Assessing the Negative Binomial-Lindley model for crash hotspot identification: Insights from Monte Carlo simulation analysis.

Identifying hazardous crash sites (or hotspots) is a crucial step in highway safety management. The Negative Binomial (NB) model is the most common model used in safety analyses and evaluations - including hotspot identification. The NB model, however, is not without limitations. In fact, this model does not perform well when data are highly dispersed, include excess zero observations, or have a long tail. Recently, the Negative Binomial-Lindley (NB-L) model has been proposed as an alternative to the NB. The NB-L model overcomes several limitations related to the NB, such as addressing the issue of excess zero observations in highly dispersed data. However, it is not clear how the NB-L model performs regarding the hotspot identification. In this paper, an innovative Monte Carlo simulation protocol was designed to generate a wide range of simulated data characterized by different means, dispersions, and percentage of zeros. Next, the NB-L model was written as a Full-Bayes hierarchical model and compared with the Full-Bayes NB model for hotspot identification using extensive simulation scenarios. Most previous studies focused on statistical fit, and showed that the NB-L model fits the data better than the NB. In this research, however, we investigated the performance of the NB-L model in identifying the hazardous sites. We showed that there is a trade-off between the NB-L and NB when it comes to hotspot identification. Multiple performance metrics were used for the assessment. Among those, the results show that the NB-L model provides a better specificity in identifying hotspots, while the NB model provides a better sensitivity, especially for highly dispersed data. In other words, while the NB model performs better in identifying hazardous sites, the NB-L model performs better, when budget is limited, by not selecting non-hazardous sites as hazardous.

A before-after evaluation of protected right-turn signal phasings by applying Empirical Bayes and Full Bayes approaches with heterogenous count data models.

Right-turn crashes (or left-turn crashes for the US or similar countries) represent over 40 % of signalized intersection crashes in Queensland, Australia. Protected right-turn phasings are a widely used countermeasure for right-turn crashes, but the research findings on their effects across different crash types and intersection types are not consistent. Methodologically, the Empirical Bayes and Full Bayes techniques are generally applied for before-after evaluations, but the inclusion of heterogeneous models within these techniques has not been considered much. Addressing these research gaps, the objective of this study is to evaluate the effectiveness of protected right-turn signal phasings at signalized intersections employing heterogeneous count data models with the Empirical Bayes and Full Bayes techniques. In particular, the Empirical Bayes approach based on random parameters Poisson-Gamma models (simulation-based Empirical Bayes), and the Full Bayes approach based on random parameters Poisson-Lognormal intervention models (simulation-based Full Bayes) are applied. A total of 69 Cross intersections (with ten treated sites) and 47 T intersections (with six treated sites) from Southeast Queensland in Australia were included in the analysis to estimate the effects of protected right-turn signal phasings on various crash types. Results show that the change of signal phasing from a permissive right-turn phasing to the protected right-turn phasing at cross and T intersections reduces about 87 % and 91 % of right-turn crashes, respectively. In addition, the effect of protected right-turn phasings on rear-end crashes was not significant. The heterogenous count data models significantly address extra Poisson variation, leading to efficient safety estimates in both simulation-based Empirical Bayes and simulation-based Full Bayes approaches. This study demonstrates the importance of accounting for unobserved heterogeneity for the before-after evaluation of engineering countermeasures.

Examining the performance of engineering treatment evaluation methodologies using the hypothetical treatment and actual treatment settings.

The selection of treatment evaluation methodology is paramount in determining reliable crash modification factors (CMFs) for engineering treatments. A lack of ground truth makes it cumbersome to examine the performance of treatment evaluation methodologies. In addition, a sound methodological framework is critical for evaluating the performances of treatment evaluation methodologies. In addressing these challenges, this study proposed a framework for assessing treatment evaluation methodologies by hypothetical treatments with known ground truth and actual real-world treatments. In particular, this study examined three before-after treatment evaluation approaches: 1) Empirical Bayes, 2) Simulation-based Empirical Bayes, and 3) Full Bayes methods. In addition, this study examined the Cross-Sectional treatment evaluation methodology. The methodological framework utilized five datasets of hypothetical treatment with known ground truth based on the hotspot identification method and a real-world dataset of wide centerline treatment on two-lane, two-way rural highways in Queensland, Australia. Results showed that all the methods could identify the ground truth of hypothetical treatments, but the Full Bayes approach better predicts the known ground truth compared to Empirical Bayes, Simulation-based Empirical Bayes, and Cross-Sectional methods. The Full Bayes approach was also found to provide the most precise estimate for real-world wide centerline treatment along rural highways compared to other methods. Moreover, the current study highlighted that the Cross-Sectional method offers a viable estimate of treatment effectiveness in case the before-period data is limited.

