considering the Bounds of the Combined Treatment Effect In estimating the combined effect of multiple treatments, it is important to recognize the potential bounds of the treatment effects. This will serve as a reality check when applying the methods in these guidelines. The bound for the maximum effect of one or more treatments is 100% (a CMF of 0). This condition represents the complete elimination of crashes. The lower

Procedure for Estimating the Combined Safety Effect of Two Treatments B-5   bound is more difficult to establish. In theory, there is no limit on the minimum reduction in crashes, and this reduction can even be negative (i.e., an increase in crashes). In practice, one may assume a minimum reduction of zero (i.e., no benefit) if the objective is to improve safety. In this case, it is assumed that analysts would eliminate treatments from consideration if the treatment is likely to increase crashes. There are other scenarios where practitioners may be interested in quantifying the combined effect of features that may increase crashes (e.g., design exceptions or comparing negative impacts of reducing program budgets). As such, analysts should consider the specific scenario, and determine the bounds of potential combined effects. Considering the Overlap among Individual Treatments Another consideration is the overlap among individual treatments. Specifically, two or more treatments may complement, replace, or counteract each other. The analyst must apply judg- ment to determine the likelihood and extent of overlap among estimated effects of the contem- plated treatments and select an appropriate method to estimate the combined safety effect. The NCHRP Report 500 series of guides may be helpful in judging the overlap of treatment effect, since they provide guidelines on identifying the target crash types for individual safety treat- ments (AASHTO 2003–2009). The following are general guidelines to assess the potential overlap among individual treat- ments, followed by five specific categories for use with these guidelines. It is necessary to consider the conditions and location in the context of potential overlapping treatment effects. Conditions are defined by setting (road type or intersection type), crash type (severity, manner of collision), period (day/night), and traffic volume (if specified). Location describes the portion of the road to which the treatment is being applied (e.g., outside lane in one travel direction, curves on two- lane highway with a radius of 400 feet to 500 feet, one approach of a signalized intersection). The following two cases describe different levels of overlap among treatments based on the associ- ated condition and location. • Case 1—Same Condition and Same Location. If the CMFs are all defined for the same con- dition 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 rural, stop-controlled intersection are likely to have a high degree of overlap as they will affect the same crashes. • Case 2—General Conditions and Non-Specific Locations. If the CMFs are all defined for general conditions and non-specific locations (e.g., overall segments, overall intersection), then the degree to which they are related will be difficult 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 intersection approaches. The effect of an approach-specific treatment on total intersection crashes is an extrapolation of the treat- ment’s approach-specific effect that generalizes the unspecified conditions of the untreated intersection approaches. Engineering judgment is critical to determine whether each treatment is likely to affect spe- cific conditions and whether these conditions overlap. Similarly, engineering judgment is used to determine whether the associated treatments interact when they are applied at relatively dis- tant locations (e.g., an adjacent segment). The related CMFs are more likely to interact when they have more conditions in common, or the treatment influences the same drivers at the same (or a nearby) location. Case A Zero Overlap in Treatment Effect. This case represents two truly independent effects. For example, consider a scenario where motorcycle and pedestrian crashes represent

B-6 Guidelines for the Development and Application of Crash Modification Factors 40% and 20% of total crashes, respectively. If the first treatment reduces motorcycle crashes by 50% and the second treatment reduces pedestrian crashes 50%, then the combined effect is a 30% reduction in total crashes. Case B Some Overlapping Treatment Effects. This case represents scenarios between Case A and Case C (i.e., the overlapping effect is between 0% and 100%). In this case, the second treatment provides some additional benefit, but the full effect of the second treatment is not real- ized due to overlap with the first treatment. For example, consider a scenario where there are 2.0 cross-median crashes and 4.0 run-off-road crashes per year on a four-lane, median divided facility. The two treatments considered are cable median barrier and shoulder rumble strips on the inside and outside shoulders. If the cable barrier reduces cross-median crashes by 50% and the rumble strips reduce cross-median and run-off-road crashes by 50%, then the estimated reduction is between 3.0 crashes per year (i.e., no additional benefit from rumble strips) and 3.5 (i.e., full effect of rumble strips). This case includes an inherent interaction effect because the second treatment can only reduce the crashes that remain after considering the effects of the first treatment. For example, if the first treatment reduces total crashes by 30%, then only 70% of crashes remain for the second treatment. Case C Complete Overlap in Treatment Effects. This case represents two non-independent effects where the second treatment targets some or all the same crash types and severities as the first treatment. For example, widening both the lane and shoulder width may target the same run-off- road, head-on, and opposite direction sideswipe crashes. If this is the case, then the effect is equal to the CMF associated with the dominant treatment. Case D Enhancing Treatment Effects. This case represents a scenario where the combined effect of two treatments is greater than the sum of their individual effects. While you cannot reduce crashes by more than 100%, it is possible that two treatments could interact to enhance the com- bined effect. For example, installing rumble strips in conjunction with shoulder widening may be more effective than the product of the individual CMFs for rumble strips and shoulder widening because the added shoulder provides recovery room for drivers alerted by the rumble strips. Case E Counteracting Treatment Effects. This case represents a scenario where the com- bined effect of two treatments is less than the effect of the most effective treatment. In this case, the second treatment may counteract the effect of the first treatment or vice versa. This is a common scenario in the evaluation of design exceptions. For example, a highway designer may consider installing advance curve warning signs to offset the potential impacts of reducing the radius of a curve due to topographical constraints. Magnitude of Individual Treatment Effects Depending on the magnitude of the individual treatment effects, the method selected to esti- mate the combined safety effect may have a nominal or significant impact on the result. Table B2 presents sample CMFs representing small and large individual effects along with the estimate of the combined safety effect based on four of the five methods from Table B1. A CMF value of 0.95 is used to represent a small effect (i.e., a 5% reduction) and a CMF of 0.70 is used to represent a large effect (i.e., a 30% reduction). These two CMF values have been combined using the various methods to show a comparison of methods within each column of Table B2. When both individual treatment effects are small, the four methods produce similar estimates of the combined effect, ranging from 0.90 to 0.95 (a difference of 0.05). When one treatment effect is small and the other is large, there is more variability in the estimates of the combined effect from the four methods. Specifically, the results range from 0.65 to 0.75 (a difference of 0.10). When both individual treatment effects are large, there is even more variability in the estimates

Procedure for Estimating the Combined Safety Effect of Two Treatments B-7   of the combined effect from the four methods. Specifically, the results range from 0.40 to 0.70 (a difference of 0.30). It is clear from Table B2 that the magnitude of the individual treatment effects has a bearing on the importance of the method selected to estimate the combined treat- ment effect. It is critical to select an appropriate method when both individual treatment effects are large; otherwise, there is potential to severely over- or underestimate the combined treat- ment effect. General Guidelines for Estimating the Combined Safety Effect of Two Treatments This research indicates that no one method for combining safety effects of two treatments out- performs the others in all cases. However, to promote implementation, it is appropriate for practi- tioners to use the following guidelines when the CMFs for two treatments apply to the same crash types and severities (in absence of the four-step process shown in Figure B1 and discussed in the following section). When CMFs apply to different crash types and severities, practitioners should follow the recommendations in the following section. • When both CMFs are less than 1.0, the Dominant Common Residuals method generally performs best (i.e., is the most accurate) across all scenarios. • When one or both CMFs are greater than 1.0, the Dominant Effect method generally per- forms best across all scenarios. • In most cases, the Dominant Effect method provides the most conservative estimate of treatment benefits and is appropriate for use in estimating the combined safety effects for single projects. This is true for typical safety projects where both CMFs are less than 1.0. Practitioners should use caution when comparing the results of the Dominant Effect method between projects as the method is likely to inconsistently underestimate the effects of dif- ferent treatment combinations. Some methods perform much better than this abbreviated guideline in specific scenarios, and following the recommendations in the previous section will provide the most consistently accurate results for estimating the effects of treatment combinations. Method Combined Effect (small-small) Combined Effect (small-large) Combined Effect (large- large) Dominant Effect = CMF1 (largest effect) 0.95 0.70 0.70 Additive Effects = 1 – [(1 – CMF1) + (1 – CMF2)] 0.90 0.65 0.40 Multiplicative = CMF1 × CMF2 0.90 0.67 0.49 Dominant Common Residuals = (CMF1 × CMF2)CMF1 0.91 0.75 0.61 Table B2. Sample CMFs illustrating importance of magnitude of effect.

B-8 This procedure is intended to guide the decision process for selecting the most appropriate method to estimate the combined effect of two treatments. Figure B1 is a flowchart that illus- trates the steps of the procedure. The decision process is based on three key factors: potential overlap of individual treatment effects, magnitude of individual treatment effects, and the appli- cability of the individual CMFs. A more detailed description of the process follows the figure and related tables, including examples to illustrate how to navigate the decision process and then how to apply the methods. The remainder of this section assumes two treatments have been identified for potential application, CMFs are available for the individual treatments in question, and the analyst would like to estimate the combined effect of the treatments. The following is a detailed description of the decision process presented in Figure B1. To set up an example that continues through the discussion, assume that an analyst is considering two treatments, centerline and shoulder rumble strips, to address safety concerns related to head- on and run-off-road crashes. Table B5 presents the CMFs and applicability of the CMFs for the individual treatments. At this point, the analyst has identified two treatments for potential application, and CMFs are available for the individual treatments in question. Given this information, the analyst can proceed to estimate the combined effect of the treatments. Step 1 Determine Potential Overlap of Individual Treatment Effects The first step is to determine the potential overlap of the individual treatment effects. As dis- cussed in the Chapter 1 subsection Considering the Overlap among Individual Treatments, two or more treatments may complement, replace, or counteract each other. The analyst must determine the likelihood and extent of overlap among the contemplated treatments and select the category from Table B6 that best matches the scenario at hand. Continuing with the example from above, the two treatments are installing centerline rumble strips and shoulder rumble strips. Centerline rumble strips target head-on, sideswipe opposite direction, and run-off-road left crashes, but may affect other crash types such as run-off-road right. Shoulder rumble strips target run-off-road right crashes, but may affect other crash types such as head-on, sideswipe opposite direction, and run-off-road left. This suggests that there is likely some overlap among the treatments, which corresponds to Case B from Table B6. C H A P T E R   2 Procedure

Procedure for Estimating the Combined Safety Effect of Two Treatments B-9   Step 1: 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 Step 2: Determine Magnitude of Individual Treatment Effects Small (< 10% change) Medium (10 - 25% change) Large (> 25% change) Step 3: Define Applicability of Individual CMFs To what crash types and severities do the individual CMFs apply? Step 4: Same Crash Type/Severity Proceed to Table B3 Step 4: Different Crash Type/Severity Proceed to Table B4 The CMFs must be applied separately because they apply to different crash types and/or severities. Figure B1. Flow chart for selecting appropriate method for combining CMFs for two treatments. 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 B3. Method selection for same crash type and severity.

