Gary Davis, Professor, Civil Engineering
In accident reconstruction, individual road accidents are treated as essentially deterministic events, although incomplete information can leave one uncertain about how exactly an accident happened. In statistical studies, on the other hand, accidents are treated as individually random, although the parameters governing their probability distributions may be modeled deterministically. Selection of one or the other of these approaches affects how data are interpreted, and here a simple deterministic model of a vehicle/pedestrian encounter is used to illustrate how naively applying statistical methods to aggregated data could lead to an ecological fallacy and to Simpson's paradox. It is suggested that these problems occur because the statistical regularities observed in accident data have no independent status but are simply the result of aggregating particular types and frequencies of mechanisms.In the U.S.A., the imposition and subsequent repeal of the 55 mph speed limit has led to an increasingly energetic debate concerning 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. Debate continues as to the causes of this relationship, and there is reason to suspect that it may be an artifact of measurement error and/or mixing of different crash types. This project undertook 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 travelling the crash site under similar conditions. Bayesian relative risk regression was 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 data set supported the existence of a U-shaped relationship, although crash risk clearly tended to increase as speed increased. The resulting logit model was then used to estimate the probability that a given speed could be considered a causal factor for each of the 10 Minnesota crashes.