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18 CHAPTER 5 Safety Evaluation This Chapter provides a summary of the results of the eval- of using crash rates in normalizing for volume differences uation of the five treatments mentioned in Chapter 4. The between the before and after periods and properly accounts first part of this Chapter gives an overview of the different for differences in crash experience and reporting practice in evaluation methods that were used to develop the CMFs. Fol- amalgamating data and results from diverse jurisdictions. lowing that is a summary of each evaluation that provides the The EB method estimates the expected crashes that would have description of the treatment, data used, methodology, and occurred in the after period () and compares that with the results. (Full details of each evaluation study are provided in a number of reported crashes in the after period (). series of appendices which can be found online at http://apps. The following steps are used to estimate : Three evaluation methods were used in this study. The 1. Identify a reference group of untreated sites that is otherwise primary, and preferred one, is the EB before-after method, similar to the treatment group. which is considered to be one of the best methods for con- 2. Use the reference group data to estimate safety performance ducting before-after studies in that it properly accounts for functions (SPFs) (mathematical equations) that predict regression to the mean. The second method utilized is the the number of crashes of different types as a function of traf- comparison group before-after method. This method does fic volumes and other site characteristics. Typically, SPFs not effectively address the bias due to regression to the mean, are negative binomial regression models that are esti- but is effective in accounting for other non-treatment effects mated using generalized linear modeling. such as those due to trends in crash reporting and changes in 3. In estimating SPFs, calibrate annual SPF multipliers (time traffic volume. The third method is based on cross-sectional trend factors) to account for the temporal effects (e.g., multiple regression models where the CMFs are derived based variation in weather, demography, and crash reporting) on the coefficients of variables in these models that pertain to on safety. the CMF. The cross-sectional regression models were used if 4. Use the SPFs, the annual SPF multipliers, and data on the sample size for the EB evaluation was limited. A secondary traffic volumes and site characteristics for each year in objective of using cross-section models for some evaluations the before period for each treatment site to estimate the was to examine the comparability of before-after and cross- number of crashes that would be predicted in each year of sectional studies, a subject of topical interest in CMF develop- the before period for each treatment site. ment, for which there is little research. An overview of these 5. Use the predicted number of crashes in the before period methods follows. More details can be found in a recent FHWA (from the SPFs) and the observed crashes in the before Guide entitled A Guide to Developing Quality Crash Modifica- period at each treatment site to estimate the EB-expected tion Factors (Gross et al., 2010). number of crashes in the before period in each site. The EB-expected crash frequency is then estimated to adjust Overview of Methods for possible bias due to regression to the mean. 6. Estimate (expected crashes in the after period if the Before-After Analysis Using treatment had not been implemented) as the product of the Empirical Bayes Method the EB-expected number of crashes in the before period The EB method properly accounts for regression to the mean and the sum of the annual SPF predictions for the after bias in before-after studies. It also overcomes the difficulties period divided by the sum of these predictions for the