Speed as a risk factor in serious run-off-road crashes: Bayesian case-control analysis with case speed uncertainty

In the United States, the imposition and subsequent repeal of the 55 mph speed limit has led to an energetic debate on the relationship between speed and the risk of being in a (fatal) crash. In addition, research done in the 1960s and 1970s suggested that crash risk is a U-shaped function of speed, with risk increasing as one travels both faster and slower than what is average on a road. This paper describes two case-control analyses of run-off-road crashes, one using data collected in Adelaide, Australia, and the other using data from Minnesota. In both analyses the speeds of the case vehicles were estimated using accident reconstruction techniques while the speeds of the controls were measured for vehicles traveling the crash site under similar conditions. Bayesian relative risk regression was then used to relate speed to crash risk, and uncertainty in the case speeds was accounted for by treating these as additional unknowns with informative priors. Neither dataset supported the existence of a U-shaped relationship, although risk of a serious or fatal run-off-road crash clearly tended to increase as speed increased.