Accounting for seasonal effects on cyclist-vehicle crashes.

Crash data is usually aggregated over time where temporal correlation contributes to the unobserved heterogeneity. Since crashes that occur in temporal proximity share some unobserved characteristics, ignoring these temporal correlations in safety modeling may lead to biased estimates and a loss of model power. Seasonality has several effects on cyclists' travel behavior (e.g., the distribution of holidays, school schedules, weather variations) and consequently cyclist-vehicle crash risk. This study aims to account for the effect of seasonality on cyclist-vehicle crashes by employing two groups of models. The first group, seasonal cyclist-vehicle crash frequency, employs four vectors of the dependent variables for each season. The second group, rainfall involved cyclist-vehicle crash frequency, employs two vectors of the dependent variables for crashes that occurred on rainy days and non-rainy days. The two model groups were investigated using three modeling techniques: Full Bayes crash prediction model with spatial effects (base model), varying intercept and slope model, and First-Order Random Walk model with a spatial-temporal interaction term. Crash and volume data for 134 traffic analysis zones (TAZ's) in the City of Vancouver were used. The results showed that the First-Order Random Walk model with spatial-temporal interaction outperformed the other developed models. Some covariates have different associations with crashes depending on the season and rainfall conditions. For example, the seasonal estimates for the bus stop density are significantly higher for the summer and spring seasons than for the winter and autumn seasons. Also, the intersection density estimate for a rainy day is significantly higher than a non-rainy day. This indicates that on a rainy day each intersection to the network adds more risk to cyclists compared to a non-rainy day.

A before-after full bayes multivariate intervention model to estimate the safety effectiveness of red light cameras.

OBJECTIVE: Intersection-related crashes account for approximately 40% of all crashes and tend to be more severe. Red-light running (RLR) crashes are most severe as almost half of these crashes result in injuries and fatalities. To reduce RLR crashes, agencies have been deploying red light cameras (RLCs). The main objective of this study was to evaluate the safety effectiveness of RLCs in the City of Miami Beach, Florida. METHOD: The full Bayes (FB) approach was conducted based on five treatment intersections with six RLCs and 14 comparison intersections without RLCs. The analysis focused on target crash types, including rear-end, sideswipe, and angle/left-turn/right-turn crashes, and crash severity. RESULTS: The FB analysis indicated a significant sudden drop in all types of target crashes immediately after the installation of RLCs. Compared to the before-period, the after-period experienced: fewer angle/left-turn/right-turn crashes, fewer sideswipe crashes, and more rear-end crashes. The sideswipe and angle/left-turn/right-turn crashes dropped immediately after the installation of RLCs and then continued to increase, but they were still lower than the before- period. The rear-end crashes dropped immediately after the installation of RLCs and then continued to increase, but they increased at a steeper rate. Major and minor approaches AADT, higher speed limit, longer amber time, length of pedestrian crosswalk, and number of driveways within the intersection influence area increased the frequency of total target, PDO, and FI crashes. Intersections with all-red interval more than two seconds, major approach with more than two through lanes, and minor approach with more than one through lane, on the contrary, resulted in a fewer number of the total target, PDO, and FI crashes. The treatment indicator showed that treatment intersections experienced fewer FI, angle/left-turn/right-turn, and sideswipe crashes and more total, PDO, and rear-end crashes compared to the non-treatment intersections. CONCLUSION: This study provides reliable estimates of the safety effectiveness of RLCs since it accounts for uncertainties in the data, regression-to-the-mean, and spillover effects.

