Improving functional form in cross-sectional regression studies to capture the non-linear safety effects of roadway attributes-Freeway median width case study.

Crash modification factors (CMFs) for several roadway attributes are based on cross-sectional regression models, in the main because of the lack of data for the preferred observational before-after study. In developing these models, little attention has been paid to those functional forms that reflect the reality that CMFs should not be single-valued, as most available ones are, but should vary with application circumstance. Using a full Bayesian Markov Chain Monte Carlo (MCMC) approach, this study aimed to improve the functional forms used to derive CMFs in cross-sectional regression models, with a focus on capturing the variability inherent in crash modification functions (CMFunctions). The estimated CMFunction for target crashes for freeway median width, used for a case study, indicates that the approach is capable of developing a function that can capture the logical reality that the CMF for a given change in a feature's value depends not only on the amount of the change but also on the original value. The results highlight the importance of using the functional forms that can capture non-linear effects of road attributes for CMF estimation in cross-sectional models. The case study provides credible CMFs for assessing the safety implications of decisions on freeway median width that could be used in improving current design practice.

Comparison of univariate and two-stage approaches for estimating crash frequency by severity-Case study for horizontal curves on two-lane rural roads.

The Highway Safety Manual (HSM) procedures apply specific safety performance functions (SPFs) and crash modification factors (CMFs) appropriate for estimating the safety effects of design and operational changes to a roadway. Although the applicability of the SPFs and CMFs may significantly vary by crash severity, they are mainly based on total crash counts, with different approaches for estimation of crashes by crash severity. The variety of approaches in the HSM and in the literature in general suggests that there may be no one best approach for all situations, and that there is a need to develop and compare alternative approaches for each potential application. This paper addresses this need by demonstrating the development and comparison of alternative approaches using horizontal curves on two-lane roads as a case study. This site type was chosen because of the high propensity for severe crashes and the potential for exploring a wide range of variables that affect this propensity. To facilitate this investigation, a two-stage modeling approach is developed whereby the proportion of crashes for each severity level is estimated as a function of roadway-specific factors and traffic attributes and then applied to an estimate of total crashes from an SPF. Using Highway Safety Information System (HSIS) curve data for Washington state, a heterogeneous negative binomial (HTNB) regression model is estimated for total crash counts and then applied with severity distribution functions (SDFs) developed by a generalized ordered probit model (GOP). To evaluate the performance of this two-stage approach, a comparison is made with predictions directly obtained from estimated univariate SPFs for crash frequency by severity and also from a fixed proportion method that has been suggested in the HSM. The results revealed that, while the two-stage SDF approach and univariate approach adopt different procedures for model estimation, their prediction accuracies are similar, and both are superior to the fixed proportion method. In short, this study highlights the potential of the two-stage SDF approach in accounting for crash frequency variations by severity levels, at least for curved two-lane road sections, and especially for the all too frequent cases where samples are too small to estimate viable univariate crash severity models.

Empirical Bayes before-after safety studies: lessons learned from two decades of experience and future directions.

The empirical Bayes (EB) methodology has been applied for over 20 years now in conducting statistically defendable before-after studies of the safety effect of treatments applied to roadway sites. The appeal of the methodology is that it corrects for regression to the mean and traffic volume and other changes not due to the measure. There is, therefore, a natural tendency to put a stamp of approval on any study that uses this methodology, and to assume that the results can then be used in specifying crash modification factors for use in developing treatments for hazardous locations, or in designing new roads using tools such as the interactive highway safety design model (IHSDM). At the other extreme are skeptics who suggest that the increased sophistication and data needs of the EB methodology are not worth the effort since alternative, less complex methods can produce equally valid results. The primary objective of this paper is to capitalize on experience gained from two decades of conducting EB studies around the world to illustrate that the EB methodology, if properly undertaken, produces results that could be substantially different and less biased than those from more conventional types of studies. A secondary objective is to emphasize that caution is needed in assessing the validity of studies undertaken with the EB methodology and in using these results for providing crash modification factors. To this end, a number of issues that are critical to the proper conduct and interpretation of EB evaluations are raised and illustrated based on lessons learned from recent experience with these studies. These include: amalgamating the effects on different crash types; the specification of the reference/comparison groups; and accounting for traffic volume changes. Current and future directions, including the improvements offered by a full Bayes approach, are discussed.

