Animal-vehicle collisions (AVCs) are common around the world and result in considerable loss of animal and human life, as well as significant property damage and regular insurance claims. Understanding their occurrence in relation to various contributing factors and being able to identify high-risk locations are valuable to AVC prevention, yielding economic, social, and environmental cost savings. However, many challenges exist in the study of AVC datasets. These include seasonality of animal activity, unknown exposure (i.e., the number of animal crossings), very low AVC counts across most sections of extensive roadway networks, and computational burdens that come with discrete response analysis using large datasets. To overcome these challenges, a Bayesian hierarchical model is proposed where the exposure is modeled with nonparametric Dirichlet process, and the number of segment-level AVCs is assumed to follow a binomial distribution. A Pólya-Gamma augmented Gibbs sampler is derived to estimate the proposed model. By using the AVC data of multiple years across about 85,000 segments of state-controlled highways in Texas, U.S., it is demonstrated that the model is scalable to large datasets, with a preponderance of zeros and clear monthly seasonality in counts, while identifying high-risk locations and key explanatory factors based on segment-specific factors (such as changes in speed limit). This can be done within the modelling framework, which provides useful information for policy-making purposes.

The increasing number of crashes occurring in work zones has received considerable attention in recent years. Previous studies have mainly focused on associations between work zone configurations and crash occurrence. Although identification of associational relations helps us understand how work zones co-exist with crashes, it does not provide interventional guidelines necessary to improve safety of work zone operations. In this paper, a causal inference model based on the potential outcome framework is proposed to rigorously infer the causal effects of work zone presence on crash risks under various work zone configurations, along with robustness tests. In developing such a causal model, three research gaps are identified and addressed: (1) potential confounding bias due to unobservable roadway characteristics; (2) potential bias caused by unobserved variables in multisource data; and (3) lack of actually observed traffic data and weather information at the exact time when a crash occurred and lack of large-scale high-granular data. The proposed methodology is applied to 5,006 work zones in Pennsylvania from 2015 to 2017, and the results are validated via a series of robustness tests. The results show that the causal effect of a work zone on crash occurrence is significantly positive, especially on roadways with high traffic volumes, on long-distance work zones, and work zones conducted during daytime. It appears that conducting work zones during nighttime with the current deployment strategies on Pennsylvania state roads does not necessarily increase crash risks, but a work zone significantly increases crash risks during day time.

Since the mid-2000s, Public–Private Partnerships (PPP) have been established in transportation infrastructure projects as an effective alternative to the traditional procurement process, such as design-bid-build where the design and construction are awarded separately and sequentially to private firms. PPP contracts ensure both greater participation of the private sector, as well as shared responsibility in project delivery. However, the interrelationship between various PPP approaches and the status of traffic safety during the project implementation has not been thoroughly explored to date. This paper seeks to provide new insights into the performance of different PPP contracting approaches by investigating them from the perspective of transportation safety. To that end, a statistical analysis is conducted in order to distinguish differences with respect to the characteristics of crashes that occurred during the contractual period of roadway projects. Using data from 645 PPP contracts that were executed across multiple States of the US between 1996 and 2011, count data models of crash frequencies are developed. To take into account the effect of unobserved factors on crash frequencies, correlated random parameter models with heterogeneity in the means are estimated. The results of the statistical analysis overall show that the determinants of crash frequencies and the magnitude of their impacts vary across PPP types. Contracts with higher cost, shorter duration, fewer lane-miles to be covered, more asset work activities, as well as contracts for roadways featuring better pavement and drainage conditions, low to medium AADT, and higher width of shoulder are more likely to observe fewer crashes. Additionally, several variables resulted in correlated random parameters (such as, contract size in lane-miles and truck percentage), with their distributional characteristics being affected by other exogenous factors (such as pavement characteristics), thus unveiling the heterogeneous patterns underpinning the safety performance of different PPP approaches.

