Investigating the Development of CMFs from Probability Analyses [Final Report]
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Investigating the Development of CMFs from Probability Analyses [Final Report]

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      The Highway Safety Manual (HSM) defines a Crash Modification Factor (CMF) as the ratio of the number of crashes expected after a modification or measure implementation to the number of crashes per unit of time estimated if the change does not take place. The success of applying methods such as the cross-sectional, and before-after analyses to estimate CMFs is highly dependent on the size of the data available and specific characteristics about the crashes under study. Significant challenges are present when evaluating the safety performance of improvements in the face of limited crash data or extremely rare crashes. A representative sample of locations is needed for a robust crash frequency safety analysis, in general, drawing a representative sample of sites will result in many sampled sites (if not all sites) having zero crashes under low crash frequency conditions. Fortunately, probability-based analysis is applicable in those cases. However, it is not completely clear how a safety effect estimated from these types of analyses relates to the definition of a CMF in the HSM that is based on crash frequency, not crash risk. This research investigated the feasibility of developing reliable CMFs for countermeasures using risk analysis.

      Through the development of a theoretical framework that links the odds ratio (OR) derived from probability-based analysis (PBA) and the true CMF, researchers proposed an alternative estimator of the CMF derived from PBA (CMF_PBA) consisting of a modification of the OR based on the base odds of crashes in the population of sites under study. Researchers demonstrated that this modified estimator is not dependent on the sampling procedure. Under the theoretical framework, researchers showed that the OR should generally exhibit bias from the true CMF. One would draw over-optimistic results if the true CMF were smaller than one or over-pessimistic results if the CMF were larger than one. Researchers used simulated scenarios to test the performance of the two probability-based estimates (CMF_PBA and OR) and a comparable frequency-based analysis estimate (CMF_FBA). The results of these analysis showed that the CMF_FBA is in general the best estimate of the three, except in the case of rare crashes (i.e., the expectation of a crash is very small). In that case, researchers found the CMF_FBA to exhibit a significant positive bias when estimating small values of the true CMF, and that both the OR and the CMF_PBA were robust against that bias. Researchers recommend the use retrospective analysis in those cases, and the adoption of the CMF_PBA over the OR when estimating roadway safety effects since the CMF_PBA performed significantly better over the OR across an ample set of scenarios, as found from the analysis of the simulation results.

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