Emanuele Sacchi

Investigating the accuracy of Bayesian techniques for before–after safety studies: The case of a “no treatment” evaluation

The main challenge in conducting observational before-after (BA) studies of road safety measures is to use a methodology that accounts for many potential confounding factors. However, it is usually difficult to evaluate and decide on the accuracy of the different safety evaluation techniques available in literature. This is mainly because the outcome of the comparison has no specific target (i.e., the effect of a specific treatment on safety is not precisely known). The objective of this paper is to compare the accuracy of some of the commonly used Bayesian methodologies for BA safety studies by applying them to locations where no safety treatment has been implemented (making the target result to be no effect). This goal was pursued within the setting of a specific case study where a recent set of collision data was available for urban signalized intersections in British Colombia (Canada) with no safety treatments implemented during the time frame considered. An assessment of the temporal stability of the data set was undertaken to exclude the presence of significant BA changes as explanation of the results reported in this paper. Both the well-known empirical Bayes and the full Bayes method with non-linear intervention models were explored for comparison. Two types of selection of the hypothetical treatment sites were used in the analysis: random, to minimize the selection bias effect, and non-random, by selecting sites with abnormal collision frequency (hotspots). Several criteria were used for comparisons including variability among the index of effectiveness for individual treatment locations, the stability of the outcome in terms of the consistency of the results of several experiments and the overall treatment effectiveness. The results showed that when sites are selected randomly for treatment, all methodologies including the simple (naïve) BA study provide reasonable results (small statistically non-significant change in collision frequency). However, when sites are selected for treatment because of high collision occurrence, the estimated index of treatment effectiveness can potentially be biased by values up to 10%. This finding can have significant impact on estimating safety benefits of treatments, especially on those that have low collision reductions. As well, the FB method seems to perform better than other evaluation techniques including the most commonly used EB method. In particular, the FB method provides higher consistency in the estimated collision reduction among treatment sites.

Multivariate Full Bayesian Hot Spot Identification and Ranking: New Technique

The present study introduces a new technique for multivariate identification and ranking of hot spots based on the Mahalanobis distance. This approach aims to extend the univariate potential for safety improvement to cases in which multiple response variables are modeled jointly. Because the literature shows that ranking techniques based on Bayesian methods are superior to those that rely simply on the observed collision count, the proposed method was developed in a full Bayesian (FB) context. The new technique involves the following steps: (a) applying multivariate Poisson–lognormal regression models to the data by means of the FB method, (b) using the estimates of the Poisson posterior means for each site to compute the multivariate (Mahalanobis) distance from what is the normal Poisson mean for similar sites, and (c) preparing an ordered list of potentially hazardous sites. This method was applied to a sample of 173 signalized intersections in the city of Vancouver, British Columbia, Canada, for the years 2008 to 2012. The study also examines the consistency of the technique itself by analyzing the mathematical intersection of ranked sites identified in subsequent time periods. Finally, the consistency of the multivariate FB ranking was assessed against the independent (separate) univariate one that is still dominant in road safety evaluations.

Conflict-Based Safety Performance Functions for Predicting Traffic Collisions by Type

In road safety analysis, safety performance functions (SPFs) are used to predict the average number of collisions per year at a road site. SPFs are a function of various amounts of exposure and, in some cases, site-specific characteristics. Exposure is a measure of opportunities for collisions to occur. The circulating traffic volume is commonly adopted for this purpose. However, not all vehicles interact unsafely at a road site. Alternatively, traffic conflicts may provide a more appropriate exposure measure for collisions because they represent only unsafe interactions between vehicles. There has been some research on this topic, mainly based on aggregated data including all conflict types. In this study a stratified analysis was conducted by type of conflict. Hence, the main objectives of this research were to establish a relationship between predicted collisions and predicted conflicts by using an SPF with traffic conflicts as an exposure measure and to predict the number of specific types of conflicts and collisions at signalized intersections. The methodological framework used was a two-phase nested modeling process in which a Poisson–gamma SPF that uses traffic volume as exposure was used to predict conflicts, which were then used in another Poisson–gamma SPF to predict collisions. The proposed approach was applied to a data set of collision frequency and average hourly conflicts for 49 signalized intersections throughout British Columbia, Canada. The results demonstrate the proportional relationship between conflicts and collisions and the importance of carrying out stratified analyses when types of conflicts are combined.

