Bayesian ranking of sites for engineering safety improvements: Decision parameter, treatability concept, statistical criterion, and spatial dependence

In recent years, there has been a renewed interest in applying statistical ranking criteria to identify sites on a road network, which potentially present high traffic crash risks or are over-represented in certain type of crashes, for further engineering evaluation and safety improvement. This requires that good estimates of ranks of crash risks be obtained at individual intersections or road segments, or some analysis zones. The nature of this site ranking problem in roadway safety is related to two well-established statistical problems known as the small area (or domain) estimation problem and the disease mapping problem. The former arises in the context of providing estimates using sample survey data for a small geographical area or a small socio-demographic group in a large area, while the latter stems from estimating rare disease incidences for typically small geographical areas. The statistical problem is such that direct estimates of certain parameters associated with a site (or a group of sites) with adequate precision cannot be produced, due to a small available sample size, the rareness of the event of interest, and/or a small exposed population or sub-population in question. Model based approaches have offered several advantages to these estimation problems, including increased precision by "borrowing strengths" across the various sites based on available auxiliary variables, including their relative locations in space. Within the model based approach, generalized linear mixed models (GLMM) have played key roles in addressing these problems for many years. The objective of the study, on which this paper is based, was to explore some of the issues raised in recent roadway safety studies regarding ranking methodologies in light of the recent statistical development in space-time GLMM. First, general ranking approaches are reviewed, which include naive or raw crash-risk ranking, scan based ranking, and model based ranking. Through simulations, the limitation of using the naive approach in ranking is illustrated. Second, following the model based approach, the choice of decision parameters and consideration of treatability are discussed. Third, several statistical ranking criteria that have been used in biomedical, health, and other scientific studies are presented from a Bayesian perspective. Their applications in roadway safety are then demonstrated using two data sets: one for individual urban intersections and one for rural two-lane roads at the county level. As part of the demonstration, it is shown how multivariate spatial GLMM can be used to model traffic crashes of several injury severity types simultaneously and how the model can be used within a Bayesian framework to rank sites by crash cost per vehicle-mile traveled (instead of by crash frequency rate). Finally, the significant impact of spatial effects on the overall model goodness-of-fit and site ranking performances are discussed for the two data sets examined. The paper is concluded with a discussion on possible directions in which the study can be extended.