Motorway crash duration and its determinants: Do durations vary across motorways?

Traffic congestion has been a growing issue in many metropolitan areas during recent years, which necessitates the identification of its key contributors and development of sustainable strategies to help decrease its adverse impacts on traffic networks. Road incidents generally and crashes specifically have been acknowledged as the cause of a large proportion of travel delays in urban areas and account for 25% to 60% of traffic congestion on motorways. Identifying the critical determinants of travel delays has been of significant importance to the incident management systems which constantly collect and store the incident duration data. This study investigates the individual and simultaneous differential effects of the relevant determinants on motorway crash duration probabilities. In particular, it applies parametric Accelerated Failure Time (AFT) hazard-based models to develop in-depth insights into how the crash-specific characteristic and the associated temporal and infrastructural determinants impact the duration. AFT models with both fixed and random parameters have been calibrated on one year of traffic crash records from two major Australian motorways in South East Queensland and the differential effects of determinants on crash survival functions have been studied on these two motorways individually. A comprehensive spectrum of commonly used parametric fixed parameter AFT models, including generalized gamma and generalized F families, have been compared to random parameter AFT structures in terms of goodness of fit to the duration data and as a result, the random parameter Weibull AFT model has been selected as the most appropriate model. Significant determinants of motorway crash duration included traffic diversion requirement, crash injury type, number and type of vehicles involved in a crash, day of week and time of day, towing support requirement and damage to the infrastructure. A major finding of this research is that the motorways under study are significantly different in terms of crash durations; such that motorway exhibits durations that are on average 19% shorter compared to the durations on motorway. The differential effects of explanatory variables on crash durations are also different on the two motorways. The detailed presented analysis confirms that, looking at the motorway network as a whole, neglecting the individual differences between roads, can lead to erroneous interpretations of duration and inefficient strategies for mitigating travel delays along a particular motorway.

Bayesian survival analysis using gene expression

This thesis developed and applied Bayesian models for the analysis of survival data. The gene expression was considered as explanatory variables within the Bayesian survival model which can be considered the new contribution in the analysis of such data. The censoring factor that is inherent of survival data has also been addressed in terms of its impact on the fitting of a finite mixture of Weibull distribution with and without covariates. To investigate this, simulation study were carried out under several censoring percentages. Censoring percentage as high as 80% is acceptable here as the work involved high dimensional data. Lastly the Bayesian model averaging approach was developed to incorporate model uncertainty in the prediction of survival.

Survival analysis of time-to-event data in respiratory health research studies

This article provides a review of techniques for the analysis of survival data arising from respiratory health studies. Popular techniques such as the Kaplan–Meier survival plot and the Cox proportional hazards model are presented and illustrated using data from a lung cancer study. Advanced issues are also discussed, including parametric proportional hazards models, accelerated failure time models, time-varying explanatory variables, simultaneous analysis of multiple types of outcome events and the restricted mean survival time, a novel measure of the effect of treatment.

Handling incomplete data in survival analysis with multiple covariates

This paper studies the missing covariate problem which is often encountered in survival analysis. Three covariate imputation methods are employed in the study, and the effectiveness of each method is evaluated within the hazard prediction framework. Data from a typical engineering asset is used in the case study. Covariate values in some time steps are deliberately discarded to generate an incomplete covariate set. It is found that although the mean imputation method is simpler than others for solving missing covariate problems, the results calculated by it can differ largely from the real values of the missing covariates. This study also shows that in general, results obtained from the regression method are more accurate than those of the mean imputation method but at the cost of a higher computational expensive. Gaussian Mixture Model (GMM) method is found to be the most effective method within these three in terms of both computation efficiency and predication accuracy.

Hazard based models for freeway traffic incident duration

Assessing and prioritising cost-effective strategies to mitigate the impacts of traffic incidents and accidents on non-recurrent congestion on major roads represents a significant challenge for road network managers. This research examines the influence of numerous factors associated with incidents of various types on their duration. It presents a comprehensive traffic incident data mining and analysis by developing an incident duration model based on twelve months of incident data obtained from the Australian freeway network. Parametric accelerated failure time (AFT) survival models of incident duration were developed, including log-logistic, lognormal, and Weibul-considering both fixed and random parameters, as well as a Weibull model with gamma heterogeneity. The Weibull AFT models with random parameters were appropriate for modelling incident duration arising from crashes and hazards. A Weibull model with gamma heterogeneity was most suitable for modelling incident duration of stationary vehicles. Significant variables affecting incident duration include characteristics of the incidents (severity, type, towing requirements, etc.), and location, time of day, and traffic characteristics of the incident. Moreover, the findings reveal no significant effects of infrastructure and weather on incident duration. A significant and unique contribution of this paper is that the durations of each type of incident are uniquely different and respond to different factors. The results of this study are useful for traffic incident management agencies to implement strategies to reduce incident duration, leading to reduced congestion, secondary incidents, and the associated human and economic losses.

