The existing studies on drivers’ injury severity include numerous statistical models that assess potential factors affecting the level of injury. These models should address specific concerns tailored to different crash characteristics. For rear-end crashes, potential correlation in injury severity may present between the two drivers involved in the same crash. Moreover, there may exist unobserved heterogeneity considering parameter effects, which may vary across both crashes and individuals. To address these concerns, a random parameters bivariate ordered probit model has been developed to examine factors affecting injury sustained by two drivers involved in the same rear-end crash between passenger cars. Taking both the within-crash correlation and unobserved heterogeneity into consideration, the proposed model outperforms the two separate ordered probit models with fixed parameters. The value of the correlation parameter demonstrates that there indeed exists significant correlation between two drivers’ injuries. Driver age, gender, vehicle, airbag or seat belt use, traffic flow, etc., are found to affect injury severity for both the two drivers. Some differences can also be found between the two drivers, such as the effect of light condition, crash season, crash position, etc. The approach utilized provides a possible use for dealing with similar injury severity analysis in future work.

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Social and economic burdens caused by truck-involved rear-end collisions are of great concern to public health and the environment. However, few efforts focused on identifying the difference of impacting factors on injury severity between car-strike-truck and truck-strike-car in rear-end collisions. In light of the above, this study focuses on illustrating the impact of variables associated with injury severity in truck-related rear-end crashes. To this end, truck involved rear-end crashes between 2006 and 2015 in the U.S. were obtained. Three random parameters ordered probit models were developed: two separate models for the car-strike-truck crashes and the truck-strike-car crashes, respectively, and one for the combined dataset. The likelihood ratio test was conducted to evaluate the significance of the difference between the models. The results show that there is a significant difference between car-strike-truck and truck-strike-car crashes in terms of contributing factors towards injury severity. In addition, indicators reflecting male, truck, starting or stopped in the road before a crash, and other vehicles stopped in lane show a mixed impact on injury severity. Corresponding implications were discussed according to the findings to reduce the possibility of severe injury in truck-involved rear-end collisions.