B-10 Guidelines for the Development and Application of Crash Modification Factors Overlap Method Case A Case D 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 estimated crashes without treatment for the applicable crash type/severity at the location of interest. 2. Apply the CMF for the second treatment to the estimated crashes without treatment for the applicable crash type/severity at the location of interest. 3. Sum the estimated change in crashes to calculate the net effect. 4. Check that the estimated change does not exceed the potential bounds of the combined treatments. If so, the estimated change is equal to the respective bound. 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 (i.e., the lowest CMF) to the estimated crashes without treatment for the applicable crash type/severity at the location of interest. 2. Apply the CMF for the second treatment to the estimated crashes without treatment for the applicable crash type/severity at the location of interest, excluding crashes associated with the most effective treatment. 3. Sum the estimated change in crashes to calculate the net effect. 4. Check that the estimated change does not exceed the potential bounds of the combined treatments. If so, the estimated change is equal to the respective bound. Case C Dominant Effect Assuming complete overlap among the treatment effects, one would expect the full benefit of only the most effective treatment. Note that this is a simplified version of Case B. Apply the CMF for the most effective treatment (i.e., the lowest CMF) to the estimated crashes without treatment for the applicable crash type/severity at the location of interest. Table B4. Method selection for different crash type and severity. Treatment CMF Applicable Crash Type Applicable Crash Severity Applicable Roadway Characteristics Source Install centerline rumble strips 0.912 Run-off-road, head- on, and sideswipe All Urban and rural, two- lane, undivided roads NCHRP 17-63 Install shoulder rumble strips 0.844 Run-off-road, head- on, and sideswipe All Urban and rural, two- lane, undivided roads NCHRP 17-63 Table B5. CMFs for centerline rumble strips only and shoulder rumble strips only. Case Description A: Zero overlap This case represents two truly independent effects where the complete benefit of both treatments is realized. B: Some overlap This case represents two treatments that both provide some level of benefit, but the second treatment has some overlap with the first. C: Complete overlap This case represents two non-independent effects where the second treatment targets some or all of the same crash types/severities as the first. D: Enhancing effects This case represents a scenario where the combined effect of two treatments is greater than the sum of their individual effects because one treatment enhances the effectiveness of the other treatment. E: Counteracting effects This case represents a scenario where the combined effect of two treatments is less than the effect of the most effective treatment because one treatment counteracts the effect of the other treatment. Table B6. Defining the overlap of individual treatment effects.

Procedure for Estimating the Combined Safety Effect of Two Treatments B-11   Step 2 Determine Magnitude of Individual Treatment Effects The second step is to determine the magnitude of the individual treatment effects based on the levels defined in Table B7. If both individual treatment effects are small (i.e., less than 10% change), there is relatively little difference between the methods. As the magnitude of effect increases, the methods produce much different estimates, and it becomes more important to select an appropriate method. Continuing with the example from above, the CMFs for target crashes are 0.912 for install- ing centerline rumble strips and 0.844 for installing shoulder rumble strips. The value of 0.912 is defined as small since it represents a change less than 10%. The value of 0.844 is defined as medium since it represents a change between 10% and 25%. Step 3 Define the Applicability of Individual CMFs The third step is to define the applicability of the individual CMFs. Specifically, identify the crash types and severities to which the individual CMFs apply. Refer to the CMF Clearinghouse for more information on the applicability of CMFs (www.cmfclearinghouse.org). Continuing with the example from above, the applicable crash type and severity for both CMFs is all run- off-road, head-on, and sideswipe crashes. Step 4 Select and Apply an Appropriate Method to Estimate the Combined Effect The fourth step is to select and apply an appropriate method to estimate the combined effect of the treatments. Follow Figure B1 and use Table B3 or Table B4 to identify the appropriate method based on the considerations in steps 1—3. Continuing with the example from above, the following is a summary of the considerations from steps 1—3. • Potential overlap: some (Case B) • Magnitude of effects: small and medium • Applicability of CMFs: same crash type and severity Based on these considerations, the Dominant Common Residuals method is most appropriate. This is determined from Table B3 (same crash type and severity), using Case B (some overlap), and the small-medium category for magnitude of effect. The following shows the application of the Dominant Common Residuals method based on the CMFs from the example above. Note that the combined CMF is applicable to run-off-road, head-on, and sideswipe crashes on urban and rural, two-lane, undivided roads. CMFCMF CMF CMF . . . CMF CMF 0.844 0.912 CMF 0.802 t 1 2 n t 0.844 t 1( ) ( ) = × × × = × = Individual Effect Assigned Magnitude < 10% change Small 10%–25% change Medium > 25% change Large Table B7. Defining the magnitude of individual treatment effects.

B-12 Guidelines for the Development and Application of Crash Modification Factors Estimating the Standard Error of the Combined Safety Effect of Multiple Treatments The standard error of the CMF is needed for several activities, such as assessing the quality of a CMF and combining multiple CMF estimates for the same treatment. Given that the use of individual CMFs to estimate the combined effect of multiple treatments occurs after the quality rating process and after the combination of individual CMFs for the same treatment, there is limited value or need for the standard error of the combined effect of multiple treatments. The standard error can be used to estimate the confidence interval of the combined CMF. Practitioners may use the confidence interval to determine a conservative estimate of whether a project is justified (BCR > 1.0), rather than using the mean CMF value. There are two methods available for estimating the standard error of the combined effect for this purpose. • The first is the simplest case and applies to scenarios where the Dominant Effect method is most appropriate to estimate the combined safety effect. Since the Dominant Effect method only applies the lowest CMF (for the most effective treatment), the standard error of the com- bined effect is the standard error associated with the CMF for the most effective treatment. • The second method uses the equation below. The method is based on the theory of multi- plying independent random variables (i.e., the Multiplicative method). While this method only applies to the combined effect from the Multiplicative method, assuming independent treatments, it could be used for any of the methods that produce a CMF that represents the combined effect (e.g., Dominant Common Residuals). The method does not recognize the potential overlap among treatment effects but does provide a reasonable upper bound on the standard error. If the treatment effects overlap, then the method will produce a conser- vatively high estimate of the standard error. [ ]( ) ( )( ) ( ) ( ) ( )= + × + −Variance CMF CMF Var CMF CMF Var CMF CMFt 12 1 22 2 t 2 Some of the recommended methods do not produce a combined CMF. Instead, they pro- duce an estimate of the combined effect based on the separate application of individual CMFs. In these cases, the user may apply the standard errors associated with the individual CMFs to estimate the potential range in results for individual crash types and severities. Extension of Method to Estimate the Combined Safety Effect of Three or More Treatments The guidelines described in this document apply to scenarios where an analyst is interested in combining individual CMFs to estimate the combined effect of two treatments. This was the spe- cific scenario investigated under this research project. It is anticipated that analysts may encounter scenarios where three or more treatments are considered for implementation at the same loca- tion. This section describes an option to extend the recommended methods for two treatments to estimate the combined effect of three or more treatments. Analysts should recognize, however, that combining more than two individual CMFs increases the potential for overlapping treatment effects, and this research did not test the accuracy of combining more than two CMFs. To estimate the effect of three or more treatments, the analyst may follow the general four-step process outlined in Figure B1 and detailed in the above section General Guidelines for Estimating the Combined Safety Effect of Two Treatments. The difference is that CMFs are combined in a pairwise process. Specifically, the analyst would first combine the two individual CMFs associated with the two most effective treatments. The result is a single estimate of the combined effect of the two most effective treatments. The analyst would then combine this estimate with the CMF for the next most effective treatment, again producing a single combined effect. The process continues until there is a single combined effect for all contemplated treatments.

B-13   This section provides additional examples to illustrate how to navigate the decision pro- cess and then how to apply an appropriate method to estimate the combined effect of two treatments. Example 1 Complete Overlap among Treatment Effects and Same Applicability An analyst is considering two treatments, lane widening and shoulder widening, to address safety concerns related to run-off-road crashes on curves along a rural, two-lane, undivided road. Table B8 presents the CMFs and applicability of the CMFs for the individual treatments. At this point, the analyst has identified two treatments for potential application, and CMFs are available for the individual treatments in question. Given this information, the analyst can proceed to estimate the combined effect of the treatments. Step 1 Determine Potential Overlap of Individual Treatment Effects The first step is to determine the potential overlap of the individual treatment effects and select the category from Table B6 that best matches the scenario at hand. Lane widening targets head-on, sideswipe opposite direction, and run-off-road crashes. Shoulder widening targets head-on, side- swipe opposite direction, and run-off-road crashes. This suggests that there is complete overlap among the treatments, which corresponds to Case C from Table B6. Specifically, this case repre- sents two non-independent effects where the second treatment targets some or all the same crash types/severities as the first. Step 2 Determine Magnitude of Individual Treatment Effects The second step is to determine the magnitude of the individual treatment effects based on the levels defined in Table B7. The CMFs for run-off-road crashes are 0.951 for lane widening and 0.630 for shoulder widening. The value of 0.951 is defined as small since it represents a change less than 10%. The value of 0.630 is defined as large since it represents a change greater 25%. Step 3 Define the Applicability of Individual CMFs The third step is to define the applicability of the individual CMFs. In this example, the appli- cable crash type and severity for both CMFs is all run-off-road crashes. C H A P T E R   3 Example Applications of Procedure

B-14 Guidelines for the Development and Application of Crash Modification Factors Step 4 Select and Apply an Appropriate Method to Estimate the Combined Effect The fourth step is to select and apply an appropriate method to estimate the combined effect of the treatments. The following is a summary of the considerations from steps 1–3 for this example. • Potential overlap: complete (Case C) • Magnitude of effects: small and large • Applicability of CMFs: same crash type and severity Based on these considerations, the Dominant Effect method is most appropriate. This is deter- mined from Table B3 (same crash type and severity), using Case C (complete overlap). Note that in this case the magnitude of effect is not applicable. The following shows the application of the Dominant Effect method based on the CMFs from the example above. Note that the combined CMF is applicable to run-off-road crashes on rural, two-lane, undivided curve sections. CMF CMF CMF 0.630 t 1 t = = Example 2 Enhancing Treatment Effects and Same Applicability An analyst is considering two treatments, installing edgeline pavement markings and shoulder rumble strips, to address safety concerns related to run-off-road crashes on rural, two-lane, undivided roads. From the CMF Clearinghouse, Table B9 presents the CMFs and applicability of the CMFs for the individual treatments. At this point, the analyst has identified two treatments for potential application, and CMFs are available for the individual treatments in question. Given this information, the analyst can proceed to estimate the combined effect of the treatments. Treatment CMF Applicable Crash Type Applicable Crash Severity Applicable Roadway Characteristics Source Widen lane width from 11 ft to 12 ft on curves 0.951 Run-off-road crashes All Rural, two-lane, undivided curves NCHRP 17-63 Widening shoulder width from 3 ft to 8 ft on curves 0.630 Run-off-road crashes All Rural, two-lane, undivided curves NCHRP 17-63 Table B8. CMFs for lane widening only and shoulder widening only on curves. Treatment CMF Applicable Crash Type Applicable Crash Severity Applicable Roadway Characteristics CMF ID Install 4-in to 6-in edgeline pavement markings 0.97 All Serious injury, Minor Injury Rural, two-lane roads 83 Install shoulder rumble strips 0.92 All Fatal, Serious injury, Minor injury Rural, two-lane roads 3430 Table B9. CMFs for installing edgeline pavement markings and shoulder rumble strips.