To minimize non-recurrent congestion, a better understanding of the factors that affect accident clearance time is crucial, in order to optimize incident management strategies. A number of methods have been developed to predict incident clearance duration, but few of those have considered the time-varying nature of certain observed factors. In addressing this gap in the literature, this study developed a grouped random parameters hazard-based duration model with time-varying covariates, while accounting for unobserved heterogeneity. Data on accidents, traffic, road inventory, and real-time weather condition were compiled for the Kaiyang freeway in 2014. Comparison of candidate models shows that the proposed model with Weibull distribution exhibits the best fit performance. The results suggest that the effects of rear-end accident, involvements of trucks or other vehicles, evening hours, and shoulder blockage on the hazard function are heterogeneous across observations. Other variables such as angle accident, injury severity, traffic volume and composition, morning or pre-dawn hours, and blockage of overtaking lane were also found to have significant but homogenous effects on accident clearance time. More importantly, the results also reveal the significant effects of the time-varying covariates (wind speed, temperature, and humidity). Accordingly, the viability and superiority of the proposed model in analyzing accident clearance time are confirmed. Overall, the results of this study are expected not only to improve traffic incident management by allowing government agencies to better understand factors affecting accident clearance times, but also to facilitate incident clearance through the recognition of time-varying pattern.

Alcohol consumption has been acknowledged as a critical determinant concerning the occurrence of vehicle crashes and their resulting injury severities. To investigate the weekly transferability and temporal stability of the contributors determining different injury severity levels in alcohol-impaired driving crashes, this paper employs two groups of random thresholds random parameters hierarchical ordered probit models. Three injury-severity categories are determined as outcome variables: no injury, minor injury and severe injury, while multiple factors are investigated as explanatory variables including driver characteristics, vehicle characteristics, roadway characteristics, environmental characteristics, crash characteristics and temporal characteristics. The weekly transferability and temporal stability of the models are examined through three groups of likelihood ratio tests. Marginal effects are also adopted to analyze the weekly transferability and temporal stability of the explanatory variables. Overall, the findings exhibit weekly variations and temporal instability while some indicators are also observed to be of relative weekly transferability including speeding, aggressive driving, proceeding, motorcycle, speed limit between 45 and 55 mph, curve, driveway, overturned, hit-fixed-object, vehicle age (5–9 years old). Besides, curve and passenger car indicators in weekday models present relative temporal stability. This paper can provide insights into preventing alcohol-impaired driving crashes and can potentially facilitate the development of the corresponding crash injury mitigation policies. More studies could be conducted integrating the advanced data-driven methods into the statistical models to simultaneously achieve inference and prediction.

Research in highway safety continues to struggle to address two potentially important issues; the role that unobserved factors may play on resulting crash and injury-severity likelihoods, and the issue of identification in safety modeling caused by the self-selective sampling inherent in commonly used safety data (the fact that drivers in observed crashes are not a random sample of the driving population, with riskier drivers being over-represented in crash data bases). This paper addresses unobserved heterogeneity using mixing distributions and attempts to provide insight into the potential sample-selection problem by considering data before and during the COVID-19 pandemic. Based on a survey of vehicle usage (vehicle miles traveled) and subsequent statistical modeling, there is evidence that riskier drivers likely made up a larger proportion of vehicle miles traveled during the pandemic than before, suggesting that the increase in injury severities observed during COVID-19 could potentially be due to the over-representation of riskier drivers in observed crash data. However, by exploring Florida crash data before and during the pandemic (and focusing on crashes where risky behaviors were observed), the empirical analysis of observed crash data suggests (using random parameters multinomial logit models of driver-injury severities with heterogeneity in means and variances) that the observed increase in injury severity during the COVID-19 pandemic (calendar year 2020) was likely due largely to fundamental changes in driver behavior and less to changes in the sample selectivity of observed crash data. The findings of this paper provide some initial guidance to future work that can begin to more rigorously explore and assess the role of selectivity and resulting identification issues that may be present when using observed crash data.

