Bayesian estimation of hourly exposure functions by crash type and time of day

The study describes an investigation of the relationship between crash occurrence and hourly volume counts for small samples of highway segments from two states: Michigan and Connecticut. We used a hierarchical Bayesian framework to fit binary regression models for predicting crash occurrence for each of four crash types: (1) single-vehicle, (2) multi-vehicle same direction, (3) multi-vehicle opposite direction, and (4) multi-vehicle intersecting direction, as a function of the hourly volume, segment length, speed limit and pavement width. The results reveal how the relationship between crashes and hourly volume varies by time of day, thus improving the accuracy of crash occurrence predictions. The results show that even accounting for time of day, the disaggregate exposure measure – hourly volume – is indeed non-linear for each of the four crash types. This implies that at any time of day, the crash occurrence is not proportional to the hourly volume. These findings help us to further understand the relationship between crash occurrence and hourly volume, segment length and other risk factors, and facilitate more meaningful comparisons of the safety record of seemingly similar highway locations.     

Explaining two-lane highway crash rates using land use and hourly exposure

This paper describes the estimation of Poisson regression models for predicting both single and multi-vehicle highway crash rates as a function of traffic density and land use, as well as ambient light conditions and time of day. The study focuses on seventeen rural, two-lane highway segments, each one-half mile in length with varying land use patterns and where actual hourly exposure values are available in the form of observed traffic counts. Land-use effects are represented by the number of driveways of various types on each segment. Hourly exposure is represented for single-vehicle crashes as the total vehicle miles traveled and volume/capacity ratio; for multi-vehicle crashes it is the product of the hourly volumes on the main highway and the roads intersecting it along the study segment. For single-vehicle crashes, the following variables were found to be significant, with a positive or negative effect as noted: daytime (06:00–19:00 h, negative effect), the natural log of the segment volume/capacity ratio (negative), percent of the segment with no passing zones (positive), shoulder width (positive), number of intersections (negative), and driveways (mixed effects by type). Good multi-vehicle crash prediction models had quite different variables: daylight conditions from 10:00–15:00 and 15:00–19:00 h (positive), number of intersections (negative), and driveways (positive for all types). The results show that traffic intensity explains differences in crash rates even when controlling for time of day and light conditions, and that these effects are quite different for single and multi-vehicle crashes. Suggestions for future research are also given.     

Differences in causality factors for single and multi-vehicle crashes on two-lane roads

Past research has found a non-linear relationship between traffic intensity or level of service (LOS) and highway crash rates. This paper investigates this relationship further by including the effects of site characteristics and estimating Poisson regression models for predicting single and multi-vehicle crashes separately. Analysis focuses on rural two-lane highways, with hourly LOS, traffic composition, and highway geometric characteristics as independent variables. The resulting models for single and multi-vehicle crashes have different explanatory variables. Single-vehicle crash rates decrease with increasing traffic intensity (lower LOS), shoulder width and sight distance. Multi-vehicle crash rates increase with the number of signals, the daily single-unit truck percentage, and the shoulder width, and decreased on principal arterials compared to other roadway classes. LOS does not significantly explain variation in the number of multi-vehicle crashes. Ongoing research by the authors is aimed at identifying other site factors, such as driveway density and intersection LOS, that can better explain the differing effects reported here and predict crash rates of both types better.     

Investigating the effect of modeling single-vehicle and multi-vehicle crashes separately on confidence intervals of Poisson-gamma models

