On the nature of over-dispersion in motor vehicle crash prediction models

Statistical modeling of traffic crashes has been of interest to researchers for decades. Over the most recent decade many crash models have accounted for extra-variation in crash counts—variation over and above that accounted for by the Poisson density. The extra-variation – or dispersion – is theorized to capture unaccounted for variation in crashes across sites. The majority of studies have assumed fixed dispersion parameters in over-dispersed crash models—tantamount to assuming that unaccounted for variation is proportional to the expected crash count. Miaou and Lord [Miaou, S.P., Lord, D., 2003. Modeling traffic crash-flow relationships for intersections: dispersion parameter, functional form, and Bayes versus empirical Bayes methods. Transport. Res. Rec. 1840, 31–40] challenged the fixed dispersion parameter assumption, and examined various dispersion parameter relationships when modeling urban signalized intersection accidents in Toronto. They suggested that further work is needed to determine the appropriateness of the findings for rural as well as other intersection types, to corroborate their findings, and to explore alternative dispersion functions. This study builds upon the work of Miaou and Lord, with exploration of additional dispersion functions, the use of an independent data set, and presents an opportunity to corroborate their findings. Data from Georgia are used in this study. A Bayesian modeling approach with non-informative priors is adopted, using sampling-based estimation via Markov Chain Monte Carlo (MCMC) and the Gibbs sampler. A total of eight model specifications were developed; four of them employed traffic flows as explanatory factors in mean structure while the remainder of them included geometric factors in addition to major and minor road traffic flows. The models were compared and contrasted using the significance of coefficients, standard deviance, chi-square goodness-of-fit, and deviance information criteria (DIC) statistics. The findings indicate that the modeling of the dispersion parameter, which essentially explains the extra-variance structure, depends greatly on how the mean structure is modeled. In the presence of a well-defined mean function, the extra-variance structure generally becomes insignificant, i.e. the variance structure is a simple function of the mean. It appears that extra-variation is a function of covariates when the mean structure (expected crash count) is poorly specified and suffers from omitted variables. In contrast, when sufficient explanatory variables are used to model the mean (expected crash count), extra-Poisson variation is not significantly related to these variables. If these results are generalizable, they suggest that model specification may be improved by testing extra-variation functions for significance. They also suggest that known influences of expected crash counts are likely to be different than factors that might help to explain unaccounted for variation in crashes across sites

Poisson, Poisson-gamma and zero-inflated regression models of motor vehicle crashes: balancing statistical fit and theory

There has been considerable research conducted over the last 20 years focused on predicting motor vehicle crashes on transportation facilities. The range of statistical models commonly applied includes binomial, Poisson, Poisson-gamma (or negative binomial), zero-inflated Poisson and negative binomial models (ZIP and ZINB), and multinomial probability models. Given the range of possible modeling approaches and the host of assumptions with each modeling approach, making an intelligent choice for modeling motor vehicle crash data is difficult. There is little discussion in the literature comparing different statistical modeling approaches, identifying which statistical models are most appropriate for modeling crash data, and providing a strong justification from basic crash principles. In the recent literature, it has been suggested that the motor vehicle crash process can successfully be modeled by assuming a dual-state data-generating process, which implies that entities (e.g., intersections, road segments, pedestrian crossings, etc.) exist in one of two states—perfectly safe and unsafe. As a result, the ZIP and ZINB are two models that have been applied to account for the preponderance of “excess” zeros frequently observed in crash count data. The objective of this study is to provide defensible guidance on how to appropriate model crash data. We first examine the motor vehicle crash process using theoretical principles and a basic understanding of the crash process. It is shown that the fundamental crash process follows a Bernoulli trial with unequal probability of independent events, also known as Poisson trials. We examine the evolution of statistical models as they apply to the motor vehicle crash process, and indicate how well they statistically approximate the crash process. We also present the theory behind dual-state process count models, and note why they have become popular for modeling crash data. A simulation experiment is then conducted to demonstrate how crash data give rise to “excess” zeros frequently observed in crash data. It is shown that the Poisson and other mixed probabilistic structures are approximations assumed for modeling the motor vehicle crash process. Furthermore, it is demonstrated that under certain (fairly common) circumstances excess zeros are observed—and that these circumstances arise from low exposure and/or inappropriate selection of time/space scales and not an underlying dual state process. In conclusion, carefully selecting the time/space scales for analysis, including an improved set of explanatory variables and/or unobserved heterogeneity effects in count regression models, or applying small-area statistical methods (observations with low exposure) represent the most defensible modeling approaches for datasets with a preponderance of zeros

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.

