Speed is a determining factor in road safety analysis. It is generally believed that an increase in speed harms road safety. However, it can also be argued that driving at high speed reduces the length of time exposure and thus the likelihood of a crash. It is therefore critical to clarify the roles that exposure and speed play in road safety analysis. This study evaluates the relationship between speed and crash risk with respect to distance and time exposure, using disaggregated crash and speed data collected from 112 road segments in Hong Kong. A joint probability model based on a full Bayesian method is applied simultaneously to model crash occurrence and crash severity. In addition, we consider the explanatory variables, including road design, weather conditions, and temporal distribution, in the proposed crash prediction model. The results indicate that average speed plays a significant role in crash risk, despite opposing correlations with respect to distance and time exposure; the correlation between speed and crash risk is positive when distance exposure is considered, but negative when time exposure is used. However, in both cases, speed is positively associated with the injury severity.
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