The rapid technological advancements in video analytics and the availability of big data have made traffic conflict techniques a viable tool for road safety assessments. They can potentially overcome many major limitations of conventional road safety practices that use crash-data analyses. However, the current traffic conflict techniques flag serious concerns regarding the context-dependence of the relationship between traffic conflicts and crashes, the lack of consideration of road user and vehicle heterogeneities in their formulation, and the exclusion of crash severity estimation from the analysis process. To overcome these limitations, this study proposes a novel application of the safety field theory to estimate crash risk and severity by modeling the safety-aware interactions of various road users in a road traffic environment. The safety field theory borrows from the Physics concept of electromagnetic fields to mathematically define the safety “buffers” that road users typically maintain around them while moving in traffic. Additionally, the model formulation explicitly accounts for exceptional circumstances (crashes and extreme conflicts) and integrates severity in the risk estimation framework to provide a holistic safety assessment framework. The proposed safety field theory application was tested by analyzing a total of 196 h of traffic movement videos collected from three signalized intersections in Brisbane, Australia and extracting the required road user trajectory information through artificial intelligence-based video analytics. Extreme value modeling of the tail distribution of the risk force generated by the interacting road user safety fields showed that it could predict the crash frequency and outcome severity more accurately than the prevalent traffic conflict indicators. Thus, the proposed approach provides a single, unified, and efficient method of accurately estimating crash risk and injury severities that can be adapted for various application contexts. The study results significantly improve the effectiveness of automated safety analysis for transport facilities and could elevate the safety prediction algorithms of real-time applications like adaptive signal control systems and Connected and Automated Vehicles.

Extreme value theory is the state-of-the-art modelling technique for estimating crash risk from traffic conflicts, with two different sampling techniques, i.e. block maxima and peak-over-threshold, at its core. However, the uncertainty associated with the estimates obtained by these sampling techniques has been too large to enable its widespread practical use. A fundamental reason for this issue is the improper selection of extreme values and a lack of a suitable and efficient sampling mechanism. This study proposes a hybrid modelling framework of machine learning and extreme value theory to estimate crash risk from traffic conflicts with an efficient sampling technique for identifying extremes. More specifically, a machine learning approach replaces the conventional sampling techniques with anomaly detection techniques since an anomaly is a data point that does not conform with the rest of the data, making it very similar to the definition of an extreme value. Six representative machine learning-based unsupervised anomaly detection algorithms have been tested in this study. They include iforest, minimum covariance determinant, one-class support vector machine, k-nearest neighbours, local outlier factor, and connectivity-based outlier factor. The extremes identified by these algorithms are then fitted to extreme value distributions for both univariate and bivariate frameworks. These algorithms were tested on a large set of traffic conflict data collected for four weekdays (6 am to 6 pm) from three four-legged intersections in Brisbane, Australia. Results indicate that the proposed hybrid models consistently outperform the conventional extreme value models, which use block maxima and peak-over-threshold as the underlying sampling technique. Among the sampling algorithms, iforest has been found to perform better than other algorithms in estimating crash risks from traffic conflicts. The proposed hybrid modelling framework represents a methodological advancement in traffic conflict-based crash estimation models and opens new avenues for exploring the possibility of utilising machine learning techniques within the existing traffic conflict techniques.

Crashes at highway-rail grade crossings often result in higher proportion of injury and fatality of the vehicle occupants as compared to other crash types, necessitating in-depth investigation to identify their causal factors. In this study, injury-severity outcomes from highway-rail grade crossing crashes are analyzed using crash data from Texas and California, which are the most vulnerable states in the United States, in terms of highway-rail grade crossing crash occurrences. The data are collected from the Federal Railroad Administration’s (FRA) Office of Safety Analysis, covering a period between 2012 and 2020. Such data often suffer from out-of-date or missing information due to cost and available resources limitations, which inevitably may lead to unobserved characteristics varying systematically across various aspects of the data. Unobserved heterogeneity is an important misspecification issue, that in turn introduces modeling bias. To address these limitations, the random parameters multinomial logit modeling framework with heterogeneity in the means and variances is employed for the econometric analysis in this paper, which effectively accounts for multilayered unobserved heterogeneity. Spatial instability of the factors affecting different injury-severity levels is investigated as well. The results indicate that the factors are not spatially stable across Texas and California, leading to the estimation of two separate state-specific models. The estimation results of the two state-specific models help identify several vehicle-, train-, vehicle driver-, weather- and crossing-specific factors affecting different injury severity outcomes. Moreover, the results also demonstrate the varying magnitude of the identified factors on injury-severity across the two states, indicating the presence of spatial instability. The findings of this study highlight the importance of accounting for unobserved heterogeneity and spatial instability to avert critical methodological issues and misleading inferences from the simple aggregation used in most econometric analysis of highway-rail grade crossing crashes.