Bayesian methodology incorporating expert judgment for ranking countermeasure effectiveness under uncertainty: Example applied to at grade railroad crossings in Korea

This paper describes the formalization and application of a methodology to evaluate the safety benefit of countermeasures in the face of uncertainty. To illustrate the methodology, 18 countermeasures for improving safety of at grade railroad crossings (AGRXs) in the Republic of Korea are considered. Akin to “stated preference” methods in travel survey research, the methodology applies random selection and laws of large numbers to derive accident modification factor (AMF) densities from expert opinions. In a full Bayesian analysis framework, the collective opinions in the form of AMF densities (data likelihood) are combined with prior knowledge (AMF density priors) for the 18 countermeasures to obtain ‘best’ estimates of AMFs (AMF posterior credible intervals). The countermeasures are then compared and recommended based on the largest safety returns with minimum risk (uncertainty). To the author's knowledge the complete methodology is new and has not previously been applied or reported in the literature. The results demonstrate that the methodology is able to discern anticipated safety benefit differences across candidate countermeasures. For the 18 at grade railroad crossings considered in this analysis, it was found that the top three performing countermeasures for reducing crashes are in-vehicle warning systems, obstacle detection systems, and constant warning time systems.

Development of accident prediction models for rural highway intersections

A study was done to develop macrolevel crash prediction models that can be used to understand and identify effective countermeasures for improving signalized highway intersections and multilane stop-controlled highway intersections in rural areas. Poisson and negative binomial regression models were fit to intersection crash data from Georgia, California, and Michigan. To assess the suitability of the models, several goodness-of-fit measures were computed. The statistical models were then used to shed light on the relationships between crash occurrence and traffic and geometric features of the rural signalized intersections. The results revealed that traffic flow variables significantly affected the overall safety performance of the intersections regardless of intersection type and that the geometric features of intersections varied across intersection type and also influenced crash type.

Further notes on the application of zero-inflated models in highway safety

The intent of this note is to succinctly articulate additional points that were not provided in the original paper (Lord et al., 2005) and to help clarify a collective reluctance to adopt zero-inflated (ZI) models for modeling highway safety data. A dialogue on this important issue, just one of many important safety modeling issues, is healthy discourse on the path towards improved safety modeling. This note first provides a summary of prior findings and conclusions of the original paper. It then presents two critical and relevant issues: the maximizing statistical fit fallacy and logic problems with the ZI model in highway safety modeling. Finally, we provide brief conclusions.

Evaluation of the Scottsdale Loop 101 automated speed enforcement demonstration program

Speeding is recognized as a major contributing factor in traffic crashes. In order to reduce speed-related crashes, the city of Scottsdale, Arizona implemented the first fixed-camera photo speed enforcement program (SEP) on a limited access freeway in the US. The 9-month demonstration program spanning from January 2006 to October 2006 was implemented on a 6.5 mile urban freeway segment of Arizona State Route 101 running through Scottsdale. This paper presents the results of a comprehensive analysis of the impact of the SEP on speeding behavior, crashes, and the economic impact of crashes. The impact on speeding behavior was estimated using generalized least square estimation, in which the observed speeds and the speeding frequencies during the program period were compared to those during other periods. The impact of the SEP on crashes was estimated using 3 evaluation methods: a before-and-after (BA) analysis using a comparison group, a BA analysis with traffic flow correction, and an empirical Bayes BA analysis with time-variant safety. The analysis results reveal that speeding detection frequencies (speeds> or =76 mph) increased by a factor of 10.5 after the SEP was (temporarily) terminated. Average speeds in the enforcement zone were reduced by about 9 mph when the SEP was implemented, after accounting for the influence of traffic flow. All crash types were reduced except rear-end crashes, although the estimated magnitude of impact varies across estimation methods (and their corresponding assumptions). When considering Arizona-specific crash related injury costs, the SEP is estimated to yield about $17 million in annual safety benefits.