Bayesian estimation of conflict-based safety performance functions

ABSTRACT Most of the current research on road safety relies on the analysis of collision data that is challenged by well-recognized availability and quality issues. Therefore, the use of surrogate safety measures such as traffic conflicts has been gaining acceptance as an alternative or complementary approach to analyze traffic safety from a broader perspective than collision data alone. However, there is a need to develop statistical techniques to analyze conflict data to support various road safety applications. This article discusses the development of conflict-based safety performance functions (SPFs) within the framework of Bayesian statistics. The Bayesian approach was selected as it represents the state-of-the-art technique in the statistical analysis of collisions. In particular, SPFs were developed to predict the number of rear-end conflicts at different intersection approaches. The functions were validated using posterior predictive checking indicators. Data for traffic conflict observations were automatically extracted with computer vision techniques at several urban and suburban intersections in British Columbia (Canada). The results indicate that the models developed have a good fit of the observed conflict data and can offer a useful tool for conducting safety analysis.

Developing crash modification functions for pedestrian signal improvement

Pedestrian signals are viable traffic control devices that help pedestrians to cross safely at intersections. Although the literature is extensive when dealing with pedestrian signals design and operations, few studies have focused on the potential safety benefits of installing pedestrian signals at intersections. Most of these studies employed simple before-after (BA) safety evaluation techniques which suffer from methodological and statistical issues. Recent advances in safety evaluation research advocate the use of crash modification functions (CMFunctions) to represent the safety effectiveness of treatments. Unlike crash modification factors (CMFs) that are represented as single values, CMFunctions account for variable treatment location characteristics (heterogeneity). Therefore, the main objective of this study was to quantify the safety impact of installing pedestrian signals at signalized intersections by developing CMFunctions within an observational BA study. The use of observational BA framework to develop the CMFunctions avoids the cross-sectional approach where the functions are derived based on a single time period and no actual treatment intervention. Treatment sites heterogeneity was incorporated into CMFunctions using fixed-effects and random-effects regression models. In addition to heterogeneity, the paper also advocates the use of CMFunctions with a time variable to acknowledge that the safety treatment (intervention) effects do not occur instantaneously but are spread over future time. This is achieved using non-linear intervention (Koyck) models, developed within a hierarchical full Bayes context. The results demonstrated the importance of considering treatment sites heterogeneity (i.e., different circulating volumes and area type among treated locations) and time trends when developing CMFunctions for pedestrian signal improvement.

A full Bayes before-after study accounting for temporal and spatial effects: evaluating the safety impact of new signal installations

Recently, important advances in road safety statistics have been brought about by methods able to address issues other than the choice of the best error structure for modeling crash data. In particular, accounting for spatial and temporal interdependence, i.e., the notion that the collision occurrence of a site or unit times depend on those of others, has become an important issue that needs further research. Overall, autoregressive models can be used for this purpose as they can specify that the output variable depends on its own previous values and on a stochastic term. Spatial effects have been investigated and applied mostly in the context of developing safety performance functions (SPFs) to relate crash occurrence to highway characteristics. Hence, there is a need for studies that attempt to estimate the effectiveness of safety countermeasures by including the spatial interdependence of road sites within the context of an observational before-after (BA) study. Moreover, the combination of temporal dynamics and spatial effects on crash frequency has not been explored in depth for SPF development. Therefore, the main goal of this research was to carry out a BA study accounting for spatial effects and temporal dynamics in evaluating the effectiveness of a road safety treatment. The countermeasure analyzed was the installation of traffic signals at unsignalized urban/suburban intersections in British Columbia (Canada). The full Bayes approach was selected as the statistical framework to develop the models. The results demonstrated that zone variation was a major component of total crash variability and that spatial effects were alleviated by clustering intersections together. Finally, the methodology used also allowed estimation of the treatments effectiveness in the form of crash modification factors and functions with time trends.