The real-time conflict prediction model using traffic flow characteristics is much less studied than the crash-based model. This study aims at exploring the relationship between conflicts and traffic flow features with the consideration of heterogeneity and developing predictive models to identify conflict-prone conditions in a real-time manner. The high-resolution trajectory data from the HighD dataset is used as empirical data. A novel method with the virtual detector approach for traffic feature extraction and a two-step framework is proposed for the trajectory data analysis. The framework consists of an exploratory study by random parameter logit model with heterogeneity in means and variances and a comparative study on several machine learning methods, including eXtreme Gradient Boosting (Boosting), Random Forest (Bagging), Support Vector Machine (Single-classifier), and Multilayer-Perceptron (Deep neural network). Results indicate that (1) traffic flow characteristics have significant impacts on the probability of conflict occurrence; (2) the statistical model considering mean heterogeneity outperforms the counterpart and lane differences variables are found to significantly impact the means of random parameters for both lane variables and lane differences variables; (3) eXtreme Gradient Boosting trained on an under-sampled dataset turns out to be the best model with the highest AUC of 0.871 and precision of 0.867, showing that re-sampling techniques can significantly improve the model performance. The proposed model is found to be sensitive to the conflict threshold. Sensitivity analysis on feature selection further confirms that the conflict risk prediction should consider both subject lane features and lane difference features, which verifies the consistency with exploratory analysis based on the statistical model. The consistency between statistical models and machine learning methods improves the interpretability of results for the latter one.

Real-time safety analysis and optimization using surrogate safety measures such as traffic conflicts and techniques such extreme value theory (EVT) models is an emerging research topic in the context of proactive traffic safety management. However, the predictive performance and temporal transferability of the existing real-time safety analysis EVT models are subject to the assumption of invariant model parameters, which do not account for the temporal variability and is not suitable for real-time traffic data analysis. This study proposes a Bayesian dynamic extreme value modeling approach for conflict-based real-time safety analysis which integrates a Bayesian dynamic linear model with the extreme value distribution. The proposed approach has several unique advantages as it: 1) allows the model parameters to be time-varying; 2) integrates the newer data with prior information to recursively update the model parameters and account for state-space changes and react to sudden trend changes; 3) accounts for temporal variability and non-stationarity in conflict extremes; and 4) quantitatively evaluates the real-time safety levels of a road facility. The proposed approach is applied for cycle-by-cycle safety analysis at four signalized intersections in the city of Surrey, British Columbia. Traffic conflicts are characterized by the modified time to collision indicator. Three traffic parameters (traffic volume, shock wave area, and platoon ratio) at the signal cycle level are considered as covariates to account for non-stationarity. Several Bayesian dynamic and static extreme value models are developed and two safety indices, namely risk of crash (RC) and return level (RL), are generated to quantitatively represent the cycle-level safety. The RC directly reflects whether a cycle is risky while the RL can evaluate the safety levels of individual cycles. The results show that the dynamic model can identify more crash-risk cycles with either a positive RC or a positive RL than the static model and is more capable of differentiating the safety levels for individual cycles in terms of RL. Overall, the dynamic model outperforms the static model in terms of the statistical fit and aggregate crash estimation accuracy.