Bayesian hierarchical analysis on crash prediction models

Traditional crash prediction models, such as generalized linear regression models, are incapable of taking into account the multilevel data structure, which extensively exists in crash data. Disregarding the possible within-group correlations can lead to the production of models giving unreliable and biased estimates of unknowns. This study innovatively proposes a -level hierarchy, viz. (Geographic region level – Traffic site level – Traffic crash level – Driver-vehicle unit level – Vehicle-occupant level) Time level, to establish a general form of multilevel data structure in traffic safety analysis. To properly model the potential cross-group heterogeneity due to the multilevel data structure, a framework of Bayesian hierarchical models that explicitly specify multilevel structure and correctly yield parameter estimates is introduced and recommended. The proposed method is illustrated in an individual-severity analysis of intersection crashes using the Singapore crash records. This study proved the importance of accounting for the within-group correlations and demonstrated the flexibilities and effectiveness of the Bayesian hierarchical method in modeling multilevel structure of traffic crash data.

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

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

Survival models of community tenure and length of hospital stay for the seriously mentally ill : a 10-year perspective

Objective: To examine the effects of personal and community characteristics, specifically race and rurality, on lengths of state psychiatric hospital and community stays using maximum likelihood survival analysis with a special emphasis on change over a ten year period of time. Data Sources: We used the administrative data of the Virginia Department of Mental Health, Mental Retardation, and Substance Abuse Services (DMHMRSAS) from 1982-1991 and the Area Resources File (ARF). Given these two sources, we constructed a history file for each individual who entered the state psychiatric system over the ten year period. Histories included demographic, treatment, and community characteristics. Study Design: We used a longitudinal, population-based design with maximum likelihood estimation of survival models. We presented a random effects model with unobserved heterogeneity that was independent of observed covariates. The key dependent variables were lengths of inpatient stay and subsequent length of community stay. Explanatory variables measured personal, diagnostic, and community characteristics, as well as controls for calendar time. Data Collection: This study used secondary, administrative, and health planning data. Principal Findings: African-American clients leave the community more quickly than whites. After controlling for other characteristics, however, race does not affect hospital length of stay. Rurality does not affect length of community stays once other personal and community characteristics are controlled for. However, people from rural areas have longer hospital stays even after controlling for personal and community characteristics. The effects of time are significantly smaller than expected. Diagnostic composition effects and a decrease in the rate of first inpatient admissions explain part of this reduced impact of time. We also find strong evidence for the existence of unobserved heterogeneity in both types of stays and adjust for this in our final models. Conclusions: Our results show that information on client characteristics available from inpatient stay records is useful in predicting not only the length of inpatient stay but also the length of the subsequent community stay. This information can be used to target increased discharge planning for those at risk of more rapid readmission to inpatient care. Correlation across observed and unobserved factors affecting length of stay has significant effects on the measurement of relationships between individual factors and lengths of stay. Thus, it is important to control for both observed and unobserved factors in estimation.

Modelling total duration of traffic incidents including incident detection and recovery time

Traffic incidents are key contributors to non-recurrent congestion, potentially generating significant delay. Factors that influence the duration of incidents are important to understand so that effective mitigation strategies can be implemented. To identify and quantify the effects of influential factors, a methodology for studying total incident duration based on historical data from an ‘integrated database’ is proposed. Incident duration models are developed using a selected freeway segment in the Southeast Queensland, Australia network. The models include incident detection and recovery time as components of incident duration. A hazard-based duration modelling approach is applied to model incident duration as a function of a variety of factors that influence traffic incident duration. Parametric accelerated failure time survival models are developed to capture heterogeneity as a function of explanatory variables, with both fixed and random parameters specifications. The analysis reveals that factors affecting incident duration include incident characteristics (severity, type, injury, medical requirements, etc.), infrastructure characteristics (roadway shoulder availability), time of day, and traffic characteristics. The results indicate that event type durations are uniquely different, thus requiring different responses to effectively clear them. Furthermore, the results highlight the presence of unobserved incident duration heterogeneity as captured by the random parameter models, suggesting that additional factors need to be considered in future modelling efforts.

A review on reliability models with covariates

Modern Engineering Asset Management (EAM) requires the accurate assessment of current and the prediction of future asset health condition. Suitable mathematical models that are capable of predicting Time-to-Failure (TTF) and the probability of failure in future time are essential. In traditional reliability models, the lifetime of assets is estimated using failure time data. However, in most real-life situations and industry applications, the lifetime of assets is influenced by different risk factors, which are called covariates. The fundamental notion in reliability theory is the failure time of a system and its covariates. These covariates change stochastically and may influence and/or indicate the failure time. Research shows that many statistical models have been developed to estimate the hazard of assets or individuals with covariates. An extensive amount of literature on hazard models with covariates (also termed covariate models), including theory and practical applications, has emerged. This paper is a state-of-the-art review of the existing literature on these covariate models in both the reliability and biomedical fields. One of the major purposes of this expository paper is to synthesise these models from both industrial reliability and biomedical fields and then contextually group them into non-parametric and semi-parametric models. Comments on their merits and limitations are also presented. Another main purpose of this paper is to comprehensively review and summarise the current research on the development of the covariate models so as to facilitate the application of more covariate modelling techniques into prognostics and asset health management.