Investigating safety effects of wider longitudinal pavement markings.

Many road authorities in Canada have been contemplating the use of wider longitudinal pavement markings (LPMs) to enhance road safety and driver comfort. However, conclusive evidence on the safety impacts of wider LPMs has not been available. To address this gap in the literature, this study was conducted to investigate the safety impacts of wider LPMs. The study adopted the Full Bayes approach to conduct a before and after safety evaluation, using data collected from 38 treatment sites (highway segments) from three Canadian jurisdictions (i.e., British Columbia, Alberta, and Quebec). Collision and traffic data were obtained from the 38 sites over a period of eight years (2008-2015). The widths of LPMs at all sites were increased between 2012 and 2013, which enables a before and after safety evaluation to investigate the impact of the wider markings on the collision frequency. The results showed an overall significant reduction in both total collisions and target collisions (i.e., run-off-the-road collisions) by 12.3 % and 19.0 %, respectively, after implementing the wider LPMs. Total collisions were reduced by 11.1 %, 27.5 %, and 1.1 % in Alberta, British Columbia, and Quebec, respectively. Similarly, a reduction in the run-off-the-road collisions that ranged between 22.7 % and 28.9 % were observed in the three jurisdictions. The results suggest that wider longitudinal pavement markings can reduce collisions and improve safety on Canadian highways. As such, road authorities should consider using this intervention to enhance road safety, particularly, at locations that experience a high frequency of run-off-the-road collisions.

Multivariate models to investigate the relationship between collision risk and reliability outcomes on horizontal curves.

This paper proposes a reliability-based framework to address the risk associated with limitations in the Available Sight Distance (ASD) on curved highway segments considering a three-dimensional (3D) sight distance computation approach. To facilitate this assessment, the ASD on horizontal curves was evaluated and an accurate inventory of curve attribute information was generated using LiDAR (Light Detection and Ranging) data in an automated and efficient manner. These datasets were then used to estimate the risk (probability of noncompliance, Pnc) associated with sight distance insufficiencies. Full Bayes multivariate Poisson log-normal safety performance functions were developed to relate the Pnc to the expected number of collisions. The results show that there was a statistically significant relationship between Pnc and collision frequency. There was also a significant correlation of 0.444 to 0.452 across collision severity levels indicating that curves with high Property-Damage-Only (PDO) collisions could be associated with higher injury and fatal (I + F) collisions. It was also found that Pnc had a greater impact on increasing PDO collisions than I + F collisions, suggesting that collisions associated with insufficient sight distance are likely to be less severe. The results of this analysis are expected to improve our understanding of the risks associated with deviations from design guidelines and quantitatively assess the safety margins due to these variations. The framework presented in this paper can be used to compare different design alternatives and investigate the influence of design deficiencies on collision occurrence across various severity levels.

Accounting for mediation in cyclist-vehicle crash models: A Bayesian mediation analysis approach.

Cyclist safety is affected by many factors on the zonal level. Previous studies have found associations between cyclist-vehicle crashes and vehicle and bike exposures, network configuration, land use, road facility, and the built environment. In addition, the network configuration, land use, and road facility were found to affect bike exposure levels. The association of zonal characteristics with both exposure and crashes may bias the development of macro-level bike safety models. This paper aims to explain these associations simultaneously using a form of Structural Equation Modelling approach. The analysis assesses the mediated effects that some variables have on crashes through their effects on bike exposure (by setting bike exposure as a mediator). Data from 134 traffic analysis zones (TAZ's) in the City of Vancouver, Canada is used as a case study. The indirect effect of network configuration, land use, and road facility on cyclist-vehicle crashes was assessed through Bayesian mediation analysis. Mediation analysis is an approach used to estimate how one variable transmits its effects to another variable through a certain mediator. These effects could be direct only, indirect only (through a certain mediator), or both direct and indirect. The results showed that the bike kilometers travelled (BKT) was a mediator of the relationship between network configuration, land use, and road facility and cyclist-vehicle crashes. The mediation analysis showed that some variables have different direct and indirect effect on cyclist-vehicle crashes. This indicates that while some variables may have negative direct association with crashes, their total crash effect can be positive after accounting for their effect through exposure. For example, bike network coverage and recreational density have negative direct association with cyclist-vehicle crashes, and positive indirect association leading to positive total effect on cyclist-vehicle crashes.