Crash prediction models still constitute one of the primary tools for estimating traffic safety. These statistical models play a vital role in various types of safety studies. With a few exceptions, they have often been employed to estimate the number of crashes per unit of time for an entire highway segment or intersection, without distinguishing the influence different sub-groups have on crash risk. The two most important sub-groups that have been identified in the literature are single- and multi-vehicle crashes. Recently, some researchers have noted that developing two distinct models for these two categories of crashes provides better predicting performance than developing models combining both crash categories together. Thus, there is a need to determine whether a significant difference exists for the computation of confidence intervals when a single model is applied rather than two distinct models for single- and multi-vehicle crashes. Building confidence intervals have many important applications in highway safety.This paper investigates the effect of modeling single- and multi-vehicle (head-on and rear-end only) crashes separately versus modeling them together on the prediction of confidence intervals of Poisson-gamma models. Confidence intervals were calculated for total (all severities) crash models and fatal and severe injury crash models. The data used for the comparison analysis were collected on Texas multilane undivided highways for the years 1997-2001. This study shows that modeling single- and multi-vehicle crashes separately predicts larger confidence intervals than modeling them together as a single model. This difference is much larger for fatal and injury crash models than for models for all severity levels. Furthermore, it is found that the single- and multi-vehicle crashes are not independent. Thus, a joint (bivariate) model which accounts for correlation between single- and multi-vehicle crashes is developed and it predicts wider confidence intervals than a univariate model for all severities. Finally, the simulation results show that separate models predict values that are closer to the true confidence intervals, and thus this research supports previous studies that recommended modeling single- and multi-vehicle crashes separately for analyzing highway segments.     

Multi-level Bayesian analyses for single- and multi-vehicle freeway crashes

This study presents multi-level analyses for single- and multi-vehicle crashes on a mountainous freeway. Data from a 15-mile mountainous freeway section on I-70 were investigated. Both aggregate and disaggregate models for the two crash conditions were developed. Five years of crash data were used in the aggregate investigation, while the disaggregate models utilized one year of crash data along with real-time traffic and weather data. For the aggregate analyses, safety performance functions were developed for the purpose of revealing the contributing factors for each crash type. Two methodologies, a Bayesian bivariate Poisson-lognormal model and a Bayesian hierarchical Poisson model with correlated random effects, were estimated to simultaneously analyze the two crash conditions with consideration of possible correlations. Except for the factors related to geometric characteristics, two exposure parameters (annual average daily traffic and segment length) were included. Two different sets of significant explanatory and exposure variables were identified for the single-vehicle (SV) and multi-vehicle (MV) crashes. It was found that the Bayesian bivariate Poisson-lognormal model is superior to the Bayesian hierarchical Poisson model, the former with a substantially lower DIC and more significant variables. In addition to the aggregate analyses, microscopic real-time crash risk evaluation models were developed for the two crash conditions. Multi-level Bayesian logistic regression models were estimated with the random parameters accounting for seasonal variations, crash-unit-level diversity and segment-level random effects capturing unobserved heterogeneity caused by the geometric characteristics. The model results indicate that the effects of the selected variables on crash occurrence vary across seasons and crash units; and that geometric characteristic variables contribute to the segment variations: the more unobserved heterogeneity have been accounted, the better classification ability. Potential applications of the modeling results from both analysis approaches are discussed.     

Model crash frequency at highway–railroad grade crossings using negative binomial regression

Despite the fact that traffic collisions at highway–railroad grade crossings (HRGXs) are rare events, the impact of HRGX crashes is nevertheless more severe than highway crashes. Empirical studies show that traffic collisions at HRGXs are mainly attributed to railway-related and/or highway-related characteristics, particularly drivers’ abnormal behavior, driving around, or through an HRGX. These factors have different effects on crash likelihood (i.e., the number of traffic collisions or crash frequency) at an HRGX. To explore the causal relationship between crash frequency and the factors related to railroad and highway systems, we used a negative binomial regression model to identify the factors that are statistically significantly associated with traffic collisions at HRGXs, and conducted relevant sensitivity analyses to investigate the marginal effect of daily highway traffic on changes in crash frequency. The empirical study shows that the number of daily trains, the number of tracks, highway separation, annual averaged daily traffic (AADT), and crossing length had statistically significant effects on the mean number of traffic collisions (all p-values?≤?0.0487). Further, the marginal effect of the AADT on the change of crash frequency indicates that crash likelihood monotonically increases with the increase of AADT.     

