Calibration of crash risk models on freeways with limited real-time traffic data using Bayesian meta-analysis and Bayesian inference approach

• We use meta-analysis and Bayesian inference to develop crash risk models with limited data.
• A systematic review was conducted by 3 different Bayesian meta-analyses.
• Informative priors for traffic variables are developed by three Bayesian meta-analyses.
• Model based on meta-regression achieve better predictive performance.
• Bayesian predictive densities analysis can identify outliers and increase model fit.

This study aimed to develop a real-time crash risk model with limited data in China by using Bayesian meta-analysis and Bayesian inference approach. A systematic review was first conducted by using three different Bayesian meta-analyses, including the fixed effect meta-analysis, the random effect meta-analysis, and the meta-regression. The meta-analyses provided a numerical summary of the effects of traffic variables on crash risks by quantitatively synthesizing results from previous studies. The random effect meta-analysis and the meta-regression produced a more conservative estimate for the effects of traffic variables compared with the fixed effect meta-analysis. Then, the meta-analyses results were used as informative priors for developing crash risk models with limited data. Three different meta-analyses significantly affect model fit and prediction accuracy. The model based on meta-regression can increase the prediction accuracy by about 15% as compared to the model that was directly developed with limited data. Finally, the Bayesian predictive densities analysis was used to identify the outliers in the limited data. It can further improve the prediction accuracy by 5.0%.