Accounting for heterogeneity among treatment sites and time trends in developing crash modification functions

Collision modification factors (CMFs) are commonly used to quantify the impact of safety countermeasures. The CMFs obtained from observational before-after (BA) studies are usually estimated by averaging the safety impact (i.e., index of effectiveness) for a group of treatment sites. The heterogeneity among the treatment locations, in terms of their characteristics, and the effect of this heterogeneity on safety treatment effectiveness are usually ignored. This is in contrast to treatment evaluations in other fields like medical statistics where variations in the magnitude (or in the direction) of response to the same treatment given to different patients are considered. This paper introduces an approach for estimating a CMFunction from BA safety studies that account for variable treatment location characteristics (heterogeneity). The treatment sites heterogeneity was incorporated into the CMFunction using fixed-effects and random-effects regression models. In addition to heterogeneity, the paper also advocates the use of CMFunctions with a time variable to acknowledge that the safety treatment (intervention) effects do not occur instantaneously but are spread over future time. This is achieved using non-linear intervention (Koyck) models, developed within a hierarchical full Bayes (FB) context. To demonstrate the approach, a case study is presented to evaluate the safety effectiveness of the "Signal Head Upgrade Program" recently implemented in the city of Surrey (British Columbia, Canada), where signal visibility was improved at several urban signalized intersections. The results demonstrated the importance of considering treatment sites heterogeneity and time trends when developing CMFunctions.