T. P. Hutchinson

Statistical modelling of injury severity, with special reference to driver and front seat passenger in single-vehicle crashes

First, the statistical analysis of injury severity is introduced by considering the following topics: Interpretation of the recorded grades of injury severity (e.g. fatal, serious, slight, none) as divisions of a continuous scale. The possible presence of errors in recording injury severity. How this is used in the statistical analysis of injury severity data, including discussion of computing methods. Secondly, attention is turned to data in which the severities of injury to two people in the same crash is given. British accident data for 1969-72 has been processed to give a cross-tabulation of the severity of injury to the driver and to the front seat passenger in four types of single-vehicle accidents (overturning and nonoverturning, each in rural and in urban areas). Three complications with this data are that the number of non-injury accidents is unknown, that the cases where a passenger was present but uninjured could not be distinguished from those where there was no passenger, and that there is inconsistency in the positioning of the thresholds separating serious from slight injury, and slight from no injury. A positive correlation between the severities of injury to the two occupants is evident in the data. This is interpreted as being largely due to the speed of the crash, and a model is developed in which the two severities jointly have a bivariate normal distribution.

A generalisation of Gumbel's bivariate logistic distribution

SummaryThe bivariate distributionF(x, y)=1/[1+exp(−x)+exp(−y)] was examined byGumbel. We have generalised this expression by raising it to an arbitarary power. Such a distribution may occur as a mixture of bivariate extreme-value distribution. As well as giving its basic properties, we have paid special attention to measures of correlation alternative to the product-moment, namely, Kendalls and Spearmans rank correlations and the product-moment correlation calculated after transforming the marginal distributions into Normal ones. An application to the multifactorial model of disease transmission is outlined.

Compound gamma bivariate distributions

SummaryBivariate distributions, which may be of special relevance to the lifetimes of two components of a system, are derived using the following approach. As the two components are part of one system and therefore exposed to similar conditions of service, there will be similarity between their lifetimes that is not shared by components belonging to different systems. The lifetime distribution for a given system is assumed to be Gamma in form (this includes the exponential as a special case; extension to the Stacey distribution, which includes the Weibull distribution, is straightforward). The scale parameter of this distribution is itself a random variable, with a Gamma distribution. We thus obtain what might be termed a compound Gamma-Gamma bivariate distribution. The cumulative distribution function of this may be expressed in terms of one of the double hypergeometric functions of Appell.Generalised hypergeometric functions play an important part in this paper, and one of Sarans triple hypergeometric functions is obtained when generalising the above model to permit the scale parameters of the distributions for the two components to be correlated, rather than identical.

A BIVARIATE NORMAL MODEL FOR INTRA-ACCIDENT CORRELATIONS OF DRIVER INJURY WITH APPLICATION TO THE EFFECT OF MASS RATIO

The data analysed consists of the joint distribution of severities of injury to vehicle drivers in head-on crashes, stratified according to the relative masses of the vehicles. On the basis of some fairly strong assumptions, a model is developed which results in the joint distribution being bivariate normal. The parameters are interpretable in terms of the effect of velocity change on injury severity, and the relative variability of velocity change and of injury severity at a particular velocity change. The predictions made by the model enjoy a considerable degree of success.

A note on applications of the competing risks model

Methods proposed for estimating the distribution of fracture strengths of cadaver legs [Searle et al., 1978] and for estimating the distribution of free speeds of vehicles [Branston, 1979] are both shown to be examples of competing risks analysis.

International statistics of road fatalities

Abstract Road safety research and policy is usually based on the statistical information collected by the police. Where deaths are concerned, however, there is another source of information—the death certificate procedure. Statistics derived from this source contain very little information about the accident events or circumstances, but they can act as a check on the police statistics. This is particularly useful for countries whose police statistics of fatalities include only those dying within a short time after the accident.