Adjusting finite sample bias in traffic safety modeling

Area of Science:

• Traffic Safety
• Statistical Modeling
• Risk Assessment

Background:

• Poisson and negative binomial regression models are standard for traffic safety analysis.
• Low event frequency (rare crashes) can cause finite sample bias in parameter estimation.
• This bias is a significant issue in traffic safety research.

Purpose of the Study:

• To apply a bias-correction procedure to Poisson and negative binomial regression models.
• To formulate a general bias-correction method.
• To evaluate the effectiveness of bias correction in traffic safety evaluations.

Main Methods:

• Developed a general bias-correction formulation for regression models.
• Illustrated bias with a single binary explanatory variable scenario.
• Conducted simulations to assess bias-corrected coefficient estimators.
• Applied the method to a case study of infrastructure safety.

Main Results:

• Bias-corrected estimators demonstrated reduced bias and smaller variance.
• The effect of bias correction was most significant with crash counts between 5 and 50.
• Case study confirmed larger bias correction magnitude for smaller crash counts.
• Identified factors influencing bias magnitude, including crash numbers and data balance.

Conclusions:

• Finite sample bias is a critical issue in traffic safety analysis due to rare crash events.
• Bias adjustment provides more accurate estimation of crash risk factors.
• The proposed bias-correction method enhances the reliability of safety evaluations.