Procedure for Estimating the Combined Safety Effect of Two Treatments B-15   Step 1 Determine Potential Overlap of Individual Treatment Effects The first step is to determine the potential overlap of the individual treatment effects and select the category from Table B6 that best matches the scenario at hand. Edgeline pavement markings target run-off-road right crashes, but may affect other crash types such as head-on, sideswipe opposite direction, and run-off-road left. Shoulder rumble strips target run-off-road right crashes, but may affect other crash types such as head-on, sideswipe opposite direction, and run-off-road left. The vertical edge of the rumble strip may enhance the visibility of the edge- line pavement marking if the edgeline is placed within the shoulder rumble strip. Specifically, this case represents a scenario where the combined effect of two treatments is greater than the sum of their individual effects because one treatment is expected to enhance the effectiveness of the other treatment. The potential for enhanced effects corresponds to Case D from Table B6. Step 2 Determine Magnitude of Individual Treatment Effects The second step is to determine the magnitude of the individual treatment effects based on the levels defined in Table B7. The CMFs are 0.97 for installing edgeline pavement markings and 0.92 for installing shoulder rumble strips. Both values are defined as small since they represent changes less than 10%. Step 3 Define the Applicability of Individual CMFs The third step is to define the applicability of the individual CMFs. In this example, the appli- cable crash type is all crashes for both CMFs. The applicable crash severity for installing pave- ment markings is serious and minor injury. The applicable crash severity for installing shoulder rumble strips is fatal, serious, and minor injury. For this example, the analyst may assume that serious injury crashes include fatal crashes for the first treatment. Step 4 Select and Apply an Appropriate Method to Estimate the Combined Effect The fourth step is to select and apply an appropriate method to estimate the combined effect of the treatments. The following is a summary of the considerations from Steps 1–3 for this example. • Potential overlap: enhancing effects (Case D) • Magnitude of effects: small and small • Applicability of CMFs: same crash type and severity Based on these considerations, the Additive Effects method is most appropriate with a max- imum reduction of 100% (i.e., CMF = 0). This is determined from Table B3 (same crash type and severity), using Case D (enhancing effects). Note that in this case the magnitude of effect is not applicable. The following shows the application of the Additive Effects method based on the CMFs from the example above. Note the combined CMF is applicable to all fatal, serious, and minor injury crashes on rural, two-lane, undivided roads. CMF 1 CMF 1 CMF . . . 1 CMF CMF 1 1 0.92 1 0.97 CMF 0.89 t 1 2 n t t [ ] [ ] ( ) ( ) ( ) ( ) ( ) = − + − + + − = − − + − = Note there are CMFs in the CMF Clearinghouse for installing edgeline rumble strips, which may represent the combined effect of installing pavement markings and shoulder rumble strips simultaneously. The CMFs that apply to fatal and injury run-off-road crashes on rural, two-lane,

B-16 Guidelines for the Development and Application of Crash Modification Factors undivided roads range from 0.53 to 0.86. This suggests that there is an enhancing effect of the combined treatment. While the Additive Effects method gives full credit to the individual treat- ment effects, it does not inflate the combined effect to reflect the potential enhancement. Example 3 Zero Overlap among Treatment Effects and Different Applicability This example involves a minor-road stop-controlled intersection located near a horizontal curve. An analyst is considering two treatments. The first treatment is installing high friction surface treatment on the curve to address single vehicle run-off-road crashes. The second treat- ment is improving sight distance on the stop-controlled approach to address multi-vehicle crashes between vehicles on the major and minor road. Table B10 presents the CMFs and appli- cability of the CMFs for the individual treatments. At this point, the analyst has identified two treatments for potential application, and CMFs are available for the individual treatments in question. Given this information, the analyst can proceed to estimate the combined effect of the treatments. Step 1 Determine Potential Overlap of Individual Treatment Effects The first step is to determine the potential overlap of the individual treatment effects and select the category from Table B6 that best matches the scenario at hand. High friction surface treatments on curves target single vehicle, run-off-road crashes. Improving intersection sight distance on a minor-road approach targets multi-vehicle crashes between vehicles on the major and minor road. This suggests that there may be no overlap among the treatment effects, cor- responding to Case A from Table B6. Specifically, this case represents two independent effects where the complete benefit of both treatments is realized. Step 2 Determine Magnitude of Individual Treatment Effects The second step is to determine the magnitude of the individual treatment effects based on the levels defined in Table B7. The CMFs are 0.70 for installing high friction surface treatment and 0.456 for improving intersection sight distance. Both values are defined as large since they represent changes greater than 25%. Step 3 Define the Applicability of Individual CMFs The third step is to define the applicability of the individual CMFs. In this example, the appli- cable crash type and severity for installing high friction surface treatment is all single vehicle crashes. The applicable crash type and severity for improving intersection sight distance is all multi-vehicle crashes between vehicles on the major and minor road. Treatment CMF Applicable Crash Type Applicable Crash Severity Applicable Roadway Characteristics Source Install high friction surface treatment on curves 0.70 Single vehicle crashes All All CMF Clearinghouse (CMF ID 198) Increase intersection sight distance to 1,320+ feet (from 500 ft–750 ft) 0.456 Multi-vehicle crashes from major and minor road All 3- and 4-legged intersections with minor-road stop control NCHRP 17- 63 Table B10. CMFs for installing high friction surface treatment only and increasing intersection sight distance only.

Procedure for Estimating the Combined Safety Effect of Two Treatments B-17   Step 4 Select and Apply an Appropriate Method to Estimate the Combined Effect The fourth step is to select and apply an appropriate method to estimate the combined effect of the treatments. The following is a summary of the considerations from steps 1–3 for this example. • Potential overlap: none (Case A) • Magnitude of effects: large and large • Applicability of CMFs: different crash type and severity Based on these considerations, the Additive Effects method is most appropriate with a maxi- mum reduction of 100% (i.e., CMF = 0). This is determined from Table B4 (different crash type and severity), using Case A (zero overlap). Note that in this case the magnitude of effect is not applicable. The following shows the application of the Additive Effects method based on the CMFs from the example above. Note that this method does not produce a combined CMF. Instead, it pro- duces an estimate of the combined effect. For this example, assume the estimated single vehicle crashes without treatment is 3.4 crashes per year, and the estimated multi-vehicle crashes between vehicles on the major and minor road is 5.2 crashes per year. 1. Apply the CMF for the first treatment to the estimated crashes without treatment for the applicable crash type/severity at the location of interest. Estimated crashes with treatment = CMF × Estimated crashes without treatment Estimated single vehicle crashes with high friction surface treatment = 0.70 × 3.4 Estimated single vehicle crashes with high friction surface treatment = 2.38 Estimated reduction in single vehicle crashes = 3.4 – 2.38 = 1.02 2. Apply the CMF for the second treatment to the estimated crashes without treatment for the applicable crash type/severity at the location of interest. Estimated multi-vehicle crashes with improved sight distance = 0.456 × 5.2 Estimated multi-vehicle crashes with improved sight distance = 2.37 Estimated reduction in multi-vehicle crashes = 5.2 – 2.37 = 2.83 3. Sum the estimated change in crashes to calculate the net effect. Sum of estimated reductions = 1.02 + 2.83 = 3.85 4. Check that the estimated change does not exceed the potential bounds of the combined treat- ments. If so, the estimated change is equal to the respective bound. Sum of estimated reductions (3.85) < Estimated crashes without treatment (8.6) Example 4 Some Overlap among Treatment Effects and Different Applicability An analyst is considering two treatments on a rural, four-lane, divided highway with a tra- versable median. The first treatment is installing high-tension cable median barrier to address cross-median crashes. The second treatment is installing shoulder rumble strips to address run- off-road and cross-median crashes. From the CMF Clearinghouse, Table B11 presents the CMFs and general applicability for the individual treatments. At this point, the analyst has identified two treatments for potential application, and CMFs are available for the individual treatments in question. Given this information, the analyst can proceed to estimate the combined effect of the treatments. Step 1 Determine Potential Overlap of Individual Treatment Effects The first step is to determine the potential overlap of the individual treatment effects and select the category from Table B6 that best matches the scenario at hand. High-tension cable

B-18 Guidelines for the Development and Application of Crash Modification Factors median barrier targets cross-median crashes, including head-on and opposite direction side- swipe. Shoulder rumble strips target run-off-road crashes as well as the head-on and opposite direction sideswipe crashes related to vehicles crossing the median. This suggests that there is some overlap among the treatment effects, corresponding to Case B from Table B6. Specifi- cally, this case represents two treatments that both provide some level of benefit in reducing cross-median crashes, and the second treatment has an additional effect on run-off-road crashes. Step 2 Determine Magnitude of Individual Treatment Effects The second step is to determine the magnitude of the individual treatment effects based on the levels defined in Table B7. The CMFs are 0.04 for installing high-tension cable median barrier and 0.87 for installing shoulder rumble strips. The CMF of 0.04 is defined as large since it represents a change greater than 25%. The CMF of 0.87 is defined as medium since it represents a change between 10% and 25%. Step 3 Define the Applicability of Individual CMFs The third step is to define the applicability of the individual CMFs. In this example, the appli- cable crash type and severity for installing high-tension cable median barrier is all cross-median crashes. The applicable crash type and severity for installing shoulder rumble strips is all run- off-road and cross-median crashes. Step 4 Select and Apply an Appropriate Method to Estimate the Combined Effect The fourth step is to select and apply an appropriate method to estimate the combined effect of the treatments. The following is a summary of the considerations from steps 1–3 for this example. • Potential overlap: some (Case B) • Magnitude of effects: large and medium • Applicability of CMFs: different crash type and severity Based on these considerations, the Dominant Effect for Overlapping Crash Types method is most appropriate. This is determined from Table B4 (different crash type and severity), using Case B (some overlap). Note that in this case the magnitude of effect is not applicable. The following shows the application of the Dominant Effect for Overlapping Crash Types method based on the CMFs from the example above. Note that this method does not produce a combined CMF. Instead, it produces an estimate of the combined effect. For this example, Treatment CMF Applicable Crash Type Applicable Crash Severity Applicable Roadway Characteristics CMF ID Install high- tension cable median barrier 0.04 Cross-median All Rural, multilane interstates with traversable medians 1967 Install shoulder rumble strips 0.87 Cross-median and run-off-road All Rural, four-lane freeways with traversable medians 6965 Table B11. CMFs for installing high-tension cable median barrier and shoulder rumble strips.