The latent class clustering and latent segmentation-based models are employed to account for heterogeneity across different groups. Further, the random parameter variants of these modeling frameworks are employed to consider heterogeneity within the group. Both of these approaches have recently gained significant attention in road safety literature. However, the similarities and differences between these two methods are seldom explained and investigated. To that end, this study proposes to compare the performance of latent class clustering and latent segmentation-based random parameter models in examining crash injury severity outcomes. These models have been developed based on an ordered logit modeling framework to accommodate the ordinal nature of injury severity levels. For examining crash injury severity outcomes, this is the first study to consider the random parameter variant of ordered modeling structure within a latent segmentation modeling scheme. The current study also tests for and incorporates temporal instability of exogenous variables across multiple years of crash data in examining injury severity outcomes. The models have been estimated by using motorcycle crash data of Queensland, Australia, from the year 2012 through 2016. The comparison exercise is also augmented by estimating aggregate level elasticity effects of exogenous variables. The comparison exercise highlights the superiority of the latent segmentation approach in examining injury severity compared to the latent class clustering-based modeling approach. Moreover, the random parameter variants of both frameworks performed better than their fixed-parameter counterparts, which highlights the need to account for both across- and within-group heterogeneity. The temporal stability tests indicate that the effects of exogenous variables on the rider injury severity are different across year-wise models.

Intentionally blocking the path of fully automated vehicles is an important dimension of pedestrians’ receptivity towards these vehicles. The monetary value of this behaviour can be obtained by asking pedestrians about their perception of the “fine” for blocking the path of a fully automated vehicle. Econometric modelling of the reported fine can shed more light on factors influencing pedestrians’ receptivity towards fully automated vehicles. However, development of such an econometric model is not straightforward due to the unique characteristics of the dependent variable: it has two fundamentally different states; it is right-truncated; and it may be fat-tailed. Despite fairly extensive methodological advancements in econometric modelling of pedestrian behaviour, there is no model that can adequately explain these characteristics. While a beta distribution in a hurdle setting has the potential to address the above complexities, its applicability in dealing with limited dependent variables in transport applications has remained, by and large, unexplored.This study aims to fill this gap by developing a new beta hurdle regression model that systematically considers the dual-state of a right-truncated dependent variable representing the fine associated with intentionally blocking a fully automated vehicle. The hypothesized model is empirically tested using data obtained from a survey administered in Queensland, Australia, and the results are compared with truncated lognormal, and truncated lognormal hurdle regression models. Results indicate that the hurdle models are superior to the non-hurdle model. The beta variant of the hurdle model provides a better statistical fit for the data that are near their right limit. In addition, parametrizing the variance of the beta distribution captures the additional heterogeneity in the data. Age, gender, education level, violations, attitudes, behaviours that appease social interactions, and perceived ease or difficulty of interacting with fully automated vehicles influence the likelihood and/or the propensity of the fine and thus are associated with the perceived monetary value of intentionally blocking the path of a fully automated vehicle.

Examining crash risk in the highly anticipated connected environment is hindered by its novelty and the consequent scarcity of relevant data. This study proposes an Extreme Value Theory approach to examine and quantify mandatory lane-changing crash risk in the traditional and connected environments using traffic conflict techniques. The CARRS-Q advanced driving simulator was utilised to collect trajectory data of 78 participants performing mandatory lane-changing manoeuvres in three randomised driving conditions: baseline (without driving aids), connected environment with perfect communication, and connected environment with communication delay. Using the exceedance statistics theory (also known as a Peak Over Threshold approach corresponding to Generalised Pareto distribution), three separate models corresponding to each driving condition were developed. Driving-related factors obtained from the driving simulator data, such as speeds, spacings, lag gaps, and remaining distances, as well as driver demographics, were used as input variables to these models. Relative crash risk analysis and characteristics of the fitted Generalised Pareto distributions were employed as indicators of safety. The findings suggest that the connected environment significantly reduces mandatory lane-changing crash risk compared with the baseline condition, with the highest risk reduction observed in the perfect communication condition. While the crash risk of the communication delay condition is higher than that of the perfect communication condition, it is lower than the baseline condition. Furthermore, a comparison of the developed model to its counterpart (i.e., Block Maxima approach) showed the better performance of the adopted approach. The findings of this study provide insights into the positive impact of the connected environment on the safety of mandatory lane-changing manoeuvres as well as confirm the veracity of Peak Over Threshold models in estimating crash risk using traffic conflict data.