Bootstrap resampling approach to disaggregate analysis of road crashes in Hong Kong

Road safety affects health and development worldwide; thus, it is essential to examine the factors that influence crashes and injuries. As the relationships between crashes, crash severity, and possible risk factors can vary depending on the type of collision, we attempt to develop separate prediction models for different crash types (i.e., single- versus multi-vehicle crashes and slight injury versus killed and serious injury crashes). Taking advantage of the availability of crash and traffic data disaggregated by time and space, it is possible to identify the factors that may contribute to crash risks in Hong Kong, including traffic flow, road design, and weather conditions. To remove the effects of excess zeros on prediction performance in a highly disaggregated crash prediction model, a bootstrap resampling method is applied. The results indicate that more accurate and reliable parameter estimates, with reduced standard errors, can be obtained with the use of a bootstrap resampling method. Results revealed that factors including rainfall, geometric design, traffic control, and temporal variations all determined the crash risk and crash severity. This helps to shed light on the development of remedial engineering and traffic management and control measures.     

Predicting crash risk and identifying crash precursors on Korean expressways using loop detector data

In order to improve traffic safety on expressways, it is important to develop proactive safety management strategies with consideration for segment types and traffic flow states because crash mechanisms have some differences by each condition. The primary objective of this study is to develop real-time crash risk prediction models for different segment types and traffic flow states on expressways. The mainline of expressways is divided into basic segment and ramp vicinity, and the traffic flow states are classified into uncongested and congested conditions. Also, Korean expressways have irregular intervals between loop detector stations. Therefore, we investigated on the effect and application of the detector stations at irregular intervals for the crash risk prediction on expressways. The most significant traffic variables were selected by conditional logistic regression analysis which could control confounding factors. Based on the selected traffic variables, separate models to predict crash risk were developed using genetic programming technique. The model estimation results showed that the traffic flow characteristics leading to crashes are differed by segment type and traffic flow state. Especially, the variables related to the intervals between detector stations had a significant influence on crash risk prediction under the uncongested condition. Finally, compared with the single model for all crashes and the logistic models used in previous studies, the proposed models showed higher prediction performance. The results of this study can be applied to develop more effective proactive safety management strategies for different segment types and traffic flow states on expressways with loop detector stations at irregular intervals.     

Safety modeling of suburban arterials in Shanghai,China

As urbanization accelerates in Shanghai, land continues to develop along suburban arterials which results in more access points along the roadways and more congested suburban arterials; all these changes have led to deterioration in traffic safety. In-depth safety analysis is needed to understand the relationship between roadway geometric design, access features, traffic characteristics, and safety. This study examined 161 road segments (each between two adjacent signalized intersections) of eight suburban arterials in Shanghai. Information on signal spacing, geometric design, access features, traffic characteristics, and surrounding area types were collected. The effect of these factors on total crash occurrence was investigated. To account for the hierarchical data structure, hierarchical Bayesian models were developed for total crashes. To identify diverse effects on different crash injury severity, the total crashes were separated into minor injury and severe injury crashes. Bivariate hierarchical Bayesian models were developed for minor injury and severe injury to account for the correlation among different severity levels. The modeling results show that the density of signal spacing along arterials has a significant influence on minor injury, severe injury, and total crash frequencies. The non-uniform signal spacing has a significant impact on the occurrence of minor injury crashes. At the segment-level, higher frequencies of minor injury, severe injury, and total crashes tend to occur for the segments with curves, those with a higher density of access points, those with a higher percentage of heavy vehicles, and those in inner suburban areas. This study is useful for applications such as related engineering safety improvements and making access management policy.     

