Application of the Poisson-Tweedie distribution in analyzing crash frequency data.

This paper describes a study that applies the Poisson-Tweedie distribution in developing crash frequency models. The Poisson-Tweedie distribution offers a unified framework to model overdispersed, underdispersed, zero-inflated, spatial, and longitudinal count data, as well as multiple response variables of similar or mixed types. The form of its variance function is simple, and can be specified as the mean added to the product of dispersion and mean raised to the power P. The flexibility of the Poisson-Tweedie distribution lies in the domain of P, which includes positive real number values. Special cases of the Poisson-Tweedie distribution models include the linear form of the negative binomial (NB1) model with P equal to 1.0, the geometric Poisson (GeoP) model with P equal to 1.5, the quadratic form of the negative binomial (NB2) model with P equal to 2.0, and the Poisson Inverse Gaussian (PIG) model with P equal to 3.0. A series of models were developed in this study using the Poisson-Tweedie distribution without any restrictions on the value of the power parameter as well as with specific values of the power parameter representing NB1, GeoP, NB2, and PIG models. The effects of fixed and varying dispersion parameters (i.e., dispersion as a function of covariates) on the variance and expected crash frequency estimates were also examined. Three years (2012-2014) of crash data from urban three-leg stop-controlled intersections and urban four-leg signalized intersections in the state of Florida were used to develop the models. The Poisson-Tweedie models or the GeoP models were found to perform better when the dispersion parameter was constant or fixed. With the varying dispersion parameter, the NB2 and PIG models were found to perform better, with both performing equally well. Also, the fixed dispersion parameter values were found to be smaller in the models with a higher value of the power parameter. The variation across the models in their estimates of weight factor, expected crash frequency, and potential for safety improvement of hazardous sites based on the empirical Bayes method was also discussed.

Compliance with multidisciplinary team meeting management recommendations.

OBJECTIVES: The objective of this study was to evaluate patient compliance with management recommendations given by a breast cancer multidisciplinary team (MDT), assess for reasons for noncompliance, and perform an exploratory assessment on breast cancer outcomes in noncompliant patients. MATERIALS AND METHODS: A retrospective analysis of prospectively collected data was undertaken for patients selected by their primary clinician to be discussed at the MDT of Breast Cancer Research Centre-WA in Perth between 1st March 2011 and the 28th February 2016. The primary objective was the rate of compliance with MDT management recommendations. Secondary objectives included factors associated with noncompliance, rate of clinical trial uptake, and impact of treatment noncompliance on breast cancer events in a subgroup of early breast cancer (EBC) patients. RESULTS AND CONCLUSION: A total of 2614 MDT management recommendations were made for 925 patients. Overall, 92% were compliant with all recommendations given. Clinical trial recruitment was successful in 84.1%. The reasons given for treatment noncompliance were fear of toxicity, choosing an alternative treatment, and treatment inconvenience. In a subset of 337 EBC patients, there was a significantly higher rate of contralateral breast cancer, distant recurrence, and breast cancer-specific death, P = .0016, in those who were noncompliant. Our study demonstrates a high rate of MDT treatment recommendation compliance and clinical trial recruitment. In a subgroup of EBC patients, noncompliance was associated with significantly worse outcomes. Attention to educating patients to minimize their fear of treatment toxicity and ensuring their understanding of evidence-based treatment may lead to lower rates of noncompliance.

Estimation of bicycle crash modification factors (CMFs) on urban facilities using zero inflated negative binomial models.

The objective of this study was to develop crash modification factors (CMFs) for bicycle crashes for different roadway segment and intersection facility types in urban areas. The study used four years (2011-2014) of crash data from Florida to quantify the safety impacts of roadway and traffic characteristics, bicycle infrastructure, and bicycle activity data on bicycle crashes. A cross-sectional analysis using Generalized Linear Model (GLM) approach with Zero Inflated Negative Binomial (ZINB) distribution was adopted to develop the relevant regression models in this study. Lane width, speed limit, and grass in the median were observed to have positive impacts on reducing bicycle crashes. On the contrary, presence of sidewalk and sidewalk barrier were found to increase the bicycle crash probabilities. Increased bicycle activity was found to reduce the bicycle crash probabilities on segments, while increased bicycle activity resulted in higher bicycle crash probabilities at intersections. Bus stops were found to increase the bicycle crash probabilities at intersections, whereas, protected signal control had a positive impact on bicycle safety. This research provides a greater insight into how various characteristics affect bicycle safety, a topic that is seldom considered by researchers and practitioners.

Spatial analysis of macro-level bicycle crashes using the class of conditional autoregressive models.