Incorporating weather into regionwide safety planning prediction models

Predicting safety on roadways is standard practice for road safety professionals and has a corresponding extensive literature. The majority of safety prediction models are estimated using roadway segment and intersection (microscale) data, while more recently efforts have been undertaken to predict safety at the planning level (macroscale). Safety prediction models typically include roadway, operations, and exposure variables—factors known to affect safety in fundamental ways. Environmental variables, in particular variables attempting to capture the effect of rain on road safety, are difficult to obtain and have rarely been considered. In the few cases weather variables have been included, historical averages rather than actual weather conditions during which crashes are observed have been used. Without the inclusion of weather related variables researchers have had difficulty explaining regional differences in the safety performance of various entities (e.g. intersections, road segments, highways, etc.) As part of the NCHRP 8-44 research effort, researchers developed PLANSAFE, or planning level safety prediction models. These models make use of socio-economic, demographic, and roadway variables for predicting planning level safety. Accounting for regional differences - similar to the experience for microscale safety models - has been problematic during the development of planning level safety prediction models. More specifically, without weather related variables there is an insufficient set of variables for explaining safety differences across regions and states. Furthermore, omitted variable bias resulting from excluding these important variables may adversely impact the coefficients of included variables, thus contributing to difficulty in model interpretation and accuracy. This paper summarizes the results of an effort to include weather related variables, particularly various measures of rainfall, into accident frequency prediction and the prediction of the frequency of fatal and/or injury degree of severity crash models. The purpose of the study was to determine whether these variables do in fact improve overall goodness of fit of the models, whether these variables may explain some or all of observed regional differences, and identifying the estimated effects of rainfall on safety. The models are based on Traffic Analysis Zone level datasets from Michigan, and Pima and Maricopa Counties in Arizona. Numerous rain-related variables were found to be statistically significant, selected rain related variables improved the overall goodness of fit, and inclusion of these variables reduced the portion of the model explained by the constant in the base models without weather variables. Rain tends to diminish safety, as expected, in fairly complex ways, depending on rain frequency and intensity.

Forecasting crashes at the planning level: Simultaneous negative binomial crash model applied in Tucson, Arizona

At least two important transportation planning activities rely on planning-level crash prediction models. One is motivated by the Transportation Equity Act for the 21st Century, which requires departments of transportation and metropolitan planning organizations to consider safety explicitly in the transportation planning process. The second could arise from a need for state agencies to establish incentive programs to reduce injuries and save lives. Both applications require a forecast of safety for a future period. Planning-level crash prediction models for the Tucson, Arizona, metropolitan region are presented to demonstrate the feasibility of such models. Data were separated into fatal, injury, and property-damage crashes. To accommodate overdispersion in the data, negative binomial regression models were applied. To accommodate the simultaneity of fatality and injury crash outcomes, simultaneous estimation of the models was conducted. All models produce crash forecasts at the traffic analysis zone level. Statistically significant (p-values < 0.05) and theoretically meaningful variables for the fatal crash model included population density, persons 17 years old or younger as a percentage of the total population, and intersection density. Significant variables for the injury and property-damage crash models were population density, number of employees, intersections density, percentage of miles of principal arterial, percentage of miles of minor arterials, and percentage of miles of urban collectors. Among several conclusions it is suggested that planning-level safety models are feasible and may play a role in future planning activities. However, caution must be exercised with such models.

Impact of traffic oscillations on freeway crash occurrences

Traffic oscillations are typical features of congested traffic flow that are characterized by recurring decelerations followed by accelerations (stop-and-go driving). The negative environmental impacts of these oscillations are widely accepted, but their impact on traffic safety has been debated. This paper describes the impact of freeway traffic oscillations on traffic safety. This study employs a matched case-control design using high-resolution traffic and crash data from a freeway segment. Traffic conditions prior to each crash were taken as cases, while traffic conditions during the same periods on days without crashes were taken as controls. These were also matched by presence of congestion, geometry and weather. A total of 82 cases and about 80,000 candidate controls were extracted from more than three years of data from 2004 to 2007. Conditional logistic regression models were developed based on the case-control samples. To verify consistency in the results, 20 different sets of controls were randomly extracted from the candidate pool for varying control-case ratios. The results reveal that the standard deviation of speed (thus, oscillations) is a significant variable, with an average odds ratio of about 1.08. This implies that the likelihood of a (rear-end) crash increases by about 8% with an additional unit increase in the standard deviation of speed. The average traffic states prior to crashes were less significant than the speed variations in congestion.