Quasi-induced exposure method: Evaluation of not-at-fault assumption

Crash rates are used to establish the relative safety of various variables of concern such as driver classes, vehicle types and roadway components. Appropriate exposure data for estimating crash rates is critical but crash databases do not contain information on driver or vehicle exposure. The quasi-induced exposure method, which uses not-at-fault driver/vehicle data as an exposure metric, is a technique used in order to overcome this problem. The basic assumption made here is that not-at-fault drivers represent the total population in question. This paper examines the validity of this assumption using the Kentucky crash database to define two samples of not-at-fault drivers. One sample included only not-at-fault drivers selected from the first two vehicles in a multi-vehicle crash (two or more vehicles involved) while the other included the not-at-fault drivers from multi-vehicle crashes with more than two vehicles involved and excluding the first two drivers. The assumption is that the randomness of the involvement of drivers in the second sample is more reasonable than the drivers in the first two vehicles involved in crashes. The results indicate that these two samples are similar; there is no statistical evidence demonstrating that both samples represent two different populations in the maneuvers and other variables/factors examined here; and they are representative simple random samples of the driver population with respect to the distribution of the driver age when there is no reasonable doubt about investigating officers’ judgments. Thus, estimating relative crash propensities for any given driver type by using the quasi-induced exposure approach will yield reasonable estimates of exposure.     

A new access density definition and its correlation with crash rates by microscopic traffic simulation method

Better access management can improve highway safety by reducing potential crashes and conflicts. To make adequate access management decisions, it is essential to understand the impact of different access types on roadway safety, usually represented by the crash rate of a roadway segment. The objective of this paper is to propose a new access density definition reflecting the impact of traffic speed variation of different access types. The traffic speed variation was obtained from a microscopic traffic simulation software package TSIS-CORSIM. A sample roadway Temple Terrace Highway was selected to perform traffic simulation. Access Weight was obtained from traffic speed variation, and access density was obtained from access weight. The proposed access density was then compared with the existing definition by analyzing their correlations with crash rates on one suburban street in Temple Terrace, Florida. The comparison demonstrates that crash rates are more highly correlated with the proposed access density than that in the previous study, which is helpful for Federal Highway Administration (FHWA), United States Department of Transportation (USDOT), and transportation consulting companies to regulate the construction, management and design of roadway segments.     

Effects of work zone presence on injury and non-injury crashes.

Work zones in the United States have approximately 700 traffic-related fatalities, 24,000 injury crashes, and 52,000 non-injury crashes every year. Due to future highway reconstruction needs, work zones are likely to increase in number, duration, and length. This study focuses on analyzing the effect of work zone duration mainly due to its policy-sensitivity. To do so, we created a unique dataset of California freeway work zones that included crash data (crash frequency and injury severity), road inventory data (average daily traffic (ADT) and urban/rural character), and work zone related data (duration, length, and location). Then, we investigated crash rates and crash frequencies in the pre-work zone and during-work zone periods. For the freeway work zones investigated in this study, the total crash rate in the during-work zone period was 21.5% higher (0.79 crashes per million vehicle kilometer (MVKM)) than the pre-work zone period (0.65 crashes per MVKM). Compared with the pre-work zone period, the increase in non-injury and injury crash rates in the during-work zone period was 23.8% and 17.3%, respectively. Next, crash frequencies were investigated using negative binomial models, which showed that frequencies increased with increasing work zone duration, length, and average daily traffic. The important finding is that after controlling for various factors, longer work zone duration significantly increases both injury and non-injury crash frequencies. The implications of the study findings are discussed in the paper.     

Bayesian random effect models incorporating real-time weather and traffic data to investigate mountainous freeway hazardous factors

Freeway crash occurrences are highly influenced by geometric characteristics, traffic status, weather conditions and drivers’ behavior. For a mountainous freeway which suffers from adverse weather conditions, it is critical to incorporate real-time weather information and traffic data in the crash frequency study. In this paper, a Bayesian inference method was employed to model one year's crash data on I-70 in the state of Colorado. Real-time weather and traffic variables, along with geometric characteristics variables were evaluated in the models. Two scenarios were considered in this study, one seasonal and one crash type based case. For the methodology part, the Poisson model and two random effect models with a Bayesian inference method were employed and compared in this study. Deviance Information Criterion (DIC) was utilized as a comparison factor. The correlated random effect models outperformed the others. The results indicate that the weather condition variables, especially precipitation, play a key role in the crash occurrence models. The conclusions imply that different active traffic management strategies should be designed based on seasons, and single-vehicle crashes have different crash mechanism compared to multi-vehicle crashes.     