Crash Modification Functions for Installation of Left-Turn Lanes at Signalized Intersection Approaches

This paper presents the results of a study that developed crash modification (CM) functions for installing left-turn lanes at signalized intersection approaches. CM functions were obtained from a longitudinal before–after safety study that accounted for treatment location characteristics (heterogeneity). This approach for developing CM functions has several advantages over the commonly used cross-sectional evaluations, which have several statistical shortcomings. The developed CM functions incorporate a time variable to acknowledge that the safety treatment effects do not occur instantaneously but are spread over future time; this result was achieved with a nonlinear intervention model with the full Bayes method. Twelve treatment sites were selected for the evaluation, along with 67 comparison sites. The treatment included the addition of one or more LT lanes for each intersection. The analysis showed significant safety improvements for fatal-plus-injury and total collisions but statistically nonsignificant reductions for property-damage-only collisions. The significant covariates included in the CM functions were the time trend, total entering volumes, and category of the new left-turn lanes installation.

Evaluating the safety impact of increased speed limits on rural highways in British Columbia

Maximum speed limits are usually set to inform drivers of the highest speed that it is safe and appropriate for ideal traffic, road and weather conditions. Many previous studies were conducted to investigate the relationship between changed speed limits and safety. The results of these studies generally show that relaxing speed limits can negatively affect safety, especially with regard to fatal and injury crashes. Despite these results, several road jurisdictions in North America continue to raise the maximum speed limits. In 2013, the British Columbia Ministry of Transportation and Infrastructure initiated a speed limits review. The review found that the 85th percentile speed on many highway segments was 10km/h higher than corresponding posted speed limits and 1300km of rural provincial highway segments were recommended for higher speed limits. Most of the highway segments had 10km/h speed limit increase with a small section having 20km/h speed limit increase. As speed limit changes can have a substantial impact on safety, the main objective of this study is to estimate the effect of the increased speed limits on crash occurrence. A before-after evaluation was undertaken with the full Bayesian technique. Overall, the evaluation showed that changed speed limits led to a statistically significant increase in fatal-plus-injury (severe) crashes of 11.1%. A crash modification function that includes changes in the treatment effect over time showed that the initial increase of the first post-implementation period may slightly decrease over time.

Evaluating Safety Benefits of the Insurance Corporation of British Columbia Road Improvement Program Using a Full Bayes Approach

The objective of this study was to conduct a time-series (before-to-after) evaluation of the safety performance of a sample of locations that have been improved under the Insurance Corporation of British Columbia (ICBC) Road Improvement Program. The program started in 1989 when ICBC established partnerships with local road authorities in British Columbia, Canada, and works cooperatively to make sound investments in road safety improvements. The overall effectiveness of the road improvement program was assessed by determining whether the frequency or severity of collisions at the improvement sites has been reduced after implementation of the improvement, and by quantifying the program costs versus the economic safety benefits to determine the return on ICBC’s road safety investment. Seventy-two urban intersections were included in the evaluation. The methodology adopted for estimating the safety benefits was a before–after study with the full Bayesian method, while the benefit–cost analysis was carried out by using two indicators: net present value and benefit–cost ratio (B/C) with a payback period of 5 years. Overall, the total reductions of severe (fatal plus injury) and nonsevere (property damage only) collision frequency for intersections with new pedestrian signal installations were found equal to −24.54% and −6.21%, respectively; −22.95% and −10.78%, respectively, for intersections with geometric design improvements; and −13.76% and −5.04%, respectively, for intersections with traffic signal upgrades. Finally, an overall B/C ratio of 4.32:1 was achieved.