Measuring safety treatment effects using full Bayes non‐linear safety performance intervention functions

Full Bayes linear intervention models have been recently proposed to conduct before–after safety studies. These models assume linear slopes to represent the time and treatment effects across the treated and comparison sites. However, the linear slope assumption can only furnish some restricted treatment profiles. To overcome this problem, a first‐order autoregressive (AR1) safety performance function (SPF) that has a dynamic regression equation (known as the Koyck model) is proposed. The non‐linear ‘Koyck’ model is compared to the linear intervention model in terms of inference, goodness‐of‐fit, and application. Both models were used in association with the Poisson‐lognormal (PLN) hierarchy to evaluate the safety performance of a sample of intersections that have been improved in the Greater Vancouver area. The two models were extended by incorporating random parameters to account for the correlation between sites within comparison–treatment pairs. Another objective of the paper is to compute basic components related to the novelty effects, direct treatment effects, and indirect treatment effects and to provide simple expressions for the computation of these components in terms of the model parameters. The Koyck model is shown to furnish a wider variety of treatment profiles than those of the linear intervention model. The analysis revealed that incorporating random parameters among matched comparison–treatment pairs in the specification of SPFs can significantly improve the fit, while reducing the estimates of the extra‐Poisson variation. Also, the proposed PLN Koyck model fitted the data much better than the Poisson‐lognormal linear intervention (PLNI) model. The novelty effects were short lived, the indirect (through traffic volumes) treatment effects were approximately within ±10%, whereas the direct treatment effects indicated a non‐significant 6.5% reduction during the after period under PLNI compared to a significant 12.3% reduction in predicted collision counts under the PLN Koyck model.