The objective of this study was to investigate the relationship between bicycle crash frequency and their contributing factors at the census block group level in Florida, USA. Crashes aggregated over the census block groups tend to be clustered (i.e., spatially dependent) rather than randomly distributed. To account for the effect of spatial dependence across the census block groups, the class of conditional autoregressive (CAR) models were employed within the hierarchical Bayesian framework. Based on four years (2011-2014) of crash data, total and fatal-and-severe injury bicycle crash frequencies were modeled as a function of a large number of variables representing demographic and socio-economic characteristics, roadway infrastructure and traffic characteristics, and bicycle activity characteristics. This study explored and compared the performance of two CAR models, namely the Besag's model and the Leroux's model, in crash prediction. The Besag's models, which differ from the Leroux's models by the structure of how spatial autocorrelation are specified in the models, were found to fit the data better. A 95% Bayesian credible interval was selected to identify the variables that had credible impact on bicycle crashes. A total of 21 variables were found to be credible in the total crash model, while 18 variables were found to be credible in the fatal-and-severe injury crash model. Population, daily vehicle miles traveled, age cohorts, household automobile ownership, density of urban roads by functional class, bicycle trip miles, and bicycle trip intensity had positive effects in both the total and fatal-and-severe crash models. Educational attainment variables, truck percentage, and density of rural roads by functional class were found to be negatively associated with both total and fatal-and-severe bicycle crash frequencies.

A Bayesian procedure for evaluating the frequency of calibration factor updates in highway safety manual (HSM) applications.

The Highway Safety Manual (HSM) presents statistical models to quantitatively estimate an agency's safety performance. The models were developed using data from only a few U.S. states. To account for the effects of the local attributes and temporal factors on crash occurrence, agencies are required to calibrate the HSM-default models for crash predictions. The manual suggests updating calibration factors every two to three years, or preferably on an annual basis. Given that the calibration process involves substantial time, effort, and resources, a comprehensive analysis of the required calibration factor update frequency is valuable to the agencies. Accordingly, the objective of this study is to evaluate the HSM's recommendation and determine the required frequency of calibration factor updates. A robust Bayesian estimation procedure is used to assess the variation between calibration factors computed annually, biennially, and triennially using data collected from over 2400 miles of segments and over 700 intersections on urban and suburban facilities in Florida. Bayesian model yields a posterior distribution of the model parameters that give credible information to infer whether the difference between calibration factors computed at specified intervals is credibly different from the null value which represents unaltered calibration factors between the comparison years or in other words, zero difference. The concept of the null value is extended to include the range of values that are practically equivalent to zero. Bayesian inference shows that calibration factors based on total crash frequency are required to be updated every two years in cases where the variations between calibration factors are not greater than 0.01. When the variations are between 0.01 and 0.05, calibration factors based on total crash frequency could be updated every three years.

Safety performance evaluation of cable median barriers on freeways in Florida.

OBJECTIVE: This article aims to evaluate the safety performance of cable median barriers on freeways in Florida. METHOD: The safety performance evaluation was based on the percentages of barrier and median crossovers by vehicle type, crash severity, and cable median barrier type (Trinity Cable Safety System [CASS] and Gibraltar system). Twenty-three locations with cable median barriers totaling about 101 miles were identified. Police reports of 6,524 crashes from years 2005-2010 at these locations were reviewed to verify and obtain detailed crash information. A total of 549 crashes were determined to be barrier related (i.e., crashes involving vehicles hitting the cable median barrier) and were reviewed in further detail to identify crossover crashes and the manner in which the vehicles crossed the barriers; that is, by either overriding, underriding, or penetrating the barriers. RESULTS: Overall, 2.6% of vehicles that hit the cable median barrier crossed the median and traversed into the opposite travel lane. Overall, 98.1% of cars and 95.5% of light trucks that hit the barrier were prevented from crossing the median. In other words, 1.9% of cars and 4.5% of light trucks that hit the barrier had crossed the median and encroached on the opposite travel lanes. There is no significant difference in the performance of cable median barrier for cars versus light trucks in terms of crossover crashes. In terms of severity, overrides were more severe compared to underrides and penetrations. The statistics showed that the CASS and Gibraltar systems performed similarly in terms of crossover crashes. However, the Gibraltar system experienced a higher proportion of penetrations compared to the CASS system. The CASS system resulted in a slightly higher percentage of moderate and minor injury crashes compared to the Gibraltar system. CONCLUSIONS: Cable median barriers are successful in preventing median crossover crashes; 97.4% of the cable median barrier crashes were prevented from crossing over the median. Of all of the vehicles that hit the barrier, 83.6% were either redirected or contained by the cable barrier system. Barrier crossover crashes were found to be more severe compared to barrier noncrossover crashes. In addition, overrides were found to be more severe compared to underrides and penetrations.

Contributing factors of crash injury severity at public highway-railroad grade crossings in the U.S.

