Modelling the hierarchical structure of road crash data--application to severity analysis.

Road crashes have an unquestionably hierarchical crash-car-occupant structure. Multilevel models are used with correlated data, but their application to crash data can be difficult. The number of sub-clusters per cluster is small, with less than two cars per crash and less than two occupants per car, whereas the number of clusters can be high, with several hundred/thousand crashes. Application of the Monte-Carlo method on observed and simulated French road crash data between 1996 and 2000 allows comparing estimations produced by multilevel logistic models (MLM), Generalized Estimating Equation models (GEE) and logistic models (LM). On the strength of a bias study, MLM is the most efficient model while both GEE and LM underestimate parameters and confidence intervals. MLM is used as a marginal model and not as a random-effect model, i.e. only fixed effects are taken into account. Random effects allow adjusting risks on the hierarchical structure, conferring an interpretative advantage to MLM over GEE. Nevertheless, great care is needed for data coding and quite a high number of crashes are necessary in order to avoid problems and errors with estimates and estimate processes. On balance, MLM must be used when the number of vehicles per crash or the number of occupants per vehicle is high, when the LM results are questionable because they are not in line with the literature or finally when the p-values associated to risk measures are close to 5%. In other cases, LM remains a practical analytical tool for modelling crash data.

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