Comparison of Bayesian techniques for the before–after evaluation of the safety effectiveness of short 2+1 road sections

In evaluating the effectiveness of a road safety treatment, the regression to the mean phenomenon is a cause for concern because of a possible overestimation of benefits. Therefore, Bayesian approaches are usually suggested as the most appropriate methodologies for before—after studies as they account for regression to the mean effects. The empirical Bayes (EB) methodology examines the estimation of the expected number of crashes that would have occurred without treatment and compares them with the crashes observed at the treated sites. Even if there is no significant regression to the mean bias, the EB technique requires a reliable and large dataset with sufficient years of observation and number of treated sites, adequate for estimating the safety effects of a treatment with acceptable standard errors. In this framework, a full Bayesian (FB) approach can mitigate the problem of using small datasets by providing more detailed causal inferences and more flexibility in selecting crash count distributions, acknowledging that a more complex methodology must be applied. With the aim of estimating the safety improvements of new, short 2 + 1 road sections in Poland limited by the existing road network, EB and FB estimations are compared and different safety performance function (SPF) model forms are used in order to evaluate the performance of the two methodologies. Results indicated that, even if crash modification factors (CMFs) resulted in similar average values, the EB trend is to underestimate CMFs compared with the more complex methodology, while overall the FB approach provided a lower standard deviation. The differences are more pronounced between the EB and FB approaches when a simple SPF model form is used for the analysed dataset. Moreover, for this specific dataset, the difference between the FB method and the EB method using a refined regression model with more variables was negligible