Comparison of Bayesian techniques for the before-after evaluation of the safety effectiveness of short 2+1 road sections.

In evaluating the effectiveness of a road safety treatment, the regression to the mean phenomenon is a cause for concern because of a possible overestimation of benefits. Therefore, Bayesian approaches are usually suggested as the most appropriate methodologies for before-after studies as they account for regression to the mean effects. The empirical Bayes (EB) methodology examines the estimation of the expected number of crashes that would have occurred without treatment and compares them with the crashes observed at the treated sites. Even if there is no significant regression to the mean bias, the EB technique requires a reliable and large dataset with sufficient years of observation and number of treated sites, adequate for estimating the safety effects of a treatment with acceptable standard errors. In this framework, a full Bayesian (FB) approach can mitigate the problem of using small datasets by providing more detailed causal inferences and more flexibility in selecting crash count distributions, acknowledging that a more complex methodology must be applied. With the aim of estimating the safety improvements of new, short 2 + 1 road sections in Poland limited by the existing road network, EB and FB estimations are compared and different safety performance function (SPF) model forms are used in order to evaluate the performance of the two methodologies. Results indicated that, even if crash modification factors (CMFs) resulted in similar average values, the EB trend is to underestimate CMFs compared with the more complex methodology, while overall the FB approach provided a lower standard deviation. The differences are more pronounced between the EB and FB approaches when a simple SPF model form is used for the analysed dataset. Moreover, for this specific dataset, the difference between the FB method and the EB method using a refined regression model with more variables was negligible.

Safety effects of wet-weather pavement markings.

While there has been increasing interest in wet-weather pavement markings due to their improved visibility and potential for enhancing road safety in wet-night conditions, there is a lack of research evaluating their safety effectiveness based on actual wet-night crash data. This paper presents the safety assessment of wet-weather pavement markings in the Atlanta District of the Texas Department of Transportation, conducted by two different evaluation approaches that are known to be rigorous and statistically defensible: Empirical-Bayes before-after analysis and full Bayes before-after analysis with comparison groups. The results from both approaches suggest that there are positive safety effects of wet-weather pavement markings for relevant crashes, providing evidence-based support for safety benefits of wet-weather markings.

A full Bayes approach for traffic conflict-based before-after safety evaluation using extreme value theory.

A full Bayes approach is proposed for traffic conflict-based before-after safety evaluations using extreme value theory. The approach combines traffic conflicts of different sites and periods and develops a uniform generalized extreme value (GEV) model for the treatment effect estimation. Moreover, a hierarchical Bayesian structure is used to link possible covariates to GEV parameters and to account for unobserved heterogeneity among different sites. The proposed approach was applied to evaluate the safety benefits of a left-turn bay extension project in the City of Surrey, Canada, in which traffic conflicts were collected from 3 treatment sites and 3 matched control sites before and after the treatment. A series of models were developed considering different combinations of covariates and their link to different GEV model parameters. Based on the best fitted model, the treatment effects were analyzed quantitatively using the odds ratio (OR) method as well as qualitatively by comparing the shapes of GEV distributions. The results show that there are significant reduction in the expected number of crashes (i.e., OR = 0.409). In addition, there are apparent changes in the shape of GEV distributions for the treatment sites, where GEV distributions shift further away from the risk of crash area after the treatment. Both of these results indicate significant safety improvements after the left-turn bay extension.

Surrogate safety and network screening: Modelling crash frequency using GPS travel data and latent Gaussian Spatial Models.