Procedure for Estimating the Combined Safety Effect of Two Treatments B-19   assume the estimated crashes without treatment is 8.9 crashes per year, which includes 2.3 cross- median head-on crashes, 1.3 cross-median sideswipe opposite direction crashes, and 5.3 run-off- road crashes. 1. Apply the CMF for the most effective treatment to the estimated crashes without treatment for the applicable crash type/severity at the location of interest. Estimated crashes with treatment = CMF × Estimated crashes without treatment Estimated cross-median crashes with high-tension cable barrier = 0.04 × 3.6 Estimated cross-median crashes with high-tension cable barrier = 0.14 Estimated reduction in cross-median crashes = 3.6 – 0.14 = 3.46 2. Apply the CMF for the second treatment to the estimated crashes without treatment for the applicable crash type/severity at the location of interest, excluding crashes associated with the most effective treatment. Note that the CMF for the first treatment was applied to all cross- median crashes. As such, cross-median crashes are excluded from further analysis, and the second treatment only applies to run-off-road crashes. Estimated run-off-road crashes with shoulder rumble strips = 0.87 × 5.3 Estimated run-off-road crashes with shoulder rumble strips = 4.61 Estimated reduction in run-off-road crashes = 5.3 – 4.61 = 0.69 3. Sum the estimated change in crashes to calculate the net effect. Sum of estimated reductions = 3.46 + 0.69 = 4.15 4. Check that the estimated change does not exceed the potential bounds of the combined treat- ments. If so, the estimated change is equal to the respective bound. Sum of estimated reductions (4.15) < Estimated crashes without treatment (8.9)

B-20 This section on supporting research provides details related to the CMF development effort to develop the procedure for estimating the combined safety effect of two treatments at the same location. The team for Project 17-63 developed CMFs for the following three combination treat- ments, including CMFs for both the individual and combined treatment effects. • 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 The remainder of this section provides details related to each of the CMF development efforts, including the methodology and related safety performance functions. Combination of Centerline and Shoulder Rumble Strip Installation For this analysis, the team was able to employ a rigorous empirical Bayes (EB) 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). The EB method is a proven technique in highway safety that can account for bias due to regression to the mean (RTM), changes in traffic volume, and temporal trends (i.e., general trends over time). The premise of this method is to estimate what would have occurred in the after period without treatment and compare that to what occurred in the after period with treat- ment. Due to changes in safety that may result from changes in RTM, traffic volume, and tem- poral trends, the count of crashes before a treatment by itself is not a good estimate of π (Hauer 1997). Instead, π is estimated from an EB procedure (Hauer 1997) in which a safety performance function (SPF) is used to first predict the number of crashes in each year of the “before” period based on locations with traffic volumes and other characteristics of the treatment sites. The sum of these annual SPF estimates (P) is then combined with the count of crashes in the before period at the treatment site (x) to obtain an estimate of the expected number of crashes before the treat- ment (m). The following equation provides an estimate of m. m w P w x Equation B11( )( ) ( )( )= + − The following equation provides the weight (w). w P Equation B21 1( )= + α C H A P T E R   4 Supporting Research

Procedure for Estimating the Combined Safety Effect of Two Treatments B-21   where, m = expected number of crashes before the treatment w = weight to estimate EB expected crashes P = sum of annual SPF estimates “before” treatment at the treatment sites α = inverse of the dispersion parameter from the SPF. Note the value of α is estimated from the SPF calibration process with the use of a maximum likelihood procedure, and a larger value of α indicates less dispersion. A factor is then applied to m to account for the length of the after period and differences in traffic volumes between the before and after periods. This factor is the sum of the annual SPF predictions for the after period divided by P, the sum of these predictions for the before period. The result, after applying this factor, is an estimate of the expected number of crashes that would have occurred in the “after” period without the treatment (π). The estimate of π is then summed over all sites in a treatment group of interest (to obtain πsum) and compared with the count of crashes during the after period in that group (λsum). The variance of π is also summed over all sections in the group of interest. The index of safety effectiveness (θ) represents the CMF and is given by the following equation. Varsum sum sum sum Equation B31 2[ ]{ }( ) ( )θ = λ π + π π The standard deviation of θ is given by the following equation. Stddev Var Var Varsum sum sum sum sum sum[ ] [ ] [ ]{ }( )( ) ( ) ( )θ = θ λ λ + π π + π π  Equation B4 12 2 2 2 2 0.5 where, θ = index of safety effectiveness (crash modification factor) π = expected number of crashes in the “after” period without treatment λ = number of reported crashes in the after period Stddev = standard deviation The selection of an appropriate reference group is critical to the EB method. A suitable refer- ence group is a group of sites that are like the treatment sites in terms of geometric and traffic characteristics except they did not receive the treatment. If a reference group is in the general vicinity of the treatment sites, it can be used to account for temporal trends (e.g., weather) that influence crashes. In this study, the reference sites were selected from the same general areas as the treatment sites, and propensity score matching was employed to identify a suitable reference group for each treatment category. Fundamental to the EB approach is the use of SPFs. An SPF is a mathematical model that predicts the mean crash frequency for locations with similar characteristics. Generalized linear modeling (GLM) techniques were applied to calibrate SPFs for each target crash type (total, fatal and injury, run-off-road, and target crashes). A log-linear relationship was specified using a negative binomial error structure, which is consistent with the state of research in developing SPFs. Model coefficients were estimated using the software package Stata. The remainder of this section presents the SPFs developed for each focus crash type. The following is the general form of the SPFs. = × ( )β × +β × + +β × Equation B5SPF length econstant+ log AADT X . . . X1 2 2 n n

B-22 Guidelines for the Development and Application of Crash Modification Factors where, length = segment length (miles) Constant = constant estimated during modeling process Log(AADT) = natural log of traffic volume β1 – βn = Coefficients estimated during modeling process X2 – Xn = variables included in given SPF Variable Coefficient Standard Error Z- score P- value Lower 95% Conf. Int. Upper 95% Conf. Int. log(AADT) 1.0165 0.0198 51.34 0.0000 0.9777 1.0553 Area Type (1=urban; 0 otherwise) 0.0622 0.0464 1.34 0.1800 -0.0287 0.1532 Terrain (1=rolling; 0 otherwise) -0.2048 0.0357 -5.73 0.0000 -0.2749 -0.1348 Speed Limit (1=50+ mph; 0 otherwise) -0.4061 0.0450 -9.02 0.0000 -0.4943 -0.3179 Lane Width (1=11 ft; 0=12 ft or 13 ft) 0.1954 0.0709 2.75 0.0060 0.0564 0.3344 Shoulder Width (continuous) -0.0429 0.0081 -5.27 0.0000 -0.0589 -0.0270 Lane Width × Shoulder Width -0.0315 0.0132 -2.38 0.0170 -0.0573 -0.0056 Indicator for Year = 2003 0.0032 0.0742 0.04 0.9660 -0.1422 0.1485 Indicator for Year = 2004 -0.0682 0.0746 -0.91 0.3610 -0.2144 0.0781 Indicator for Year = 2005 -0.0355 0.0740 -0.48 0.6310 -0.1806 0.1096 Indicator for Year = 2006 -0.0307 0.0743 -0.41 0.6790 -0.1764 0.1149 Indicator for Year = 2007 -0.0094 0.0738 -0.13 0.8990 -0.1540 0.1352 Indicator for Year = 2008 0.0472 0.0737 0.64 0.5220 -0.0973 0.1916 Indicator for Year = 2009 -0.0461 0.0745 -0.62 0.5360 -0.1920 0.0999 Indicator for Year = 2010 -0.0889 0.0750 -1.19 0.2360 -0.2358 0.0580 Indicator for Year = 2011 -0.1210 0.0774 -1.56 0.1180 -0.2727 0.0306 Indicator for Year = 2012 -0.2515 0.0794 -3.17 0.0020 -0.4071 -0.0960 Constant -7.0646 0.1880 -37.58 0.0000 -7.4330 -6.6962 alpha (α) 0.4219 0.0247 0.3762 0.4731 Table B12. Total crash SPF for centerline rumble strips. Variable Coefficient Standard Error Z- score P- value Lower 95% Conf. Int. Upper 95% Conf. Int. log(AADT) 1.0190 0.0262 38.88 0.0000 0.9676 1.0703 Area Type (1=urban; 0 otherwise) 0.0676 0.0598 1.13 0.2580 -0.0497 0.1849 Terrain (1=rolling; 0 otherwise) -0.2010 0.0464 -4.33 0.0000 -0.2919 -0.1101 Speed Limit (1=50+ mph; 0 otherwise) -0.4142 0.0587 -7.06 0.0000 -0.5293 -0.2992 Lane Width (1=11 ft; 0=12 ft or 13 ft) 0.3718 0.0922 4.03 0.0000 0.1910 0.5525 Shoulder Width (continuous) -0.0335 0.0109 -3.09 0.0020 -0.0548 -0.0122 Lane Width * Shoulder Width -0.0672 0.0172 -3.91 0.0000 -0.1009 -0.0336 Indicator for Year = 2003 -0.0109 0.0935 -0.12 0.9070 -0.1941 0.1724 Indicator for Year = 2004 -0.1292 0.0951 -1.36 0.1740 -0.3156 0.0571 Indicator for Year = 2005 -0.0520 0.0938 -0.55 0.5800 -0.2359 0.1319 Indicator for Year = 2006 -0.0091 0.0940 -0.10 0.9230 -0.1935 0.1752 Indicator for Year = 2007 0.0080 0.0928 0.09 0.9310 -0.1739 0.1898 Indicator for Year = 2008 -0.0537 0.0944 -0.57 0.5700 -0.2388 0.1314 Indicator for Year = 2009 -0.0683 0.0947 -0.72 0.4710 -0.2538 0.1172 Indicator for Year = 2010 -0.2321 0.0976 -2.38 0.0170 -0.4234 -0.0407 Indicator for Year = 2011 -0.3184 0.1024 -3.11 0.0020 -0.5190 -0.1177 Indicator for Year = 2012 -0.4898 0.1064 -4.60 0.0000 -0.6984 -0.2812 Constant -7.9930 0.2476 -32.28 0.0000 -8.4784 -7.5076 alpha (α) 0.3888 0.0382 0.3208 0.4713 Table B13. Fatal and injury crash SPF for centerline rumble strips.