Another look at the safety effects of horizontal curvature on rural two-lane highways.

Crash Modification Factors (CMFs) are used to represent the effects on crashes of changes to highway design elements and are usually obtained from observational studies based on reported crashes. The design element of interest for this paper is horizontal curvature on rural 2-lane highways. The data for this study came from the Washington State database in the Highway Safety Information System (HSIS). Crash prediction models are developed for curve sections on rural 2-lane highway and the tangent sections up- and down-stream of the curve sections. Different negative binomial models were developed for segments on level grades (<3%), moderate grades (3-6%), and steep grades (>6%) to account for the confounding effects of gradient. The relationships between crashes at different traffic volumes and deflection angles are explored to illustrate how to get estimates of CMFs for increases in the minimum radius, considering the effect of increased tangent length for sharper curves, an effect that is overlooked in the Highway Safety Manual CMF, in addition to the effect of gradient. The results of that exploration indicated that even at different design speeds and deflection angles, the CMF estimates for incremental increases in radius lie within the same range, and that the crash reduction rate (CRR) is higher at segments on higher grades compared to the ones on lower grades.

Investigating the influence on safety of retrofitting Italian motorways with barriers meeting a new EU standard.

OBJECTIVE: A new European Union (EU) regulation for safety barriers, which is based on performance, has encouraged road agencies to perform an upgrade of old barriers, with the expectation that there will be safety benefits at the retrofitted sites. The new class of barriers was designed and installed in compliance with the 1998 (European Norm) EN 1317 standards for road restraint systems, which lays down common requirements for the testing and certification of road restraint systems in all countries of the European Committee for Standardization (CEN). Both the older and new barriers are made of steel and are installed in such a way as to avoid vehicle intrusion, but the older ones are thought to be only effective at low speeds and large angles of impact. The new standard seeks to remedy this by providing better protection at higher speeds. This article seeks to quantify the effect on the frequency of fatal and injury crashes of retrofitting motorways with barriers meeting the new standards. METHODS: The estimation of the crash modification was carried out by performing an empirical Bayes before-after analysis based on data from the A18 Messina-Catania motorway in Italy. The methodology has the great advantage to account for the regression to the mean effects. Besides, to account for time trend effects and dispersion of crash data, a modified calibration methodology of safety performance was used. RESULTS: This study, based on data collected on 76 km of motorway in the period 2000-2012, derived Crash Modification Factor point estimates that indicate reductions of 72% for run-off-road fatal and injury crashes and 38% in total fatal and injury crashes that could be expected by upgrading an old safety barrier by complying with new EU 1317 standards. The estimated benefit-cost ratio of 5.57 for total crashes indicates that the treatment is cost effective. CONCLUSIONS: The magnitude of this benefit indicates that the retrofits are cost-effective even for total crashes and should continue in any European country inasmuch as the estimated Crash Modification Factors are based on treatment sites that are reasonably representative of all European motorways.

Using micro-simulation to investigate the safety impacts of transit design alternatives at signalized intersections.

This study investigates the use of crash prediction models and micro-simulation to develop an effective surrogate safety assessment measure at the intersection level. With the use of these tools, hypothetical scenarios can be developed and explored to evaluate the safety impacts of design alternatives in a controlled environment, in which factors not directly associated with the design alternatives can be fixed. Micro-simulation models are developed, calibrated, and validated. Traffic conflicts in the micro-simulation models are estimated and linked with observed crash frequency, which greatly alleviates the lengthy time needed to collect sufficient crash data for evaluating alternatives, due to the rare and infrequent nature of crash events. A set of generalized linear models with negative binomial error structure is developed to correlate the simulated conflicts with the observed crash frequency in Toronto, Ontario, Canada. Crash prediction models are also developed for crashes of different impact types and for transit-involved crashes. The resulting statistical significance and the goodness-of-fit of the models suggest adequate predictive ability. Based on the established correlation between simulated conflicts and observed crashes, scenarios are developed in the micro-simulation models to investigate the safety effects of individual transit line elements by making hypothetical modifications to such elements and estimating changes in crash frequency from the resulting changes in conflicts. The findings imply that the existing transit signal priority schemes can have a negative effect on safety performance, and that the existing near-side stop positioning and streetcar transit type can be safer at their current state than if they were to be replaced by their respective counterparts.

