Further compelling evidence for safety-in-numbers: It is more than meets the eye

In the extant road safety literature, estimating safety-in-numbers is dominated by conventional cross-sectional methods in which active mode (pedestrian or cyclist) volume together with motorised traffic volume are present in regression models explaining active mode safety directly. There is "direct" evidence for safety-in-numbers when the coefficient associated with active mode volume is negative (safety improves as volume increases) or when it is smaller than one (safety decreases at a lower rate compared to the rate of increase in active mode volume). In this article we extend the concept of safety-in-numbers in the traffic safety field, introducing "indirect" safety-in-numbers, which constitutes a new form of evidence for this phenomenon. We provide empirical evidence to support this, discussing that using an approach based on heterogeneity in mean modelling-a form of random parameters (slopes) models-it is possible to reveal "indirect" safety-in-numbers effects. Therefore, such models can reveal further compelling evidence for safety-in-numbers. Accurate knowledge of safety-in-numbers effects (both direct and indirect) and their underlying mechanisms can help provide robust motives for promoting active travel and will have valuable implications for the design of road safety interventions.