Can a safety-in-numbers effect and a hazard-in-numbers effect co-exist in the same data?

Abstract

Safety-in-numbers denotes a non-linear relationship between exposure (traffic volume) and the number of accidents, characterised by declining risk as traffic volume increases. There is safety-in-numbers when the number of accidents increases less than proportional to traffic volume, e.g. a doubling of traffic volume is associated with less than a doubling of the number of accidents. Hazard-in-numbers, a less-used concept, refers to the opposite effect: the number of accidents increases more than in proportion to traffic volume, e.g. is more than doubled when traffic volume is doubled. This paper discusses whether a safety-in-numbers effect and a hazard-in-numbers effect can co-exist in the same data. It is concluded that both effects can exist in a given data set. The paper proposes to make a distinction between partial safety-in-numbers and complete safety-in-numbers. Another issue that has been raised in discussions about the safety-in-numbers effect is whether the effect found in some studies is an artefact created by the way exposure was measured. The paper discusses whether measuring exposure as a rate or a share, e.g. kilometres travelled per inhabitant per year, will generate a safety-in-numbers effect as a statistical artefact. It is concluded that this is the case. The preferred measure of exposure is a count of the number of road users. The count should not be converted to a rate or to the share any group of road user contribute to total traffic volume.