Propensity scores-potential outcomes framework to incorporate severity probabilities in the Highway Safety Manual crash prediction algorithm

Accurate estimation of the expected number of crashes at different severity levels for entities with and without countermeasures plays a vital role in selecting countermeasures in the framework of the safety management process. The current practice is to use the American Association of State Highway and Transportation Officials’ Highway Safety Manual crash prediction algorithms, which combine safety performance functions and crash modification factors, to estimate the effects of safety countermeasures on different highway and street facility types. Many of these crash prediction algorithms are based solely on crash frequency, or assume that severity outcomes are unchanged when planning for, or implementing, safety countermeasures. Failing to account for the uncertainty associated with crash severity outcomes, and assuming crash severity distributions remain unchanged in safety performance evaluations, limits the utility of the Highway Safety Manual crash prediction algorithms in assessing the effect of safety countermeasures on crash severity. This study demonstrates the application of a propensity scores-potential outcomes framework to estimate the probability distribution for the occurrence of different crash severity levels by accounting for the uncertainties associated with them. The probability of fatal and severe injury crash occurrence at lighted and unlighted intersections is estimated in this paper using data from Minnesota. The results show that the expected probability of occurrence of fatal and severe injury crashes at a lighted intersection was 1 in 35 crashes and the estimated risk ratio indicates that the respective probabilities at an unlighted intersection was 1.14 times higher compared to lighted intersections. The results from the potential outcomes-propensity scores framework are compared to results obtained from traditional binary logit models, without application of propensity scores matching. Traditional binary logit analysis suggests that the probability of occurrence of severe injury crashes is higher at lighted intersections compared to unlighted intersections, which contradicts the findings obtained from the propensity scores-potential outcomes framework. This finding underscores the importance of having comparable treated and untreated entities in traffic safety countermeasure evaluations.     

Mixed logit model-based driver injury severity investigations in single- and multi-vehicle crashes on rural two-lane highways

Crashes occurring on rural two-lane highways are more likely to result in severe driver incapacitating injuries and fatalities. In this study, mixed logit models are developed to analyze driver injury severities in single-vehicle (SV) and multi-vehicle (MV) crashes on rural two-lane highways in New Mexico from 2010 to 2011. A series of significant contributing factors in terms of driver behavior, weather conditions, environmental characteristics, roadway geometric features and traffic compositions, are identified and their impacts on injury severities are quantified for these two types of crashes, respectively. Elasticity analyses and transferability tests were conducted to better understand the models’ specification and generality. The research findings indicate that there are significant differences in causal attributes determining driver injury severities between SV and MV crashes. For example, more severe driver injuries and fatalities can be observed in MV crashes when motorcycles or trucks are involved. Dark lighting conditions and dusty weather conditions are found to significantly increase MV crash injury severities. However, SV crashes demonstrate different characteristics influencing driver injury severities. For example, the probability of having severe injury outcomes is higher when vans are identified in SV crashes. Drivers’ overtaking actions will significantly increase SV crash injury severities. Although some common attributes, such as alcohol impaired driving, are significant in both SV and MV crash severity models, their effects on different injury outcomes vary substantially. This study provides a better understanding of similarities and differences in significant contributing factors and their impacts on driver injury severities between SV and MV crashes on rural two-lane highways. It is also helpful to develop cost-effective solutions or appropriate injury prevention strategies for rural SV and MV crashes.     