Procedure for Estimating the Combined Safety Effect of Two Treatments B-23   Variable Coefficient Standard Error Z- score P- value Lower 95% Conf. Int. Upper 95% Conf. Int. log(AADT) 0.5426 0.0242 22.43 0.0000 0.4952 0.5900 Terrain (1=mountainous; 0 otherwise) 0.4070 0.1134 3.59 0.0000 0.1847 0.6292 Speed Limit (1=50+ mph; 0 otherwise) -0.1116 0.0674 -1.66 0.0980 -0.2436 0.0205 Lane Width (1=11 ft; 0=12 ft or 13 ft) 0.7063 0.0951 7.42 0.0000 0.5198 0.8928 Shoulder Width (continuous) -0.0291 0.0125 -2.32 0.0200 -0.0537 -0.0045 Lane Width × Shoulder Width -0.0986 0.0183 -5.38 0.0000 -0.1345 -0.0627 Indicator for Year = 2003 0.0868 0.1018 0.85 0.3940 -0.1128 0.2863 Indicator for Year = 2004 0.0477 0.1028 0.46 0.6430 -0.1539 0.2493 Indicator for Year = 2005 0.2078 0.1001 2.08 0.0380 0.0115 0.4040 Indicator for Year = 2006 0.1314 0.1014 1.30 0.1950 -0.0673 0.3301 Indicator for Year = 2007 0.1382 0.1012 1.37 0.1720 -0.0602 0.3366 Indicator for Year = 2008 0.1580 0.1011 1.56 0.1180 -0.0400 0.3561 Indicator for Year = 2009 0.0398 0.1031 0.39 0.6990 -0.1623 0.2419 Indicator for Year = 2010 0.0945 0.1026 0.92 0.3570 -0.1065 0.2956 Indicator for Year = 2011 0.0219 0.1066 0.21 0.8370 -0.1870 0.2308 Indicator for Year = 2012 -0.0673 0.1096 -0.61 0.5390 -0.2822 0.1475 Constant -4.9246 0.2279 -21.61 0.0000 -5.3713 -4.4779 alpha (α) 0.4160 0.0424 0.3407 0.5081 Table B14. Run-off-road crash SPF for centerline rumble strips. Variable Coefficient Standard Error Z- score P- value Lower 95% Conf. Int. Upper 95% Conf. Int. log(AADT) 0.5708 0.0257 22.23 0.0000 0.5204 0.6211 Area Type (1=urban; 0 otherwise) 0.0980 0.0692 1.42 0.1570 -0.0376 0.2335 Terrain (1=mountainous; 0 otherwise) 0.3985 0.1122 3.55 0.0000 0.1786 0.6183 Speed Limit (1=50+ mph; 0 otherwise) -0.0716 0.0667 -1.07 0.2830 -0.2023 0.0591 Lane Width (1=11 ft; 0=12 ft or 13 ft) 0.6860 0.0924 7.42 0.0000 0.5049 0.8672 Shoulder Width (continuous) -0.0332 0.0122 -2.73 0.0060 -0.0571 -0.0094 Lane Width × Shoulder Width -0.0957 0.0177 -5.41 0.0000 -0.1304 -0.0611 Indicator for Year = 2003 0.0745 0.0982 0.76 0.4480 -0.1179 0.2669 Indicator for Year = 2004 0.0067 0.0995 0.07 0.9470 -0.1884 0.2017 Indicator for Year = 2005 0.1645 0.0970 1.70 0.0900 -0.0256 0.3546 Indicator for Year = 2006 0.0783 0.0983 0.80 0.4260 -0.1144 0.2711 Indicator for Year = 2007 0.1310 0.0974 1.35 0.1790 -0.0599 0.3219 Indicator for Year = 2008 0.1393 0.0975 1.43 0.1530 -0.0518 0.3304 Indicator for Year = 2009 0.0332 0.0992 0.33 0.7380 -0.1612 0.2275 Indicator for Year = 2010 0.0492 0.0994 0.49 0.6210 -0.1457 0.2440 Indicator for Year = 2011 0.0122 0.1027 0.12 0.9050 -0.1891 0.2135 Indicator for Year = 2012 -0.1134 0.1061 -1.07 0.2850 -0.3214 0.0946 Constant -5.0672 0.2317 -21.87 0.0000 -5.5212 -4.6131 alpha (α) 0.4139 0.0401 0.3422 0.5005 Table B15. Target crash SPF for centerline rumble strips.

B-24 Guidelines for the Development and Application of Crash Modification Factors Variable Coefficient Standard Error Z- score P- value Lower 95% Conf. Int. Upper 95% Conf. Int. log(AADT) 0.1148 0.1588 0.72 0.4700 -0.1965 0.4261 Area Type (1=urban; 0 otherwise) 1.2014 0.2675 4.49 0.0000 0.6771 1.7256 Speed Limit (1=50+ mph; 0 otherwise) -0.6647 0.3510 -1.89 0.0580 -1.3527 0.0232 Lane Width (1=11 ft; 0=12 ft or 13 ft) 0.8643 0.4466 1.94 0.0530 -0.0110 1.7396 Shoulder Width (continuous) 0.0839 0.0489 1.72 0.0860 -0.0119 0.1798 Lane Width × Shoulder Width -0.1709 0.0773 -2.21 0.0270 -0.3223 -0.0195 Indicator for Year = 2006 0.0553 0.2174 0.25 0.7990 -0.3708 0.4814 Indicator for Year = 2007 -0.2013 0.2301 -0.87 0.3820 -0.6522 0.2497 Indicator for Year = 2008 0.1182 0.2143 0.55 0.5810 -0.3018 0.5383 Indicator for Year = 2009 0.0696 0.2175 0.32 0.7490 -0.3566 0.4958 Indicator for Year = 2010 -0.0270 0.2202 -0.12 0.9020 -0.4586 0.4046 Indicator for Year = 2011 0.1540 0.2132 0.72 0.4700 -0.2638 0.5718 Indicator for Year = 2012 -0.1870 0.2286 -0.82 0.4130 -0.6351 0.2611 Constant -0.1770 1.3863 -0.13 0.8980 -2.8940 2.5401 alpha (α) 0.0783 0.0589 0.0179 0.3423 Table B16. Total crash SPF for shoulder rumble strips. Variable Coefficient Standard Error Z- score P- value Lower 95% Conf. Int. Upper 95% Conf. Int. log(AADT) 0.2283 0.2534 0.90 0.3680 -0.2684 0.7250 Area Type (1=urban; 0 otherwise) 1.4351 0.3951 3.63 0.0000 0.6606 2.2096 Speed Limit (1=50+ mph; 0 otherwise) -0.2038 0.5649 -0.36 0.7180 -1.3109 0.9034 Lane Width (1=11 ft; 0=12 ft or 13 ft) 1.0508 0.5916 1.78 0.0760 -0.1087 2.2102 Shoulder Width (continuous) -0.0267 0.0785 -0.34 0.7340 -0.1806 0.1272 Lane Width × Shoulder Width -0.1631 0.1016 -1.61 0.1080 -0.3622 0.0359 Indicator for Year = 2006 -0.0419 0.2970 -0.14 0.8880 -0.6240 0.5402 Indicator for Year = 2007 -0.2420 0.3080 -0.79 0.4320 -0.8456 0.3616 Indicator for Year = 2008 0.1388 0.2827 0.49 0.6240 -0.4153 0.6929 Indicator for Year = 2009 0.1333 0.2863 0.47 0.6410 -0.4279 0.6946 Indicator for Year = 2010 -0.2935 0.3125 -0.94 0.3480 -0.9059 0.3190 Indicator for Year = 2011 -0.0533 0.2967 -0.18 0.8570 -0.6349 0.5282 Indicator for Year = 2012 -0.4466 0.3293 -1.36 0.1750 -1.0921 0.1989 Constant -1.7774 2.2068 -0.81 0.4210 -6.1028 2.5479 alpha (α) 0.0376 0.1198 0.0001 19.4069 Table B17. Fatal and injury crash SPF for shoulder rumble strips.

Procedure for Estimating the Combined Safety Effect of Two Treatments B-25   Variable Coefficient Standard Error Z- score P- value Lower 95% Conf. Int. Upper 95% Conf. Int. log(AADT) 0.2751 0.1162 2.37 0.0180 0.0473 0.5029 Area Type (1=urban; 0 otherwise) -0.1448 0.2481 -0.58 0.5590 -0.6311 0.3414 Terrain1 (1=mountainous; 0=flat) 1.1534 0.5510 2.09 0.0360 0.0736 2.2333 Terrain2 (1=rolling; 0=flat) 0.5699 0.5437 1.05 0.2950 -0.4958 1.6357 Speed Limit (1=50+ mph; 0 otherwise) -0.3346 0.2709 -1.24 0.2170 -0.8655 0.1964 Lane Width (1=11 ft; 0=12 ft or 13 ft) 0.8376 0.4315 1.94 0.0520 -0.0081 1.6833 Shoulder Width (continuous) -0.0472 0.0328 -1.44 0.1500 -0.1115 0.0171 Lane Width × Shoulder Width -0.0918 0.0760 -1.21 0.2270 -0.2408 0.0572 Indicator for Year = 2007 0.2270 0.4209 0.54 0.5900 -0.5980 1.0519 Indicator for Year = 2008 0.0846 0.3922 0.22 0.8290 -0.6842 0.8533 Indicator for Year = 2009 0.2288 0.3896 0.59 0.5570 -0.5349 0.9924 Indicator for Year = 2010 0.1111 0.3907 0.28 0.7760 -0.6546 0.8767 Indicator for Year = 2011 0.2360 0.3879 0.61 0.5430 -0.5243 0.9963 Indicator for Year = 2012 -0.0219 0.3943 -0.06 0.9560 -0.7947 0.7510 Constant -2.6433 1.2837 -2.06 0.0390 -5.1594 -0.1273 alpha (α) 0.1964 0.0961 0.0753 0.5124 Table B18. Run-off-road crash SPF for shoulder rumble strips. Variable Coefficient Standard Error Z- score P- value Lower 95% Conf. Int. Upper 95% Conf. Int. log(AADT) 0.3393 0.1137 2.99 0.0030 0.1165 0.5620 Area Type (1=urban; 0 otherwise) -0.1857 0.2410 -0.77 0.4410 -0.6581 0.2867 Terrain1 (1=mountainous; 0=flat) 1.2699 0.5501 2.31 0.0210 0.1917 2.3480 Terrain2 (1=rolling; 0=flat) 0.6700 0.5433 1.23 0.2180 -0.3949 1.7348 Speed Limit (1=50+ mph; 0 otherwise) -0.2089 0.2697 -0.77 0.4390 -0.7374 0.3196 Lane Width (1=11 ft; 0=12 ft or 13 ft) 0.8020 0.4233 1.89 0.0580 -0.0276 1.6315 Shoulder Width (continuous) -0.0514 0.0319 -1.61 0.1070 -0.1139 0.0111 Lane Width × Shoulder Width -0.0811 0.0746 -1.09 0.2770 -0.2272 0.0650 Indicator for Year = 2007 0.2945 0.4040 0.73 0.4660 -0.4975 1.0864 Indicator for Year = 2008 0.0959 0.3778 0.25 0.8000 -0.6446 0.8364 Indicator for Year = 2009 0.1851 0.3763 0.49 0.6230 -0.5523 0.9226 Indicator for Year = 2010 0.1389 0.3757 0.37 0.7120 -0.5975 0.8752 Indicator for Year = 2011 0.2571 0.3731 0.69 0.4910 -0.4741 0.9883 Indicator for Year = 2012 -0.0552 0.3805 -0.15 0.8850 -0.8010 0.6906 Constant -3.3114 1.2576 -2.63 0.0080 -5.7763 -0.8465 alpha (α) 0.2073 0.0923 0.0866 0.4962 Table B19. Target crash SPF for shoulder rumble strips.

