Motor vehicle crashes are one of the leading causes of death in the United States. Traffic safety research targets at understanding the cause of crash, preventing the crash, and mitigating crash severity. This dissertation focuses on the driver-related traffic safety issues, in particular, on developing and implementing contemporary statistical modeling techniques on driving risk research on Naturalistic Driving Study data. The dissertation includes 5 chapters. In Chapter 1, I introduced the backgrounds of traffic safety research and naturalistic driving study. In Chapter 2, the state-of-practice statistical methods were implemented on individual driver risk assessment using NDS data. The study showed that critical-incident events and driver demographic characteristics can serve as good predictors for identifying risky drivers. In Chapter 3, I developed and evaluated a novel Bayesian random exposure method for Poisson regression models to account for situations where the exposure information needs to be estimated. Simulation studies and real data analysis on Cellphone Pilot Analysis study data showed that, random exposure models have significantly better model fitting performances and higher parameter coverage probabilities as compared to traditional fixed exposure models. The advantage is more apparent when the values of Poisson regression coefficients are large. In Chapter 4, I performed comprehensive simulation-based performance analyses to investigate the type-I error, power and coverage probabilities on summary effect size in classical meta-analysis models. The results shed some light for reference on the prospective and retrospective performance analysis in meta-analysis research. In Chapter 5, I implemented classical- and Bayesian-approach multi-group hierarchical models on 100-Car data. Simulation-based retrospective performance analyses were used to investigate the powers and parameter coverage probabilities among different hierarchical models. The results showed that under fixed-effects model context, complex secondary tasks are associated with higher driving risk. / Ph. D.