Crash costs in the United States by crash geometry.

MAIN OBJECTIVES: This study was conducted to estimate the costs per crash for three police-coded crash severity groupings within 16 selected crash geometry types and within two speed limit categories (or=50 mph). METHODS: We merged previously developed costs per victim by abbreviated injury scale (AIS) score into U.S. crash data files that scored injuries in both the AIS and police-coded severity scales to estimate injury costs, then aggregated the estimates into costs per crash by maximum injury severity. RESULTS: The most costly crashes were non-intersection fatal/disabling injury crashes on a road with a speed limit of 50 miles per hour or higher where multiple vehicles crashed head-on or a single vehicle struck a human (over 1.69 US dollars and 1.16 million US dollars per crash, respectively). The annual cost of police-reported run-off-road collisions, which include both rollovers and object impacts, represented 34% of total costs. CONCLUSIONS: This paper provides cost estimates useful for evaluating roadway countermeasures and for designing vehicles to minimize crash harm. It gives unit costs of crashes by type in the coding system used by the police. The costs are in an appropriate form for economic analysis of countermeasures addressing locally defined problems identified by analyzing police crash reports.

Temporal transferability and updating of zonal level accident prediction models.

This paper examines the temporal transferability of the zonal accident prediction models by using appropriate evaluation measures of predictive performance to assess whether the relationship between the dependent and independent variables holds reasonably well across time. The two temporal contexts are the years 1996 and 2001, with updated 1996 models being used to predict 2001 accidents in each traffic zone of the City of Toronto. The paper examines alternative updating methods for temporal transfer by imagining that only a sample of 2001 data is available. The sensitivity of the performance of the updated models to the 2001 sample size is explored. The updating procedures examined include the Bayesian updating approach and the application of calibration factors to the 1996 models. Models calibrated for the 2001 samples were also explored, but were found to be inadequate. The results show that the models are not transferable in a strict statistical sense. However, relative measures of transferability indicate that the transferred models yield useful information in the application context. Also, it is concluded that the updated accident models using the calibration factors produce better results for predicting the number of accidents in the year 2001 than using the Bayesian approach.

Estimating the safety performance of urban road transportation networks.

Transportation planning models are typically used to estimate future traffic patterns, peak period traffic, travel time, and various environmental or other related traffic flow characteristics. Unfortunately, traffic safety is seldom, if ever, explicitly considered proactively during the transportation planning process. This omission is attributed to various factors, including the lack of available tools needed to estimate the number of crashes during this process. To help fill this void, the research on which this paper is based aimed, as a primary objective, to develop a tool that would allow the estimation of crashes on digital or coded urban transportation networks during the planning process. The secondary objective of the research was to describe how the predictive models should be applied on these networks and explain the important issues and limitations surrounding their application. To accomplish these objectives, safety performance functions specifically created for this work were applied to two sample digital networks created with the help of EMME/2, a software package widely used in transportation planning. The results showed that it is possible to predict crashes on digital transportation networks, but confirmed the reality that the accuracy of the predictions is directly related to the precision of the traffic flow estimates. The crash predictions are also sensitive to how the digital network is coded, and it is shown how appropriate adjustments can be made.

Crash reduction following installation of centerline rumble strips on rural two-lane roads.