Experimental evaluation of hotspot identification methods

Identifying crash “hotspots”, “blackspots”, “sites with promise”, or “high risk” locations is standard practice in departments of transportation throughout the US. The literature is replete with the development and discussion of statistical methods for hotspot identification (HSID). Theoretical derivations and empirical studies have been used to weigh the benefits of various HSID methods; however, a small number of studies have used controlled experiments to systematically assess various methods. Using experimentally derived simulated data—which are argued to be superior to empirical data, three hot spot identification methods observed in practice are evaluated: simple ranking, confidence interval, and Empirical Bayes. Using simulated data, sites with promise are known a priori, in contrast to empirical data where high risk sites are not known for certain. To conduct the evaluation, properties of observed crash data are used to generate simulated crash frequency distributions at hypothetical sites. A variety of factors is manipulated to simulate a host of ‘real world’ conditions. Various levels of confidence are explored, and false positives (identifying a safe site as high risk) and false negatives (identifying a high risk site as safe) are compared across methods. Finally, the effects of crash history duration in the three HSID approaches are assessed. The results illustrate that the Empirical Bayes technique significantly outperforms ranking and confidence interval techniques (with certain caveats). As found by others, false positives and negatives are inversely related. Three years of crash history appears, in general, to provide an appropriate crash history duration.

Zoledronic acid once-yearly : what role in the prevention of non-vertebral osteoporotic fractures?

Osteoporosis is the most common bone disease. Low levels of oestrogens or testosterone are risk factors for primary osteoporosis. The most common cause of secondary osteoporosis is glucocorticoid treatment, but there are many other secondary causes of osteoporosis. Osteoporosis can be secondary to anti-oestrogen treatment for hormone-sensitive breast cancer and to androgen-deprivation therapy for prostate cancer. Zoledronic is the most potent bisphosphonate at inhibiting bone resorption. In osteoporosis, zoledronic acid increases bone mineral density for at least a year after a single intravenous administration. The efficacy and safety of extended release (once-yearly) zoledronic acid in the treatment of osteoporosis is reviewed.

Vitamin D and injury prevention

Vitamin D, along with calcium, may help decrease the risk of falls and fractures in older adults. Sunlight and other sources of ultraviolet radiation are not recommended because they increase the risk of skin cancers and sun-induced eye disorders. Rather, vitamin D and calcium needs should be met through foods and dietary supplements. As a preventive measure to reduce the risk of falls and fractures, it is recommended that older adults meet the 2005 Dietary Guidelines and consume 1000 IU of vitamin D, preferably as vitamin D3.

Visual assessment of pedestrian crashes

Of the numerous factors that play a role in fatal pedestrian collisions, the time of day, day of the week, and time of year can be significant determinants. More than 60% of all pedestrian collisions in 2007 occurred at night, despite the presumed decrease in both pedestrian and automobile exposure during the night. Although this trend is partially explained by factors such as fatigue and alcohol consumption, prior analysis of the Fatality Analysis Reporting System database suggests that pedestrian fatalities increase as light decreases after controlling for other factors. This study applies graphical cross-tabulation, a novel visual assessment approach, to explore the relationships among collision variables. The results reveal that twilight and the first hour of darkness typically observe the greatest frequency of pedestrian fatal collisions. These hours are not necessarily the most risky on a per mile travelled basis, however, because pedestrian volumes are often still high. Additional analysis is needed to quantify the extent to which pedestrian exposure (walking/crossing activity) in these time periods plays a role in pedestrian crash involvement. Weekly patterns of pedestrian fatal collisions vary by time of year due to the seasonal changes in sunset time. In December, collisions are concentrated around twilight and the first hour of darkness throughout the week while, in June, collisions are most heavily concentrated around twilight and the first hours of darkness on Friday and Saturday. Friday and Saturday nights in June may be the most dangerous times for pedestrians. Knowing when pedestrian risk is highest is critically important for formulating effective mitigation strategies and for efficiently investing safety funds. This applied visual approach is a helpful tool for researchers intending to communicate with policy-makers and to identify relationships that can then be tested with more sophisticated statistical tools.