Improving road safety requires accurate network screening methods to identify and prioritize sites in order to maximize the effectiveness of implemented countermeasures. In screening, hotspots are commonly identified using statistical models and ranking criteria derived from observed crash data. However, collision databases are subject to errors, omissions, and underreporting. More importantly, crash-based methods are reactive and require years of crash data. With the arrival of new technologies including Global Positioning System (GPS) trajectory data, proactive surrogate safety methods have gained popularity as an alternative approach for screening. GPS-enabled smartphones can collect reliable and spatio-temporally rich driving data from regular drivers using an inexpensive, simple, and user-friendly tool. However, few studies to date have analyzed large volumes of smartphone GPS data and considered surrogate-safety modelling techniques for network screening. The purpose of this paper is to propose a surrogate safety screening approach based on smartphone GPS data and a Full Bayesian modelling framework. After processing crash data and GPS data collected in Quebec City, Canada, several surrogate safety measures (SSMs), including vehicle manoeuvres (hard braking) and measures of traffic flow (congestion, average speed, and speed variation), were extracted. Then, spatial crash frequency models incorporating the extracted SSMs were proposed and validated. A Latent Gaussian Spatial Model was estimated using the Integrated Nested Laplace Approximation (INLA) technique. While the INLA Negative Binomial models outperformed alternative models, incorporating spatial correlations provided the greatest improvement in model fit. Relationships between SSMs and crash frequency established in previous studies were generally supported by the modelling results. For example, hard braking, congestion, and speed variation were all positively linked to crash counts at the intersection level. Network screening based on SSMs presents a substantial contribution to the field of road safety and works towards the elimination of crash data in evaluation and monitoring.

A full Bayesian approach to appraise the safety effects of pedestrian countdown signals to drivers.

Although they are meant for pedestrians, pedestrian countdown signals (PCSs) give cues to drivers about the length of the remaining green phase, hence affecting drivers' behavior at intersections. This study focuses on the evaluation of the safety effectiveness of PCSs to drivers, in the cities of Jacksonville and Gainesville, Florida, using crash modification factors (CMFs) and crash modification functions (CMFunctions). A full Bayes (FB) before-and-after with comparison group method was used to quantify the safety impacts of PCSs to drivers. The CMFs were established for distinctive categories of crashes based on crash type (rear-end and angle collisions) and severity level (total, fatal and injury (FI), and property damage only (PDO) collisions). The CMFs findings indicated that installing PCSs result in a significant improvement of drivers' safety, at a 95% Bayesian credible interval (BCI), for total, PDO, and rear-end collisions. The results of FI and angle crashes were not significant. The CMFunctions indicate that the treatment effectiveness varies considerably with post-treatment time and traffic volume. Nevertheless, the CMFs on rear-end crashes are observed to decline with post-treatment time. In summary, the results suggest the usefulness of PCSs for drivers. The findings of this study may prompt a need for a broader research to investigate the need to design PCSs that will serve the purpose not only of pedestrians, but drivers as well.

Use of empirical and full Bayes before-after approaches to estimate the safety effects of roadside barriers with different crash conditions.

INTRODUCTION: Although many researchers have estimated the crash modification factors (CMFs) for specific treatments (or countermeasures), there is a lack of prior studies that have explored the variation of CMFs. Thus, the main objectives of this study are: (a) to estimate CMFs for the installation of different types of roadside barriers, and (b) to determine the changes of safety effects for different crash types, severities, and conditions. METHOD: Two observational before-after analyses (i.e. empirical Bayes (EB) and full Bayes (FB) approaches) were utilized in this study to estimate CMFs. To consider the variation of safety effects based on different vehicle, driver, weather, and time of day information, the crashes were categorized based on vehicle size (passenger and heavy), driver age (young, middle, and old), weather condition (normal and rain), and time difference (day time and night time). RESULTS: The results show that the addition of roadside barriers is safety effective in reducing severe crashes for all types and run-off roadway (ROR) crashes. On the other hand, it was found that roadside barriers tend to increase all types of crashes for all severities. The results indicate that the treatment might increase the total number of crashes but it might be helpful in reducing injury and severe crashes. In this study, the variation of CMFs was determined for ROR crashes based on the different vehicle, driver, weather, and time information. PRACTICAL APPLICATIONS: Based on the findings from this study, the variation of CMFs can enhance the reliability of CMFs for different roadway conditions in decision making process. Also, it can be recommended to identify the safety effects of specific treatments for different crash types and severity levels with consideration of the different vehicle, driver, weather, and time of day information.