Rural two-lane roads generally lack physical measures such as wide medians or barriers to separate opposing traffic flows. As a result, a major crash problem on these roads involves vehicles crossing the centerline and either sideswiping or striking the front ends of opposing vehicles. These types of opposing-direction crashes account for about 20% all fatal crashes on rural two-lane roads and result in about 4,500 fatalities annually in the US. The present study evaluated a potential engineering countermeasure for such crashes-installation of rumble strips along the centerlines of undivided rural two-lane roads to alert distracted, fatigued, or speeding motorists whose vehicles are about to cross the centerlines and encroach into opposing traffic lanes. Data were analyzed for approximately 210 miles of treated roads in seven states before and after installation of centerline rumble strips. An empirical Bayes before-after procedure was employed to properly account for regression to the mean while normalizing for differences in traffic volume and other factors between the before and after periods. Overall results indicated significant reductions for all injury crashes combined (14%, 95% confidence interval (95% CI) = 5-23%) as well as for frontal and opposing-direction sideswipe injury crashes (25%, 95% CI = 6-44%)--the primary target of centerline rumble strips. In light of their effectiveness and relatively low installation costs, consideration should be given to installing centerline rumble strips more widely on rural two-lane roads to reduce the risk of frontal and opposing-direction sideswipe crashes.

Comprehensive and human capital crash costs by maximum police-reported injury severity within selected crash types.

This paper presents estimates for both the economic and comprehensive costs per crash for three police-coded severity groupings within 16 selected crash types and within two speed limit categories (or=50 mph). The economic costs are hard dollar costs. The comprehensive costs include economic costs and quality of life losses. We merged previously developed costs per victim keyed on the Abbreviated Injury Scale (AIS) into US crash data files that scored injuries in both the AIS and police-coded severity scales to produce per crash estimates. The most costly crashes were non-intersection fatal/disabling injury crashes on a road with a speed limit of 50 miles per hour or higher where multiple vehicles crashed head-on or a single vehicle struck a human (over 1.69 and $1.16 million per crash, respectively). The annual cost of police-reported run-off-road collisions, which include both rollovers and object impacts, represented 34% of total costs.

Methodology to develop crash modification functions for road safety treatments with fully specified and hierarchical models.

Crash modification factors (CMFs) for road safety treatments are developed as multiplicative factors that are used to reflect the expected changes in safety performance associated with changes in highway design and/or the traffic control features. However, current CMFs have methodological drawbacks. For example, variability with application circumstance is not well understood, and, as important, correlation is not addressed when several CMFs are applied multiplicatively. These issues can be addressed by developing safety performance functions (SPFs) with components of crash modification functions (CM-Functions), an approach that includes all CMF related variables, along with others, while capturing quantitative and other effects of factors and accounting for cross-factor correlations. CM-Functions can capture the safety impact of factors through a continuous and quantitative approach, avoiding the problematic categorical analysis that is often used to capture CMF variability. There are two formulations to develop such SPFs with CM-Function components - fully specified models and hierarchical models. Based on sample datasets from two Canadian cities, both approaches are investigated in this paper. While both model formulations yielded promising results and reasonable CM-Functions, the hierarchical model was found to be more suitable in retaining homogeneity of first-level SPFs, while addressing CM-Functions in sub-level modeling. In addition, hierarchical models better capture the correlations between different impact factors.

Integrated traffic conflict model for estimating crash modification factors.

Crash modification factors (CMFs) for road safety treatments are usually obtained through observational models based on reported crashes. Observational Bayesian before-and-after methods have been applied to obtain more precise estimates of CMFs by accounting for the regression-to-the-mean bias inherent in naive methods. However, sufficient crash data reported over an extended period of time are needed to provide reliable estimates of treatment effects, a requirement that can be a challenge for certain types of treatment. In addition, these studies require that sites analyzed actually receive the treatment to which the CMF pertains. Another key issue with observational approaches is that they are not causal in nature, and as such, cannot provide a sound "behavioral" rationale for the treatment effect. Surrogate safety measures based on high risk vehicle interactions and traffic conflicts have been proposed to address this issue by providing a more "causal perspective" on lack of safety for different road and traffic conditions. The traffic conflict approach has been criticized, however, for lacking a formal link to observed and verified crashes, a difficulty that this paper attempts to resolve by presenting and investigating an alternative approach for estimating CMFs using simulated conflicts that are linked formally to observed crashes. The integrated CMF estimates are compared to estimates from an empirical Bayes (EB) crash-based before-and-after analysis for the same sample of treatment sites. The treatment considered involves changing left turn signal priority at Toronto signalized intersections from permissive to protected-permissive. The results are promising in that the proposed integrated method yields CMFs that closely match those obtained from the crash-based EB before-and-after analysis.