B-26 Guidelines for the Development and Application of Crash Modification Factors Variable Coefficient Standard Error Z- score P- value Lower 95% Conf. Int. Upper 95% Conf. Int. log(AADT) 1.0939 0.0493 22.21 0.0000 0.9974 1.1905 Area Type (1=urban; 0 otherwise) -0.1445 0.1246 -1.16 0.2460 -0.3887 0.0996 Terrain (1=mountainous; 0 otherwise) -0.3433 0.1924 -1.78 0.0740 -0.7204 0.0338 Speed Limit (1=50+ mph; 0 otherwise) -0.1947 0.1283 -1.52 0.1290 -0.4461 0.0567 Lane Width (1=11 ft; 0=12 ft or 13 ft) 0.7394 0.1818 4.07 0.0000 0.3831 1.0956 Lane Width × Shoulder Width -0.1034 0.0294 -3.51 0.0000 -0.1611 -0.0457 Indicator for Year = 2003 0.1981 0.1686 1.18 0.2400 -0.1323 0.5285 Indicator for Year = 2004 0.0140 0.1720 0.08 0.9350 -0.3231 0.3512 Indicator for Year = 2005 -0.0379 0.1736 -0.22 0.8270 -0.3782 0.3023 Indicator for Year = 2006 0.0837 0.1705 0.49 0.6230 -0.2505 0.4180 Indicator for Year = 2007 -0.0576 0.1730 -0.33 0.7390 -0.3966 0.2814 Indicator for Year = 2008 0.0702 0.1725 0.41 0.6840 -0.2680 0.4083 Indicator for Year = 2009 0.0290 0.1724 0.17 0.8660 -0.3088 0.3669 Indicator for Year = 2010 -0.1805 0.1756 -1.03 0.3040 -0.5247 0.1637 Indicator for Year = 2011 -0.1073 0.1803 -0.60 0.5520 -0.4608 0.2461 Indicator for Year = 2012 -0.0244 0.1806 -0.13 0.8930 -0.3783 0.3296 Constant -8.3076 0.4773 -17.40 0.0000 -9.2431 -7.3721 alpha (α) 0.4675 0.0538 0.3731 0.5858 Table B20. Total crash SPF for combination of centerline and shoulder rumble strips. Variable Coefficient Standard Error Z- score P- value Lower 95% Conf. Int. Upper 95% Conf. Int. log(AADT) 1.2163 0.0666 18.27 0.0000 1.0858 1.3468 Area Type (1=urban; 0 otherwise) -0.4785 0.1813 -2.64 0.0080 -0.8338 -0.1232 Terrain (1=mountainous; 0 otherwise) -0.7454 0.2488 -3.00 0.0030 -1.2332 -0.2577 Speed Limit (1=50+ mph; 0 otherwise) -0.2314 0.1742 -1.33 0.1840 -0.5728 0.1100 Lane Width (1=11 ft; 0=12 ft or 13 ft) 0.4481 0.2422 1.85 0.0640 -0.0266 0.9228 Lane Width × Shoulder Width -0.0878 0.0396 -2.22 0.0260 -0.1653 -0.0103 Indicator for Year = 2003 -0.0088 0.2189 -0.04 0.9680 -0.4379 0.4203 Indicator for Year = 2004 -0.0355 0.2173 -0.16 0.8700 -0.4615 0.3904 Indicator for Year = 2005 -0.1721 0.2227 -0.77 0.4400 -0.6085 0.2644 Indicator for Year = 2006 -0.1420 0.2220 -0.64 0.5220 -0.5771 0.2930 Indicator for Year = 2007 -0.4480 0.2319 -1.93 0.0530 -0.9026 0.0066 Indicator for Year = 2008 -0.2813 0.2294 -1.23 0.2200 -0.7309 0.1684 Indicator for Year = 2009 -0.1486 0.2215 -0.67 0.5020 -0.5829 0.2856 Indicator for Year = 2010 -0.6672 0.2399 -2.78 0.0050 -1.1375 -0.1969 Indicator for Year = 2011 -0.4677 0.2433 -1.92 0.0550 -0.9446 0.0092 Indicator for Year = 2012 -0.3883 0.2405 -1.61 0.1060 -0.8597 0.0830 Constant -9.9505 0.6450 -15.43 0.0000 -11.2146 -8.6864 alpha (α) 0.5349 0.0949 0.3777 0.7574 Table B21. Fatal and injury crash SPF for combination of centerline and shoulder rumble strips.

Procedure for Estimating the Combined Safety Effect of Two Treatments B-27   Variable Coefficient Standard Error Z- score P- value Lower 95% Conf. Int. Upper 95% Conf. Int. log(AADT) 0.4859 0.0593 8.20 0.0000 0.3697 0.6020 Terrain (1=mountainous; 0 otherwise) 0.6483 0.2768 2.34 0.0190 0.1057 1.1908 Speed Limit (1=50+ mph; 0 otherwise) 0.3807 0.2616 1.46 0.1460 -0.1321 0.8935 Lane Width (1=11 ft; 0=12 ft or 13 ft) 1.2929 0.3456 3.74 0.0000 0.6155 1.9703 Shoulder Width (continuous) -0.0461 0.0371 -1.24 0.2140 -0.1187 0.0266 Lane Width × Shoulder Width -0.2061 0.0530 -3.89 0.0000 -0.3099 -0.1022 Indicator for Year = 2003 0.2212 0.2113 1.05 0.2950 -0.1930 0.6354 Indicator for Year = 2004 -0.3031 0.2359 -1.29 0.1990 -0.7655 0.1592 Indicator for Year = 2005 -0.2575 0.2338 -1.10 0.2710 -0.7157 0.2007 Indicator for Year = 2006 -0.0718 0.2252 -0.32 0.7500 -0.5132 0.3696 Indicator for Year = 2007 0.0300 0.2191 0.14 0.8910 -0.3993 0.4594 Indicator for Year = 2008 -0.1649 0.2288 -0.72 0.4710 -0.6135 0.2836 Indicator for Year = 2009 -0.2012 0.2308 -0.87 0.3830 -0.6537 0.2512 Indicator for Year = 2010 -0.1904 0.2290 -0.83 0.4060 -0.6392 0.2583 Indicator for Year = 2011 -0.1121 0.2334 -0.48 0.6310 -0.5696 0.3455 Indicator for Year = 2012 -0.3132 0.2487 -1.26 0.2080 -0.8006 0.1741 Constant -4.5388 0.6615 -6.86 0.0000 -5.8353 -3.2423 alpha (α) 0.2203 0.0805 0.1077 0.4507 Table B22. Run-off-road crash SPF for combination of centerline and shoulder rumble strips. Variable Coefficient Standard Error Z- score P- value Lower 95% Conf. Int. Upper 95% Conf. Int. log(AADT) 0.5345 0.0569 9.39 0.0000 0.4229 0.6460 Terrain (1=mountainous; 0 otherwise) 0.4231 0.2683 1.58 0.1150 -0.1027 0.9489 Speed Limit (1=50+ mph; 0 otherwise) 0.4520 0.2541 1.78 0.0750 -0.0460 0.9500 Lane Width (1=11 ft; 0=12 ft or 13 ft) 1.1693 0.3315 3.53 0.0000 0.5195 1.8191 Shoulder Width (continuous) -0.0513 0.0354 -1.45 0.1470 -0.1207 0.0180 Lane Width × Shoulder Width -0.1953 0.0510 -3.83 0.0000 -0.2952 -0.0954 Indicator for Year = 2003 0.1786 0.2039 0.88 0.3810 -0.2210 0.5782 Indicator for Year = 2004 -0.3356 0.2271 -1.48 0.1400 -0.7808 0.1096 Indicator for Year = 2005 -0.3176 0.2263 -1.40 0.1610 -0.7612 0.1260 Indicator for Year = 2006 -0.0763 0.2157 -0.35 0.7240 -0.4990 0.3464 Indicator for Year = 2007 0.0013 0.2110 0.01 0.9950 -0.4123 0.4148 Indicator for Year = 2008 -0.1351 0.2180 -0.62 0.5350 -0.5623 0.2921 Indicator for Year = 2009 -0.1214 0.2180 -0.56 0.5780 -0.5487 0.3058 Indicator for Year = 2010 -0.2763 0.2229 -1.24 0.2150 -0.7132 0.1606 Indicator for Year = 2011 -0.0712 0.2221 -0.32 0.7480 -0.5065 0.3641 Indicator for Year = 2012 -0.2937 0.2372 -1.24 0.2160 -0.7587 0.1713 Constant -4.8442 0.6359 -7.62 0.0000 -6.0905 -3.5978 alpha (α) 0.2210 0.0755 0.1131 0.4315 Table B23. Target crash SPF for combination of centerline and shoulder rumble strips.

