A comparison of two methods for estimating the effect of a countermeasure in the presence of regression effects

Abstract

The report studies the problem of estimating in a non-experimental before-and-after investigation the effect of a countermeasure on the number of traffic accidents at road junctions. The accidents are assumed to occur according to a Poisson process with different intensities at different junctions. The junctions studied in this investigation are assumed to have been selected with the blackspot-technique, i.e. junctions with high numbers of accidents during the before-period have been chosen for the investigation. In the mathematical model this has the consequence that the number of accidents occurring during the before-period at a selected junction has a truncated Poisson distribution. During the after-period the number of accidents has a Poisson distribution (without restrictions), so that the number of accidents on the average decreases between the periods even if the countermeasure has no effect. The magnitude of this regression effect is studied in the report. The observed numbers of accidents during the before and after period are used to estimate the pure effect of the countermeasure both with an intuitive method and with the maximum likelihood method. The characteristics of the two methods of estimation are illustrated with the aid of simulation studies. In general the maximum likelihood method appears preferable, mainly because it produces estimates with higher precision.