The covariance between the number of accidents and the number of victims in multivariate analysis of accident related outcomes

Abstract

In this study some statistical issues involved in the simultaneous analysis of accident related outcomes of the road traffic process are investigated. Since accident related outcomes like the number of victims, fatalities or accidents show interdependencies, their simultaneous analysis requires that these interdependencies are taken into account. One particular interdependency is the number of fatal accidents that is always smaller than the number of fatalities as at least one fatality results from a fatal accident. More generally, when the number of accidents increases, the number of people injured as a result of these accidents will also increase. Since dependencies between accident related outcomes are reflected in the variance-covariance structure of the outcomes, the main focus of the present study is on establishing this structure. As this study shows it is possible to derive relatively simple expressions for estimates of the variances and covariances of (logarithms of) accidents and victim counts. One example reveals a substantial effect of the inclusion of covariance terms in the estimation of a confidence region of a mortality rate. The accuracy of the estimated variance-covariance structure of the accident related outcomes is evaluated using samples of real life accident data from The Netherlands. Additionally, the effect of small expected counts on the variance estimate of the logarithm of the counts is investigated.