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.

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.

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.

Spatial analysis and geographic variation of fatal and injury crashes in mazandaran province from 2006 to 2010.

BACKGROUND: Road safety and traffic accidents change in time and space. Although, time variations have always been considered the subject being focused by researchers, the effect of spatial correlation and spatial components on the risk of accident have been less investigated. Due to its specific geographical position, Mazandaran Province is one of the highest traffic provinces. This study aims to investigate the factors influencing suburban crashes of Mazandaran province by considering the spatial correlation. METHODS: This study is aggregated (descriptive -analytical) and the study period was 2006 to 2010. Social and environmental factors effects on the risk of accidents have been studied considering the correlation structure of the regions and regardless of this structure with Poisson regression, negative binomial and Full Bayes hierarchical models. Geographical pattern of risk distribution for the observed values of SMRs and the estimated values after smoothing have been plotted and analyzed. RESULTS: Comparing the measures of models goodness of fit indicates that hierarchical Bayes model fits the data better. Plotting the geographical pattern, the north central parts of the province have been identified as the high-risk areas. Human factors were identified as the important factors for the risk of accident. CONCLUSIONS: The purpose of this procedure is to separate the random effect of residuals correlation. Using this method, the measure of the model goodness of fit got reduced reflecting a better model than the prototype model. The significance of the structured spatial effect shows the existence of unknown explanatory variables with correlated structure whose identification and control can reduce the risk of accidents.

Accounting for heterogeneity among treatment sites and time trends in developing crash modification functions.

Collision modification factors (CMFs) are commonly used to quantify the impact of safety countermeasures. The CMFs obtained from observational before-after (BA) studies are usually estimated by averaging the safety impact (i.e., index of effectiveness) for a group of treatment sites. The heterogeneity among the treatment locations, in terms of their characteristics, and the effect of this heterogeneity on safety treatment effectiveness are usually ignored. This is in contrast to treatment evaluations in other fields like medical statistics where variations in the magnitude (or in the direction) of response to the same treatment given to different patients are considered. This paper introduces an approach for estimating a CMFunction from BA safety studies that account for variable treatment location characteristics (heterogeneity). The treatment sites heterogeneity was incorporated into the CMFunction 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 (FB) context. To demonstrate the approach, a case study is presented to evaluate the safety effectiveness of the "Signal Head Upgrade Program" recently implemented in the city of Surrey (British Columbia, Canada), where signal visibility was improved at several urban signalized intersections. The results demonstrated the importance of considering treatment sites heterogeneity and time trends when developing CMFunctions.

Bayesian methodology to estimate and update safety performance functions under limited data conditions: a sensitivity analysis.

In road safety studies, decision makers must often cope with limited data conditions. In such circumstances, the maximum likelihood estimation (MLE), which relies on asymptotic theory, is unreliable and prone to bias. Moreover, it has been reported in the literature that (a) Bayesian estimates might be significantly biased when using non-informative prior distributions under limited data conditions, and that (b) the calibration of limited data is plausible when existing evidence in the form of proper priors is introduced into analyses. Although the Highway Safety Manual (2010) (HSM) and other research studies provide calibration and updating procedures, the data requirements can be very taxing. This paper presents a practical and sound Bayesian method to estimate and/or update safety performance function (SPF) parameters combining the information available from limited data with the SPF parameters reported in the HSM. The proposed Bayesian updating approach has the advantage of requiring fewer observations to get reliable estimates. This paper documents this procedure. The adopted technique is validated by conducting a sensitivity analysis through an extensive simulation study with 15 different models, which include various prior combinations. This sensitivity analysis contributes to our understanding of the comparative aspects of a large number of prior distributions. Furthermore, the proposed method contributes to unification of the Bayesian updating process for SPFs. The results demonstrate the accuracy of the developed methodology. Therefore, the suggested approach offers considerable promise as a methodological tool to estimate and/or update baseline SPFs and to evaluate the efficacy of road safety countermeasures under limited data conditions.