Estimation of rear-end vehicle crash frequencies in urban road tunnels

According to The Handbook of Tunnel Fire Safety, over 90% (55 out of 61 cases) of fires in road tunnels are caused by vehicle crashes (especially rear-end crashes). It is thus important to develop a proper methodology that is able to estimate the rear-end vehicle crash frequency in road tunnels. In this paper, we first analyze the time to collision (TTC) data collected from two road tunnels of Singapore and conclude that Inverse Gaussian distribution is the best-fitted distribution to the TTC data. An Inverse Gaussian regression model is hence used to establish the relationship between the TTC and its contributing factors. We then proceed to introduce a new concept of exposure to traffic conflicts as the mean sojourn time in a given time period that vehicles are exposed to dangerous scenarios, namely, the TTC is lower than a predetermined threshold value. We further establish the relationship between the proposed exposure to traffic conflicts and crash count by using negative binomial regression models. Based on the limited data samples used in this study, the negative binomial regression models perform well although a further study using more data is needed.     

Modeling crash outcome probabilities at rural intersections: application of hierarchical binomial logistic models

It is important to examine the nature of the relationships between roadway, environmental, and traffic factors and motor vehicle crashes, with the aim to improve the collective understanding of causal mechanisms involved in crashes and to better predict their occurrence. Statistical models of motor vehicle crashes are one path of inquiry often used to gain these initial insights. Recent efforts have focused on the estimation of negative binomial and Poisson regression models (and related deviants) due to their relatively good fit to crash data. Of course analysts constantly seek methods that offer greater consistency with the data generating mechanism (motor vehicle crashes in this case), provide better statistical fit, and provide insight into data structure that was previously unavailable. One such opportunity exists with some types of crash data, in particular crash-level data that are collected across roadway segments, intersections, etc. It is argued in this paper that some crash data possess hierarchical structure that has not routinely been exploited. This paper describes the application of binomial multilevel models of crash types using 548 motor vehicle crashes collected from 91 two-lane rural intersections in the state of Georgia. Crash prediction models are estimated for angle, rear-end, and sideswipe (both same direction and opposite direction) crashes. The contributions of the paper are the realization of hierarchical data structure and the application of a theoretically appealing and suitable analysis approach for multilevel data, yielding insights into intersection-related crashes by crash type.     

Studying the effect of weather conditions on daily crash counts using a discrete time-series model

In previous research, significant effects of weather conditions on car crashes have been found. However, most studies use monthly or yearly data and only few studies are available analyzing the impact of weather conditions on daily car crash counts. Furthermore, the studies that are available on a daily level do not explicitly model the data in a time-series context, hereby ignoring the temporal serial correlation that may be present in the data. In this paper, we introduce an integer autoregressive model for modelling count data with time interdependencies. The model is applied to daily car crash data, metereological data and traffic exposure data from the Netherlands aiming at examining the risk impact of weather conditions on the observed counts. The results show that several assumptions related to the effect of weather conditions on crash counts are found to be significant in the data and that if serial temporal correlation is not accounted for in the model, this may produce biased results.     

Relationship between crash rate and hourly traffic flow on interurban motorways

This paper describes the relationship between crash incidence rates and hourly traffic volume and discusses the influence of traffic on crash severity, based on observations made on 2000 km of French interurban motorways over 2 years. Incidence rates involving property damage-only crashes and injury-crashes are highest when traffic is lightest (under 400 vehicles/h). These incidence rates are at their lowest when traffic flows at a rate of 1000-1500 vehicles/h. For heavier traffic flows, crash incidence rates increase steadily as traffic increases on 2- and 3-lane motorways and inflect on 2-lane motorways when traffic increases to a level of 3000 vehicles/h. For an equivalent light traffic level, the number of crashes is higher on three-lane than on 2-lane motorways and higher at weekends (when truck traffic is restricted) than on weekdays. In heavy traffic, the number of crashes is higher on weekdays. We found no significant difference between the number of daytime and night-time crashes, whatever the traffic. No difference was observed in crash severity by number of lanes or period in the week for a given level of traffic. However, severity is greater at night and when hourly traffic is light. Compared to the number of vehicles on the road, light traffic is a safety problem in terms of frequency and severity, and road safety campaigns targeting motorway users to influence their behavior in these driving conditions should be introduced.