Adjusting finite sample bias in traffic safety modeling

Poisson and negative binomial regression models are fundamental statistical analysis tools for traffic safety evaluation. The regression parameter estimation could suffer from the finite sample bias when event frequency is low, which is commonly observed in safety research as crashes are rare events. In this study, we apply a bias-correction procedure to the parameter estimation of Poisson and NB regression models. We provide a general bias-correction formulation and illustrate the finite sample bias through a special scenario with a single binary explanatory variable. Several factors affecting the magnitude of bias are identified, including the number of crashes and the balance of the crash counts within strata of a categorical explanatory variable. Simulations are conducted to examine the properties of the bias-corrected coefficient estimators. The results show that the bias-corrected estimators generally provide less bias and smaller variance. The effect is especially pronounced when the crash count in one stratum is between 5 and 50. We apply the proposed method to a case study of infrastructure safety evaluation. Three scenarios were evaluated, all crashes collected in three years, and two hypothetical situations, where crash information was collected for "half-year" and "quarter-year" periods. The case-study results confirm that the magnitude of bias correction is larger for smaller crash counts. This paper demonstrates the finite sample bias associated with the small number of crashes and suggests bias adjustment can provide more accurate estimation when evaluating the impacts of crash risk factors.