Magnitude of selection bias in road safety epidemiology, a primer
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In the field of road safety epidemiology, it is common to use responsibility analyses to assess the effect of a given factor on the risk of being responsible for an accident, among drivers involved in an accident only. Using the SCM framework, we formally showed in previous works that the causal odds-ratio of a given factor correlated with high speed cannot be unbiasedly estimated through responsibility analyses if inclusion into the dataset depends on the accident severity. The objective of this present work is to present numerical results to give a first quantification of the magnitude of the selection bias induced by responsibility analyses. We denote the binary variables by X the exposure of interest, V the high speed, F the driving fault, R the responsibility of a severe accident, A the severe accident, and W a set of categorical confounders. We illustrate the potential bias by comparing the causal effect of interest of X on R, COR(X,R|W=w), and the estimable odds-ratio available in responsibility analyses, OR(X,R|W=w, A=1). By considering a binary exposure, and by varying a set of parameters, we describe a situation where X could represent alcohol or cannabis intoxication. We confirm that the estimable odds-ratio available in responsibility analyses is a biased measure of the causal effect when X is correlated with high speed V and V is related to the accident severity A. In this case, the magnitude of the bias is all the more important that these two relationships are strong. When X is likely to increase the risk to drive fast V, the estimable odds-ratio underestimates the causal effect. When X is likely to decrease the risk to drive fast V, the estimable odds-ratio upperestimates the causal effect. The values of the different causal quantities considered here are from one to five times higher (or lower) than the estimable quantity available in responsability analyses.
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