B-28 Guidelines for the Development and Application of Crash Modification Factors 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. 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. The two com- bined treatments 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. A cross-sectional study design is a type of observational study used to analyze a representative sample at a specific point in time. The safety effect is estimated by taking the ratio of the average crash frequency for two groups, one with the feature of interest and the other without the feature of interest. For this method to work, the two groups should be similar in all regards except for the feature of interest. To minimize differences among the groups, propensity score matching was employed, and multivariate regression models were used to estimate the safety effects of one feature while controlling for other characteristics that vary among sites. Multivariate regression was used to develop a statistical relationship between the dependent variable and a set of predictor variables. In this case, crash frequency was the dependent vari- able of interest, and several predictor variables were considered, including lane width, shoulder width, and other roadway and operational characteristics. Coefficients were estimated during the modeling process for each of the predictor variables. The coefficients represent the expected change in the dependent variable (crash frequency) due to a unit change in the predictor vari- able, all else being equal. The current state-of-the-practice for developing crash prediction models is to assume a log- linear relationship between crash frequency and site characteristics. GLM techniques were applied to develop the models, and a log-linear relationship was specified using a negative binomial error structure. The negative binomial error structure also has advantages over the Poisson distribution in that it allows for over-dispersion of the variance that is often present in crash data. There are several potential sources of bias in the development of crash prediction models. The following is a list of potential sources of bias with an explanation of how they were addressed. • Selection of appropriate functional form. Functional form relates to both the overall form of the model and the form of each independent variable. The current state-of-the-practice was used for the overall form of the model (i.e., log-linear relationship), and exploratory data analysis techniques were used to identify an appropriate form for each predictor. • Correlation among independent variables. Correlation refers to the degree of association among variables. A high degree of correlation among the predictor variables makes it difficult to determine a reliable estimate of the effects of specific predictor variables. The correlation matrix was examined to determine the extent of correlation among independent variables and used to prioritize variables for inclusion. • Over-fitting of prediction models. Over-fitting is related to the concept of diminishing returns. At some point, it is not worth adding any more independent variables to the model because they do not significantly improve the model fit. Over-fitting also increases the oppor- tunity to introduce inter-correlation between independent variables, and the opportunity for small sample issues when considering indicator variables. Several combinations of predictor variables were considered, and relative goodness-of-fit (GOF) measures were employed to penalize models with greater estimated parameters.

Procedure for Estimating the Combined Safety Effect of Two Treatments B-29   The multivariate models were developed by identifying base models with traffic volume only, exploring the effects of adding other predictor variables to the models, and then selecting the final model. Having developed the base models for each crash type (traffic volume only), additional variables were considered. Once a variable was included in the model, the estimated parameters and associated standard errors were examined to determine the following: • Is the direction of effect (i.e., expected decrease or increase in crashes) in general agreement with expectations? • Does the magnitude of the effect seem reasonable? • Are the parameters of the model estimated with statistical significance? • Does the estimated over-dispersion parameter improve significantly? The remainder of this section presents the SPFs developed for each focus crash type (i.e., total, fatal and injury, run-off-road, and target crashes). The following is the general form of the SPFs. = × ( )β × +β × + +β × Equation B6SPF length econstant+ log AADT X . . . X1 2 2 n n where, length = segment length (miles) Constant = constant estimated during modeling process Log(AADT) = natural log of traffic volume β1 – βn = Coefficients estimated during modeling process X2 – Xn = variables included in given SPF Variable Coefficient Standard Error Z- score P-value Lower 95% Conf. Int. Upper 95% Conf. Int. State 1 (1=Washington; 0=Illinois) -0.3155 0.0427 -7.39 0.0000 -0.3992 -0.2319 State 1 (1=Ohio; 0=Illinois) 0.4170 0.0340 12.27 0.0000 0.3504 0.4836 11-ft lanes and 4-ft shoulders -0.0057 0.0634 -0.09 0.9290 -0.1299 0.1186 11-ft lanes and 8-ft shoulders -0.1140 0.0756 -1.51 0.1320 -0.2622 0.0342 12-ft lanes and 3-ft shoulders -0.0794 0.0589 -1.35 0.1780 -0.1949 0.0360 12-ft lanes and 4-ft shoulders -0.1359 0.0566 -2.40 0.0160 -0.2468 -0.0250 12-ft lanes and 8-ft shoulders -0.1621 0.0558 -2.91 0.0040 -0.2715 -0.0528 log(AADT) 0.7858 0.0217 36.13 0.0000 0.7432 0.8284 Constant -5.0209 0.1733 -28.98 0.0000 -5.3605 -4.6813 alpha (α) 0.4016 0.0219 0.3609 0.4469 Note: Baseline for lane and shoulder combinations is 11-ft lanes and 3-ft shoulders. Table B24. Total crash SPF for lane and shoulder width on tangents. Variable Coefficient Standard Error Z- score P-value Lower 95% Conf. Int. Upper 95% Conf. Int. State 1 (1=Washington; 0=Illinois) 0.2750 0.0677 4.06 0.0000 0.1423 0.4077 State 1 (1=Ohio; 0=Illinois) 0.5594 0.0554 10.09 0.0000 0.4508 0.6681 11-ft lanes and 4-ft shoulders 0.0147 0.1006 0.15 0.8840 -0.1826 0.2119 11-ft lanes and 8-ft shoulders -0.4195 0.1268 -3.31 0.0010 -0.6679 -0.1711 12-ft lanes and 3-ft shoulders -0.2288 0.0949 -2.41 0.0160 -0.4149 -0.0427 12-ft lanes and 4-ft shoulders -0.1904 0.0885 -2.15 0.0310 -0.3638 -0.0170 12-ft lanes and 8-ft shoulders -0.3291 0.0879 -3.74 0.0000 -0.5014 -0.1567 log(AADT) 0.9338 0.0365 25.57 0.0000 0.8622 1.0054 Constant -7.7936 0.2945 -26.46 0.0000 -8.3708 -7.2164 alpha (α) 0.3639 0.0460 0.2840 0.4663 Note: Baseline for lane and shoulder combinations is 11-ft lanes and 3-ft shoulders. Table B25. Fatal and injury crash SPF for lane and shoulder width on tangents.

B-30 Guidelines for the Development and Application of Crash Modification Factors Variable Coefficient Standard Error Z- score P-value Lower 95% Conf. Int. Upper 95% Conf. Int. State 1 (1=Washington; 0=Illinois) 0.3578 0.0599 5.97 0.0000 0.2403 0.4752 State 1 (1=Ohio; 0=Illinois) 0.5174 0.0511 10.13 0.0000 0.4173 0.6175 11-ft lanes and 4-ft shoulders -0.1984 0.0895 -2.22 0.0270 -0.3739 -0.0230 11-ft lanes and 8-ft shoulders -0.3696 0.1084 -3.41 0.0010 -0.5820 -0.1572 12-ft lanes and 3-ft shoulders -0.3096 0.0825 -3.75 0.0000 -0.4714 -0.1479 12-ft lanes and 4-ft shoulders -0.3538 0.0779 -4.54 0.0000 -0.5065 -0.2011 12-ft lanes and 8-ft shoulders -0.4941 0.0780 -6.33 0.0000 -0.6470 -0.3412 log(AADT) 0.6818 0.0323 21.14 0.0000 0.6186 0.7451 Constant -5.3626 0.2558 -20.96 0.0000 -5.8640 -4.8612 alpha (α) 0.4130 0.0414 0.3393 0.5026 Note: Baseline for lane and shoulder combinations is 11-ft lanes and 3-ft shoulders. Table B26. Run-off-road crash SPF for lane and shoulder width on tangents. Variable Coefficient Standard Error Z- score P-value Lower 95% Conf. Int. Upper 95% Conf. Int. State 1 (1=Washington; 0=Illinois) 0.2492 0.0564 4.41 0.0000 0.1386 0.3598 State 1 (1=Ohio; 0=Illinois) 0.5613 0.0468 11.99 0.0000 0.4696 0.6531 11-ft lanes and 4-ft shoulders -0.1999 0.0840 -2.38 0.0170 -0.3645 -0.0353 11-ft lanes and 8-ft shoulders -0.3571 0.1010 -3.53 0.0000 -0.5551 -0.1590 12-ft lanes and 3-ft shoulders -0.2961 0.0772 -3.84 0.0000 -0.4473 -0.1449 12-ft lanes and 4-ft shoulders -0.3722 0.0731 -5.09 0.0000 -0.5155 -0.2289 12-ft lanes and 8-ft shoulders -0.4366 0.0726 -6.02 0.0000 -0.5789 -0.2944 log(AADT) 0.7629 0.0302 25.24 0.0000 0.7037 0.8222 Constant -5.8411 0.2407 -24.27 0.0000 -6.3129 -5.3694 alpha (α) 0.3699 0.0349 0.3075 0.4450 Note: Baseline for lane and shoulder combinations is 11-ft lanes and 3-ft shoulders. Table B27. Target crash SPF for lane and shoulder width on tangents. Variable Coefficient Standard Error Z- score P-value Lower 95% Conf. Int. Upper 95% Conf. Int. State (1=Washington; 0=Ohio) -0.7749 0.0829 -9.35 0.0000 -0.9374 -0.6124 11-ft lanes and 4-ft shoulders 0.0907 0.1429 0.63 0.5260 -0.1895 0.3709 11-ft lanes and 8-ft shoulders -0.2105 0.1678 -1.25 0.2100 -0.5394 0.1184 12-ft lanes and 2-ft shoulders -0.1230 0.1577 -0.78 0.4360 -0.4322 0.1862 12-ft lanes and 4-ft shoulders -0.1343 0.1290 -1.04 0.2980 -0.3872 0.1186 12-ft lanes and 8-ft shoulders -0.2745 0.1373 -2.00 0.0460 -0.5436 -0.0053 1/degree of curve -0.1414 0.0789 -1.79 0.0730 -0.2961 0.0132 log(AADT) 0.7499 0.0505 14.85 0.0000 0.6509 0.8489 Constant -3.8411 0.3975 -9.66 0.0000 -4.6202 -3.0620 alpha (α) 0.4690 0.0735 0.3449 0.6376 Note: Baseline for lane and shoulder combinations is 11-ft lanes and 2-ft shoulders. Table B28. Total crash SPF for lane and shoulder width on curves.