Investigation of models for relating roundabout safety to predicted speed.

Despite widespread recognition of operating speed as a key safety-related variable for roundabouts, there is no consensus on the best models for capturing the relationship between crashes and speed, or, for that matter, on how speed can be estimated in situations where it cannot be observed (such as when a roundabout is being designed or redesigned). This paper uses US and Italian roundabout approach-level data to investigate models relating safety to various measures of predicted speed. This is an indirect approach for developing safety models for estimating the effects of design features, the premise being that these features can better predict speed, which, in turn, can be used as a predictor of crash frequency. After exploring various possibilities, the approach average speed (AAS) - defined as the average of entry, upstream circulating and exiting speeds in this study - was found to be the speed measure that best predicts safety. US data were used to develop a Bayesian Poisson-gamma safety model based on predicted AAS with random coefficients and varying dispersion parameter. This model structure was not appropriate for the Italian data used to examine whether the approach could be generalized to data for another country. For that data, a zero-inflated Poisson (ZIP) model was found to be suitable. Notwithstanding the heterogeneity of the model structure, the investigation suggests that the indirect approach for evaluating the safety of a roundabout is a sound one in that it can preserve model parsimony while capturing the effects of design changes that affect safety.

Safety effectiveness of converting signalized intersections to roundabouts.

Roundabouts may be new builds but often are conversions from existing intersections. When contemplating the later, there is a need to estimate the safety effects of conversions. Several studies have estimated large reductions in crashes and severity; however, these results pertain mainly to conversions from unsignalized intersections. Results for conversions from signalized intersections have been less conclusive or consistent and tend to be somewhat dated. The objective of this study was to fill this void by estimating the safety effectiveness of converting signalized intersections to roundabouts. Several states helped to identify signalized intersections that were converted to roundabouts in the recent past. In total, 28 conversions were identified in the United States. The empirical Bayes (EB) method was employed in an observational before-after study to estimate the safety effects. Data from select states were also used in a cross-sectional analysis to investigate the compatibility of results from cross-sectional and before-after studies. The EB results indicated a safety benefit for converting signalized intersections to roundabouts. There were reductions in both total and injury crashes, with a larger benefit for injury crashes. Further analysis indicated that the safety benefit of roundabouts for total crashes decreased as traffic volumes increase, a result that suggests the need for the development of a crash modification function, a task for which more data would be required. The safety benefit for injury crashes was sustained across all traffic volumes. Both trends were supported by the cross-sectional analysis. Based on the analysis, it appears that roundabouts have the potential to significantly reduce crashes and severity at signalized intersections. A key aspect of the study was the estimation of the standard deviation of the distribution of the CMF in addition to the conventionally estimated standard error of the mean CMF value. For some CMFs, especially the CMFs for total crashes, the standard deviation of the distribution was larger than the standard error of the mean value of the CMF, indicating substantial variation in the treatment effect across sites.

Comparison of empirical Bayes and full Bayes approaches for before-after road safety evaluations.

The empirical Bayes (EB) approach has now gained wide acceptance among researchers as the much preferred one for the before-after evaluation of road safety treatments. In this approach, the before period crash experience at treated sites is used in conjunction with a crash prediction model for untreated reference sites to estimate the expected number of crashes that would have occurred without treatment. This estimate is compared to the count of crashes observed after treatment to evaluate the effect of the treatment. This procedure accounts for regression-to-the-mean effects that result from the natural tendency to select for treatment those sites with high observed crash frequencies. Of late, a fully Bayesian (FB) approach has been suggested as a useful, though complex alternative to the empirical Bayes approach in that it is believed to require less data for untreated reference sites, it better accounts for uncertainty in data used, and it provides more detailed causal inferences and more flexibility in selecting crash count distributions. This paper adds to the literature on comparing the two Bayesian approaches through empirical applications. The main application is an evaluation of the conversion of road segments from a four-lane to a three-lane cross-section with two-way left-turn lanes (also known as road diets). For completeness, the paper also summarizes the results of an earlier application pertaining to the evaluation of conversion of rural intersections from unsignalized to signalized control. For both applications, the estimated safety effects from the two approaches are comparable.