INTRODUCTION: The Moving Ahead for Progress in the 21st Century (MAP-21) includes a separate program that supports safety improvements to reduce the number of fatalities and injuries at public highway-railroad grade crossings (HRGCs). This study identifies the significant factors affecting crash injury severity at public HRGCs in the United States. METHOD: Crashes from 2009 through 2013 on 5,528 public HRGCs, extracted from the Federal Railroad Administration database, were used in the analysis. A comprehensive list of risk factors was explored. Examples include predictors related to geographic region of crash, geometry (e.g., area type and pavement marking type), railroad (e.g., warning device type and railroad class), traffic (e.g., train speed and vehicles annual average daily traffic "AADT"), highway user (e.g., driver age and gender), and environment (e.g., lighting and weather conditions). The study used the mixed logit model to better capture the complex highway user behavior at HRGCs. RESULTS: Female highway users were at higher risk of involvement in injuries and fatalities compared to males. Higher train speeds, very old drivers, open areas, concrete road surface types, and railroad equipment striking highway users before crash, were all found to increase the injury likelihood. On the other hand, young and middle-age drivers, non-passing of standing vehicles at HRGCs, industrial areas, and presence of warning bells were found to reduce injuries and fatalities. CONCLUSIONS: The mixed logit model succeeded in identifying contributing factors of crash severity at public HRGCs and potential countermeasures to reduce both fatalities and injuries are suggested. PRACTICAL APPLICATIONS: It is important to install warning bells at public HRGCs, especially at those with high number of injury and fatality crashes. Enforcement of traffic nearby HRGCs is necessary to prevent vehicles from overtaking of standing vehicles.

Analyzing pedestrian crash injury severity at signalized and non-signalized locations.

This study identifies and compares the significant factors affecting pedestrian crash injury severity at signalized and unsignalized intersections. The factors explored include geometric predictors (e.g., presence and type of crosswalk and presence of pedestrian refuge area), traffic predictors (e.g., annual average daily traffic (AADT), speed limit, and percentage of trucks), road user variables (e.g., pedestrian age and pedestrian maneuver before crash), environmental predictors (e.g., weather and lighting conditions), and vehicle-related predictors (e.g., vehicle type). The analysis was conducted using the mixed logit model, which allows the parameter estimates to randomly vary across the observations. The study used three years of pedestrian crash data from Florida. Police reports were reviewed in detail to have a better understanding of how each pedestrian crash occurred. Additionally, information that is unavailable in the crash records, such as at-fault road user and pedestrian maneuver, was collected. At signalized intersections, higher AADT, speed limit, and percentage of trucks; very old pedestrians; at-fault pedestrians; rainy weather; and dark lighting condition were associated with higher pedestrian severity risk. For example, a one-percent higher truck percentage increases the probability of severe injuries by 1.37%. A one-mile-per-hour higher speed limit increases the probability of severe injuries by 1.22%. At unsignalized intersections, pedestrian walking along roadway, middle and very old pedestrians, at-fault pedestrians, vans, dark lighting condition, and higher speed limit were associated with higher pedestrian severity risk. On the other hand, standard crosswalks were associated with 1.36% reduction in pedestrian severe injuries. Several countermeasures to reduce pedestrian injury severity are recommended.

Prioritizing Highway Safety Manual's crash prediction variables using boosted regression trees.

The Highway Safety Manual (HSM) recommends using the empirical Bayes (EB) method with locally derived calibration factors to predict an agency's safety performance. However, the data needs for deriving these local calibration factors are significant, requiring very detailed roadway characteristics information. Many of the data variables identified in the HSM are currently unavailable in the states' databases. Moreover, the process of collecting and maintaining all the HSM data variables is cost-prohibitive. Prioritization of the variables based on their impact on crash predictions would, therefore, help to identify influential variables for which data could be collected and maintained for continued updates. This study aims to determine the impact of each independent variable identified in the HSM on crash predictions. A relatively recent data mining approach called boosted regression trees (BRT) is used to investigate the association between the variables and crash predictions. The BRT method can effectively handle different types of predictor variables, identify very complex and non-linear association among variables, and compute variable importance. Five years of crash data from 2008 to 2012 on two urban and suburban facility types, two-lane undivided arterials and four-lane divided arterials, were analyzed for estimating the influence of variables on crash predictions. Variables were found to exhibit non-linear and sometimes complex relationship to predicted crash counts. In addition, only a few variables were found to explain most of the variation in the crash data.

Effect of driver's age and side of impact on crash severity along urban freeways: a mixed logit approach.

