A fully Bayesian multivariate approach to before-after safety evaluation

This paper presents a fully Bayesian multivariate approach to before-after safety evaluation. Although empirical Bayes (EB) methods have been widely accepted as statistically defensible safety evaluation tools in observational before-after studies for more than a decade, EB has some limitations such that it requires a development and calibration of reliable safety performance functions (SPFs) and the uncertainty in the EB safety effectiveness estimates may be underestimated when a fairly large reference group is not available. This is because uncertainty (standard errors) of the estimated regression coefficients and dispersion parameter in SPFs is not reflected in the final safety effectiveness estimate of EB.Fully Bayesian (FB) methodologies in safety evaluation are emerging as the state-of-the-art methods that have a potential to overcome the limitations of EB in that uncertainty in regression parameters in the FB approach is propagated throughout the model and carries through to the final safety effectiveness estimate. Nonetheless, there have not yet been many applications of fully Bayesian methods in before-after studies. Part of reasons is the lack of documentation for a step-by-step FB implementation procedure for practitioners as well as an increased complexity in computation. As opposed to the EB methods of which steps are well-documented in the literature for practitioners, the steps for implementing before-after FB evaluations have not yet been clearly established, especially in more general settings such as a before-after study with a comparison group/comparison groups. The objectives of this paper are two-fold: (1) to develop a fully Bayesian multivariate approach jointly modeling crash counts of different types or severity levels for a before-after evaluation with a comparison group/comparison groups and (2) to establish a step-by-step procedure for implementing the FB methods for a before-after evaluation with a comparison group/comparison groups.The fully Bayesian multivariate approach introduced in this paper has additional advantages over the corresponding univariate approaches (whether classical or Bayesian) in that the multivariate approach can recover the underlying correlation structure of the multivariate crash counts and can also lead to a more precise safety effectiveness estimate by taking into account correlations among different crash severities or types for estimation of the expected number of crashes. The new method is illustrated with the multivariate crash count data obtained from expressways in Korea for 13 years to assess the safety effectiveness of decreasing the posted speed limit.