Procedure for Estimating the Combined Safety Effect of Two Treatments B-31   Variable Coefficient Standard Error Z- score P-value Lower 95% Conf. Int. Upper 95% Conf. Int. State (1=Washington; 0=Ohio) -0.3147 0.1346 -2.34 0.0190 -0.5786 -0.0509 11-ft lanes and 4-ft shoulders 0.1183 0.2150 0.55 0.5820 -0.3030 0.5396 11-ft lanes and 8-ft shoulders -0.4534 0.2645 -1.71 0.0860 -0.9719 0.0650 12-ft lanes and 2-ft shoulders -0.2828 0.2552 -1.11 0.2680 -0.7829 0.2174 12-ft lanes and 4-ft shoulders -0.1789 0.1975 -0.91 0.3650 -0.5661 0.2083 12-ft lanes and 8-ft shoulders -0.4176 0.2145 -1.95 0.0520 -0.8380 0.0028 1/degree of curve -0.2503 0.1416 -1.77 0.0770 -0.5279 0.0272 log(AADT) 0.7275 0.0758 9.60 0.0000 0.5790 0.8760 Constant -4.9578 0.6036 -8.21 0.0000 -6.1409 -3.7748 alpha (α) 0.4940 0.1827 0.2393 1.0199 Note: Baseline for lane and shoulder combinations is 11-ft lanes and 2-ft shoulders. Table B29. Fatal and injury crash SPF for lane and shoulder width on curves. Variable Coefficient Standard Error Z- score P-value Lower 95% Conf. Int. Upper 95% Conf. Int. State (1=Washington; 0=Ohio) -0.2548 0.1203 -2.12 0.0340 -0.4906 -0.0190 11-ft lanes and 4-ft shoulders 0.1079 0.1839 0.59 0.5570 -0.2524 0.4683 11-ft lanes and 8-ft shoulders -0.4617 0.2306 -2.00 0.0450 -0.9137 -0.0097 12-ft lanes and 2-ft shoulders -0.0499 0.2030 -0.25 0.8060 -0.4478 0.3480 12-ft lanes and 4-ft shoulders -0.1386 0.1683 -0.82 0.4100 -0.4684 0.1913 12-ft lanes and 8-ft shoulders -0.5967 0.1904 -3.13 0.0020 -0.9699 -0.2235 1/degree of curve -0.4179 0.1393 -3.00 0.0030 -0.6909 -0.1449 log(AADT) 0.6597 0.0677 9.74 0.0000 0.5270 0.7924 Constant -3.9134 0.5347 -7.32 0.0000 -4.9614 -2.8653 alpha (α) 0.9188 0.1626 0.6494 1.2999 Note: Baseline for lane and shoulder combinations is 11-ft lanes and 2-ft shoulders. Table B30. Run-off-road crash SPF for lane and shoulder width on curves. Variable Coefficient Standard Error Z- score P-value Lower 95% Conf. Int. Upper 95% Conf. Int. State (1=Washington; 0=Ohio) -0.3881 0.1142 -3.40 0.0010 -0.6120 -0.1642 11-ft lanes and 4-ft shoulders 0.1193 0.1781 0.67 0.5030 -0.2297 0.4684 11-ft lanes and 8-ft shoulders -0.4916 0.2250 -2.18 0.0290 -0.9326 -0.0506 12-ft lanes and 2-ft shoulders -0.0548 0.1962 -0.28 0.7800 -0.4393 0.3296 12-ft lanes and 4-ft shoulders -0.1484 0.1631 -0.91 0.3630 -0.4681 0.1712 12-ft lanes and 8-ft shoulders -0.5529 0.1822 -3.03 0.0020 -0.9101 -0.1957 1/degree of curve -0.3589 0.1275 -2.81 0.0050 -0.6089 -0.1090 log(AADT) 0.6733 0.0656 10.26 0.0000 0.5447 0.8019 Constant -3.8550 0.5175 -7.45 0.0000 -4.8692 -2.8407 alpha (α) 0.9086 0.1494 0.6582 1.2542 Note: Baseline for lane and shoulder combinations is 11-ft lanes and 2-ft shoulders. Table B31. Target crash SPF for lane and shoulder width on curves.

B-32 Guidelines for the Development and Application of Crash Modification Factors 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. The two individual treatment effects were defined as: • Individual intersection sight distance (ISD) effect: Available ISD of more than 1,320 ft com- pared 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 The combined treatment effect was defined as available ISD of more than 1,320 ft and inter- section angle of 85 degrees to 90 degrees compared to baseline conditions for both. The previous section described the general cross-sectional study design. Again, for this method to work, the two groups should be similar in all regards except for the feature of interest. To min- imize differences among the groups, propensity score matching was employed, and multivariate regression models were used to estimate the safety effects of one feature while controlling for other characteristics that vary among sites. Multivariate regression was used to develop a statistical relationship between the dependent variable and a set of predictor variables. In this case, crash frequency was the dependent variable of interest and several predictor variables were considered, including ISD, intersection angle, and other roadway and operational characteristics. Coefficients were estimated during the modeling process for each of the predictor variables. The coefficients represent the expected change in the dependent variable (crash frequency) due to a unit change in the predictor vari- able, all else being equal. The current state-of-the-practice for developing crash prediction models is to assume a log- linear relationship between crash frequency and site characteristics. GLM techniques were applied to develop the models, and a log-linear relationship was specified using a negative binomial error structure. The negative binomial error structure also has advantages over the Poisson distribution in that it allows for over-dispersion of the variance that is often present in crash data. There are several potential sources of bias in the development of crash prediction models. The following is a list of potential sources of bias with an explanation of how they were addressed. • Selection of appropriate functional form. Functional form relates to both the overall form of the model and the form of each independent variable. The current state-of-the-practice was used for the overall form of the model (i.e., log-linear relationship), and exploratory data analysis techniques were used to identify an appropriate form for each predictor. • Correlation among independent variables. Correlation refers to the degree of association among variables. A high degree of correlation among the predictor variables makes it difficult to determine a reliable estimate of the effects of specific predictor variables. The correlation matrix was examined to determine the extent of correlation among independent variables and used to prioritize variables for inclusion. • Over-fitting of prediction models. Over-fitting is related to the law of diminishing returns. At some point, it is not worth adding any more independent variables to the model because they do not significantly improve the model fit. Over-fitting also increases the opportunity to introduce correlation in the model. Several combinations of predictor variables were con- sidered, and relative GOF measures were employed to penalize models with more estimated parameters. The multivariate models were developed by identifying base models with traffic volume only, exploring the effects of adding other predictor variables to the models, and then selecting the final model. Having developed the base models for each crash type (traffic volume only),

Procedure for Estimating the Combined Safety Effect of Two Treatments B-33   additional variables were considered. Once a variable was included in the model, the estimated parameters and associated standard errors were examined to determine: • Is the direction of effect (i.e., expected decrease or increase in crashes) in general agreement with expectations? • Does the magnitude of the effect seem reasonable? • Are the parameters of the model estimated with statistical significance? • Does the estimated over-dispersion parameter improve significantly? The remainder of this section presents the SPFs developed for each focus crash type (i.e., total target, fatal and injury target, and right-angle crashes). The following is the general form of the SPFs. X= ( ) ( )β × +β × +β × + +β × Equation B7SPF econstant+ log AADT Major log AADT Minor . . . X1 2 3 3 n n where, length = segment length (miles) Constant = constant estimated during modeling process Log(AADT Major) = natural log of major-road traffic volume Log(AADT Minor) = natural log of minor-road traffic volume β1 – βn = Coefficients estimated during modeling process X3 – Xn = variables included in given SPF Variable Coefficient Standard Error Z- score P-value Lower 95% Conf. Int. Upper 95% Conf. Int. log(AADT Major) 0.7008 0.1555 4.51 0.0000 0.3960 1.0055 log(AADT Minor) 0.5475 0.1285 4.26 0.0000 0.2958 0.7993 Approaches (1=4-legged; 0=3- legged) 0.3956 0.2298 1.72 0.0850 -0.0547 0.8459 Direction (1=left; 0=right) 0.5978 0.2137 2.80 0.0050 0.1790 1.0166 Lane Width (1=12+ ft; 0 otherwise) -0.7026 0.2210 -3.18 0.0010 -1.1358 -0.2694 State 1 (1=North Carolina; 0=Ohio) -0.7008 0.2796 -2.51 0.0120 -1.2489 -0.1528 State 2 (1=Washington; 0=Ohio) -0.9531 0.3114 -3.06 0.0020 -1.5635 -0.3428 ISD = 500–750 0.7862 0.2648 2.97 0.0030 0.2673 1.3052 Intersection Angle = 50°–75° 0.8812 0.2838 3.11 0.0020 0.3250 1.4374 ISD and Intersection Angle Combination 0.7573 0.4512 1.68 0.0930 -0.1269 1.6416 Constant -11.6491 1.6827 -6.92 0.0000 -14.9470 -8.3511 alpha (α) 2.0650 0.4632 1.3304 3.2053 Table B32. Total target crash SPF for ISD and intersection angle. Variable Coefficient Standard Error Z- score P-value Lower 95% Conf. Int. Upper 95% Conf. Int. log(AADT Major) 0.6785 0.2066 3.28 0.0010 0.2737 1.0834 log(AADT Minor) 0.3882 0.1581 2.46 0.0140 0.0785 0.6980 Direction (1=left; 0=right) 0.7111 0.2869 2.48 0.0130 0.1488 1.2733 State 1 (1=North Carolina; 0=Ohio) -1.4426 0.3640 -3.96 0.0000 -2.1560 -0.7292 State 2 (1=Washington; 0=Ohio) -1.2501 0.3802 -3.29 0.0010 -1.9953 -0.5050 ISD = 500–750 1.3023 0.3732 3.49 0.0000 0.5708 2.0338 Intersection Angle = 50°–75° 1.5540 0.3803 4.09 0.0000 0.8087 2.2993 ISD and Intersection Angle Combination 0.1944 0.8343 0.23 0.8160 -1.4408 1.8296 Constant -11.3587 2.2317 -5.09 0.0000 -15.7327 -6.9847 alpha (α) 2.4519 0.8078 1.2855 4.6766 Table B33. Fatal and injury target crash SPF for ISD and intersection angle.

B-34 Guidelines for the Development and Application of Crash Modification Factors Variable Coefficient Standard Error Z- score P-value Lower 95% Conf. Int. Upper 95% Conf. Int. log(AADT Major) 0.6978 0.2243 3.11 0.0020 0.2581 1.1375 log(AADT Minor) 0.7770 0.1976 3.93 0.0000 0.3897 1.1642 Approaches (1=4-legged; 0=3- legged) 1.0985 0.3521 3.12 0.0020 0.4083 1.7886 Direction (1=left; 0=right) 0.5158 0.3059 1.69 0.0920 -0.0836 1.1153 Lane Width (1=12+ ft; 0 otherwise) -1.1093 0.3272 -3.39 0.0010 -1.7506 -0.4680 State 1 (1=North Carolina; 0=Ohio) -0.9164 0.3826 -2.40 0.0170 -1.6663 -0.1665 State 2 (1=Washington; 0=Ohio) -2.1091 0.5114 -4.12 0.0000 -3.1114 -1.1068 ISD = 500–750 1.3293 0.4270 3.11 0.0020 0.4923 2.1662 Intersection Angle = 50°–75° 1.6804 0.4408 3.81 0.0000 0.8164 2.5443 ISD and Intersection Angle Combination 1.9234 0.6110 3.15 0.0020 0.7259 3.1210 Constant -14.4170 2.5796 -5.59 0.0000 -19.4729 -9.3610 alpha (α) 3.2530 0.8777 1.9170 5.5201 Table B34. Right-angle crash SPF for ISD and intersection angle.

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