INTRODUCTION: This study identifies geometric, traffic, environmental, vehicle-related, and driver-related predictors of crash injury severity on urban freeways. METHOD: The study takes advantage of the mixed logit model's ability to account for unobserved effects that are difficult to quantify and may affect the model estimation, such as the driver's reaction at the time of crash. Crashes of 5 years occurring on 89 urban freeway segments throughout the state of Florida in the United States were used. Examples of severity predictors explored include traffic volume, distance of the crash to the nearest ramp, and detailed driver's age, vehicle types, and sides of impact. To show how the parameter estimates could vary, a binary logit model was compared with the mixed logit model. RESULTS: It was found that the at-fault driver's age, traffic volume, distance of the crash to the nearest ramp, vehicle type, side of impact, and percentage of trucks significantly influence severity on urban freeways. Additionally, young at-fault drivers were associated with a significant severity risk increase relative to other age groups. It was also observed that some variables in the binary logit model yielded illogic estimates due to ignoring the random variation of the estimation. Since the at-fault driver's age and side of impact were significant random parameters in the mixed logit model, an in-depth investigation was performed. It was noticed that back, left, and right impacts had the highest risk among middle-aged drivers, followed by young drivers, very young drivers, and finally, old and very old drivers. IMPACT ON INDUSTRY: To reduce side impacts due to lane changing, two primary strategies can be recommended. The first strategy is to conduct campaigns to convey the hazardous effect of changing lanes at higher speeds. The second is to devise in-vehicle side crash avoidance systems to alert drivers of a potential crash risk. CONCLUSIONS: The study provided a promising approach to screening the predictors before fitting the mixed logit model using the random forest technique. Furthermore, potential countermeasures were proposed to reduce the severity of impacts.

Using multivariate adaptive regression splines (MARS) to develop crash modification factors for urban freeway interchange influence areas.

Crash modification factors (CMFs) are used to measure the safety impacts of changes in specific geometric characteristics. Their development has gained much interest following the adoption of CMFs by the recently released Highway Safety Manual (HSM) and SafetyAnalyst tool in the United States. This paper describes a study to develop CMFs for interchange influence areas on urban freeways in the state of Florida. Despite the very different traffic and geometric conditions that exist in interchange influence areas, most previous studies have not separated them from the rest of the freeway system in their analyses. In this study, a promising data mining method known as multivariate adaptive regression splines (MARS) was applied to develop CMFs for median width and inside and outside shoulder widths for "total" and "fatal and injury" (FI) crashes. In addition, CMFs were also developed for the two most frequent crash types, i.e., rear-end and sideswipe. MARS is characterized by its ability to accommodate the nonlinearity in crash predictors and to allow the impact of more than one geometric variable to be simultaneously considered. The methodology further implements crash predictions from the model to identify changes in geometric design features. Four years of crashes from 2007 to 2010 were used in the analysis and the results showed that MARS's prediction capability and goodness-of-fit statistics outperformed those of the negative binomial model. The influential variables identified included the outside and inside shoulder widths, median width, lane width, traffic volume, and shoulder type. It was deduced that a 2-ft increase in the outside and inside shoulders (from 10ft to 12ft) reduces FI crashes by 10% and 33%, respectively. Further, a 42-ft reduction in the median width (from 64ft to 22ft) increases the rear-end, total, and FI crashes by 473%, 263%, and 223%, respectively.

Identifying traditional and nontraditional predictors of crash injury severity on major urban roadways.

OBJECTIVE: This study identifies and compares the factors that contribute to injury severity on urban freeways and arterials and recommends potential countermeasures to enhance the safety of both facilities. The study makes use of an extensive data set from the State of Florida in the United States. To obtain a more complete picture, this study explores both traditional and nontraditional severity predictors. Some traditional predictors include traffic volume, speed limit, and road surface condition. The nontraditional predictors are comprised of those rarely explored in previous severity studies, including crash distance to the nearest ramp location, detailed vehicle types, and lighting and weather conditions. METHODS: The analysis was conducted using the ordered and binary probit models, which are well suited for the inherently ordered property of injury severity. RESULTS: An important finding is the significance of the distance of crash to the nearest ramp junction/access point, for which the increase in the distance yielded a severity increase at both facilities. Other significant factors included traffic volume, speed limit, at-fault driver's age, road surface condition, alcohol and drug involvement, and left and right shoulder widths. In comparing both facilities, sport utility vehicles (SUVs) and pickup trucks showed a fatality/severity increase on freeways and a decrease on arterials. Furthermore, the detailed list of variables such as crash time provided pertinent severity trend information that showed that, compared to the other periods, the afternoon peak period had the highest reduction in fatality/severity. CONCLUSIONS: Both probit models succeeded in identifying significant severity predictors for each facility. The binary probit model outperformed the ordered probit model based on the higher elasticities (marginal effects) for the fatality/severity probability change, as well as the goodness of fit. As such, this study provides the guidelines for assessing the impact of important roadway and traffic characteristics on crash injury severity along freeways and arterials.