Development of planning level transportation safety tools using Geographically Weighted Poisson Regression.

A common technique used for the calibration of collision prediction models is the Generalized Linear Modeling (GLM) procedure with the assumption of Negative Binomial or Poisson error distribution. In this technique, fixed coefficients that represent the average relationship between the dependent variable and each explanatory variable are estimated. However, the stationary relationship assumed may hide some important spatial factors of the number of collisions at a particular traffic analysis zone. Consequently, the accuracy of such models for explaining the relationship between the dependent variable and the explanatory variables may be suspected since collision frequency is likely influenced by many spatially defined factors such as land use, demographic characteristics, and traffic volume patterns. The primary objective of this study is to investigate the spatial variations in the relationship between the number of zonal collisions and potential transportation planning predictors, using the Geographically Weighted Poisson Regression modeling technique. The secondary objective is to build on knowledge comparing the accuracy of Geographically Weighted Poisson Regression models to that of Generalized Linear Models. The results show that the Geographically Weighted Poisson Regression models are useful for capturing spatially dependent relationships and generally perform better than the conventional Generalized Linear Models.

Development of comprehensive accident models for two-lane rural highways using exposure, geometry, consistency and context variables.

In Europe, approximately 60% of road accident fatalities occur on two-lane rural roads. Thus, research to develop and enhance explanatory and predictive models for this road type continues to be of interest in mitigating these accidents. To this end, this paper describes a novel and extensive data collection and modeling effort to define accident models for two-lane road sections based on a unique combination of exposure, geometry, consistency and context variables directly related to the safety performance. The first part of the paper documents how these were identified for the segmentation of highways into homogeneous sections. Next, is a description of the extensive data collection effort that utilized differential cinematic GPS surveys to define the horizontal alignment variables, and road safety inspections (RSIs) to quantify the other road characteristics related to safety. The final part of the paper focuses on the calibration of models for estimating the expected number of accidents on homogeneous sections that can be characterized by constant values of the explanatory variables. Several candidate models were considered for calibration using the Generalized Linear Modeling (GLM) approach. After considering the statistical significance of the parameters related to exposure, geometry, consistency and context factors, and goodness of fit statistics, 19 models were ranked and three were selected as the recommended models. The first of the three is a base model, with length and traffic as the only predictor variables; since these variables are the only ones likely to be available network-wide, this base model can be used in an empirical Bayesian calculation to conduct network screening for ranking "sites with promise" of safety improvement. The other two models represent the best statistical fits with different combinations of significant variables related to exposure, geometry, consistency and context factors. These multiple variable models can be used, with caution, and in conjunction with results from other studies, to derive accident modification factors for these variables for design applications, and in safety assessment for smaller samples of sites for which these variables can be assembled with relative ease.

Validation of a Full Bayes methodology for observational before-after road safety studies and application to evaluation of rural signal conversions.

The objective of the study on which the paper is based was to explore the application of fully Bayesian methods for before-after road safety studies. Several variations of the methodology were evaluated with a simulated dataset in which hypothetical treatments with no safety effect were randomly assigned to high accident locations to mimic the common site selection process in road jurisdictions. It was confirmed that the fully Bayesian method by estimating no safety effect can account for the regression-to-the-mean that results from this biased site selection process. The fully Bayesian method was then applied to California rural intersection data to evaluate the safety effect of conversion from stop to signalized control. The results were then compared with those from the empirical Bayesian method, currently the accepted approach for conducting unbiased before-after evaluations. This comparison was generally favorable in that FB can provide similar results as EB.