With the increasing advancements in autonomous vehicle (AV) technologies, the forecasts of AV market shares seem to follow an ever-growing trend. This leads to the inherent need for proactive safety evaluations of AV impacts on other road users. To that end, this study proposes a modeling framework for the proactive assessment of pedestrian safety in AV environments. The proposed framework relies on the Extreme Value Theory (EVT), with the peak over threshold modeling technique, to develop an estimate of AV-pedestrian collisions using AV-pedestrian conflicts. The proposed framework was applied to two AV datasets, collected from three locations in the US and Singapore, using the operating AV fleets of two developers, Motional and Lyft. Both datasets included trajectory data for the subject AV, as well as LiDAR point clouds and annotated video data from AV cameras to capture the trajectories of surrounding road users. The datasets were processed to extract the AV-pedestrian conflicts along with the corresponding conflict indicators, mainly the post-encroachment time (PET) and time-to-collision (TTC). Relevant covariates were introduced to the proposed models to enhance their performance and prediction accuracy, including turning movements and conflict speeds. The results indicate an alarming risk to pedestrians when interacting with AVs, especially at the early stages of AV adoption. The expected number of collisions ranged from 4 to 5.5 per million vehicle kilometers travelled (VKT) of the AVs. With the addition of the covariates, the expected number of collisions went down to a range of 2.3–3.7 per million VKT, but with a narrower confidence interval of the resulting estimate and a better fit. The introduced approach shows promising prospects for the application of EVT methods to address AV safety impacts. It also invites future applications to address issues of concern for pedestrian safety in different conditions of urban traffic.

Driver’s response to a pedestrian crossing requires braking, whereby both excess and inadequate braking is directly associated with crash risk. The highly anticipated connected environment aims to increase drivers’ situational awareness by providing advanced information and assisting them during critical driving tasks such as braking. Focussing on this crucial behaviour and combined with the promise of a connected environment, the objective of this study is to examine the braking behaviour of drivers in response to a pedestrian at a zebra crossing in a connected environment. Seventy-eight participants from diverse backgrounds performed this driving task in the CARRS-Q Advanced Driving Simulator in two randomised driving scenarios: a baseline scenario (without driving aids) and a connected environment (with driving aids) scenario. A Weibull accelerated failure time duration modelling approach is adopted to model the braking behaviour of drivers. In particular, this duration model is specified to capture the panel nature of the data and unobserved heterogeneity through correlated grouped random parameters with heterogeneity-in-the-means in the Bayesian framework. Results indicate that, for most drivers in the connected environment, it takes longer to reduce their speed with less speed variation and a larger safety margin. In addition, a decision tree analysis for the braking time suggests that for older drivers, when the distance to the zebra crossing is larger in the connected environment than that in the baseline scenario, braking time is likely to increase. The model also reveals that the braking time of female drivers is longer in the connected environment compared to that of male drivers. Overall, the connected environment is associated with increased braking time by providing advanced information, giving drivers additional time to smoothly reduce their speed in response to a pedestrian at a zebra crossing, and ultimately making the vehicle–pedestrian interaction safer.

