Assessing quality of crash modification factors estimated by empirical Bayes before-after methods
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Assessing quality of crash modification factors estimated by empirical Bayes before-after methods CHEN Ying(陈英)1, 2, WU Ling-tao(吴玲涛)3, HUANG Zhong-xiang(黄中祥)1 1. School of Traffic and Transportation Engineering, Changsha University of Science & Technology, Changsha 410114, China; 2. School of Architecture, Changsha University of Science & Technology, Changsha 410114, China; 3. Center for Transportation Safety, Texas A&M Transportation Institute, Bryan, Texas, 77847, USA © Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract: Before-after study with the empirical Bayes (EB) method is the state-of-the-art approach for estimating crash modification factors (CMFs). The EB method not only addresses the regression-to-the-mean bias, but also improves accuracy. However, the performance of the CMFs derived from the EB method has never been fully investigated. This study aims to examine the accuracy of CMFs estimated with the EB method. Artificial realistic data (ARD) and real crash data are used to evaluate the CMFs. The results indicate that: 1) The CMFs derived from the EB before-after method are nearly the same as the true values. 2) The estimated CMF standard errors do not reflect the true values. The estimation remains at the same level regardless of the pre-assumed CMF standard error. The EB before-after study is not sensitive to the variation of CMF among sites. 3) The analyses with real-world traffic and crash data with a dummy treatment indicate that the EB method tends to underestimate the standard error of the CMF. Safety researchers should recognize that the CMF variance may be biased when evaluating safety effectiveness by the EB method. It is necessary to revisit the algorithm for estimating CMF variance with the EB method. Key words: traffic safety; empirical Bayes; crash modification factor; safety effectiveness evaluation Cite this article as: CHEN Ying, WU Ling-tao, HUANG Zhong-xiang. Assessing quality of crash modification factors estimated by empirical Bayes before-after methods [J]. Journal of Central South University, 2020, 27(8): 2259−2268. DOI: https://doi.org/10.1007/s11771-020-4447-2.
1 Introduction Roadway safety management includes seven steps: network screening, diagnosis, countermeasure selection, economic appraisal, project prioritization, and safety effectiveness evaluation. Evaluation is the last step. Nevertheless, it plays a critical role in the whole management process. The evaluation assesses how crashes (number and severity) have changed due to the
treatment(s) [1, 2]. The safety effectiveness is typically represented in the form of a crash reduction factor (CRF) or a crash modification factor (CMF) [3, 4]. Safety analysts have proposed various approaches to estimate CMFs for treatments: simple before-after study (also known as naïve before-after study), before-after studies with comparison group, before-after studies with empirical Bayes (EB) method, full Bayes (FB) before-after studies, regression modeling approach, and recently
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