Evaluating Time Trend Correction Approaches Associated with Empirical Bayes Before-after Study for Road Safety

The Empirical Bayes (EB) before-after study is used extensively for reliable safety evaluation. The EB method has the advantage of addressing confounding factors, including the regression-to-the-mean phenomenon and change of traffic volume. The EB method can also address the time trend effect by two approaches, i.e., the Yearly Multiplier (YM) and the Simple Crash Ratio of a Reference group (SCRR). However, the use of the YM without adjusting the over-dispersion parameter may induce a biased estimation of the Bayesian inference. This study aims to provide the systematic evaluation of the two approaches for correcting the time trend. To achieve this, a numerical example and its sensitivity analysis are presented. The bias due to the use of the YM is also measured based on the empirical data from Korean freeways. The findings of this study show the EB method with SCRR would be a useful approach as a time trend correction approach, especially when the reference group has experienced a considerable time trend.