Motorcyclists’ at-fault status is an important factor influencing crash injury severity in that intrinsically unsafe riders tend to be at fault and are the ones likely to be involved in severe crashes. However, this endogeneity issue and its influence on model estimations have seldom been investigated with regard to motorcyclist crash severity analysis. This study proposes a simultaneous model system to account for the endogenous effects of at-fault status in the motorcyclists’ injury severity analysis. Four Bayesian simultaneous models were developed using motorcyclist crash injury data from Queensland, Australia, from the year 2017 through 2018, including an independent binary and independent ordered Probit model, a simultaneous binary-ordered Probit model without recursive structure, a simultaneous binary-ordered Probit model with a recursive structure, and a simultaneous random-parameters binary-ordered Probit model with a recursive structure. The results of all simultaneous models indicate the existence of endogeneity associated with at-fault status in the injury outcome analysis. In particular, the endogenous relationship is detected by the significant cross-equation correlations in the simultaneous models. The model comparison by Deviance Information Criteria highlights the superiority of the simultaneous random-parameters model with a recursive structure. It was found that exogenous variables such as traffic sign-controlled measures, posted speed limits of 100–110 km/h, the presence of vertical grades, rider age 16–24 years, and unlicensed influenced injury severity indirectly through at-fault status, and ignoring these indirect influences could result in biased estimates. The presence of random parameters, such as collisions with heavy vehicles and riders over 59 years, highlights the importance of considering heterogeneity. The simultaneous random-parameters model with a recursive structure model revealed that the critical factors contributing to riders’ at-fault status included unlicensed riders and posted speed limits of 100–110 km/h, and the crucial factors influencing riders’ injury levels included head-on crashes, collisions with heavy vehicles, darkness-unlighted, and riders over 59 years old. The proposed model system demonstrates the importance of considering both endogeneity and heterogeneity for modeling the injury severity of motorcyclists.

Overturned crashes are associated with a disproportionate number of severe injuries and fatalities, while hit-fixed-object crashes are acknowledged as the most frequent single-vehicle crashes. To investigate the temporal stability and differences of contributing factors determining different injury severity levels in overturned and hit-fixed-object crashes on rural roads accompanied by speeding driving, this paper estimates two groups of correlated random parameters logit models with heterogeneity in the means (one group relating to overturned crashes and the other relating to hit-fixed-object crashes). Three injury-severity categories are determined as outcome variables: severe injury, minor injury and no injury, while multiple factors are investigated as explanatory variables including driver, vehicle, roadway, environmental, and crash characteristics. The overall temporal instability and non-transferability between overturned and hit-fixed-object crashes are captured through likelihood ratio tests. Marginal effects are adopted to further exhibit temporal variations of the explanatory variables. Despite the overall temporal instability, some variables still present relative temporal stability such as alcohol, truck, aggressive driving, vehicle age (>14 years old), and speed limit (<45 mph). This non-transferability between overturned and hit-fixed-object crashes provides insights into developing differentiated strategies targeted at mitigating and preventing different types of crashes. Besides, out-of-sample prediction is undertaken given the captured temporal instability and non-transferability of overturned and hit-fixed-object crash observations. More studies can be conducted to accommodate the spatial instability, under-reporting of severe-injury crashes, the trade-off between model predictive capability, inference capability, and selectivity bias.

Numerous statistical and data-driven modeling frameworks have estimated rear-end crashes and crash-prone events from macroscopic traffic states which are at the heart of traffic flow modelling and control. However, existing frameworks focus on critical events and exclude a vast majority of safer interactions, which are essential information with respect to identifying the trade-offs between congestion management and rear-end crash prevention.This study proposes a flexible conflict-based framework to extract safety information from freeway macroscopic traffic state variables (i.e., speed and density) by utilizing the information from all underlying car-following interactions. Time spent in conflict (TSC) is introduced as the total time spent by all vehicles in rear-end conflicts based on a given conflict measure and a threshold to be determined flexibly. Using the NGSIM vehicle trajectory dataset, we show that the proportion of stopping distance (PSD) is more desirable than several event-based conflict measures (e.g., time to collision) for describing TSC based on macroscopic state variables. Besides, it is shown that PSD provides explicit safety information about the entire travel time for each macroscopic state because it applies to all car-following interactions.This paper proposes a hybrid methodological framework combining probabilistic and machine learning models to develop the relationships between safety and macroscopic state variables within a flexible conflict-based safety assessment framework. At first, probabilistic and Machine learning models are separately developed to estimate PSD-based TSC using only macroscopic stte variables. Each approach is evaluated comprehensively against empirical observations using the NGSIM vehicle trajectory dataset. While the machine learning approach has better predictive accuracy for a fixed rear-end conflict threshold (i.e., PSDcr), the probabilistic approach has a better explaining capability and captures TSC using flexible conflict thresholds. Utilizing the advantages of these two approaches, the proposed hybrid framework satisfactorily predicts TSC corresponding to PSD