Optimism about safety and group-serving interpretations of safety among pedestrians and cyclists in relation to road use in general and under low light conditions

Drivers are known to be optimistic about their risk of crash involvement, believing that they are less likely to be involved in a crash than other drivers. However, little comparative research has been conducted among other road users. In addition, optimism about crash risk is conceptualised as applying only to an individual’s assessment of his or her personal risk of crash involvement. The possibility that the self-serving nature of optimism about safety might be generalised to the group-level as a cyclist or a pedestrian, i.e., becoming group-serving rather than self-serving, has been overlooked in relation to road safety. This study analysed a subset of data collected as part of a larger research project on the visibility of pedestrians, cyclists and road workers, focusing on a set of questionnaire items administered to 406 pedestrians, 838 cyclists and 622 drivers. The items related to safety in various scenarios involving drivers, pedestrians and cyclists, allowing predictions to be derived about group differences in agreement with items based on the assumption that the results would exhibit group-serving bias. Analysis of the responses indicated that specific hypotheses about group-serving interpretations of safety and responsibility were supported in 22 of the 26 comparisons. When the nine comparisons relevant to low lighting conditions were considered separately, seven were found to be supported. The findings of the research have implications for public education and for the likely acceptance of messages which are inconsistent with current assumptions and expectations of pedestrians and cyclists. They also suggest that research into group-serving interpretations of safety, even for temporary roles rather than enduring groups, could be fruitful. Further, there is an implication that gains in safety can be made by better educating road users about the limitations of their visibility and the ramifications of this for their own road safety, particularly in low light.

Best practice for prevention and treatment of cardiovascular disease through an equity lens : a review

Background: Despite declining rates of cardiovascular disease (CVD) mortality in developed countries, lower socioeconomic groups continue to experience a greater burden of the disease. There are now many evidence-based treatments and prevention strategies for the management of CVD and it is essential that their impact on the more disadvantaged group is understood if socioeconomic inequalities in CVD are to be reduced. Aims: To determine whether key interventions for CVD prevention and treatment are effective among lower socioeconomic groups, to describe barriers to their effectiveness and the potential or actual impact of these interventions on the socioeconomic gradient in CVD. Methods: Interventions were selected from four stages of the CVD continuum. These included smoking reduction strategies, absolute risk assessment, cardiac rehabilitation, secondary prevention medications, and heart failure self-management programmes. Electronic searches were conducted using terms for each intervention combined with terms for socioeconomic status (SES). Results: Only limited evidence was found for the effectiveness of the selected interventions among lower SES groups and there was little exploration of socioeconomic-related barriers to their uptake. Some broad themes and key messages were identified. In the majority of findings examined, it was clear that the underlying material, social and environmental factors associated with disadvantage are a significant barrier to the effectiveness of interventions. Conclusion: Opportunities to reduce socioeconomic inequalities occur at all stages of the CVD continuum. Despite this, current treatment and prevention strategies may be contributing to the widening socioeconomic-CVD gradient. Further research into the impact of best-practice interventions for CVD upon lower SES groups is required.

Cyberbullying prevention : one primary school’s approach

Bullying in all its forms including cyberbullying is a continuing problem in schools. Given the severe consequences it can have on students (socially, psychologically and physically) it is not surprising that a number of intervention programs have been developed, with most advocating a whole school approach. The current study compared students’ self-reports on bullying between schools with and without a Philosophy for Children (P4C) approach. A sample of 35 students in the P4C school and a matched sample of 35 students in other schools between the ages of 10 and 13 completed the Student Bullying Survey. Results indicated that while there were significant differences in incidences of face-to-face bullying, there were similar results from both cohorts in relation to cyberbullying. Both groups of students felt that teachers were more likely to prevent face-to-face bullying than cyberbullying. Findings indicate that teachers and guidance counsellors need to be as overt in teaching strategies about cyberbullying as they are in teaching strategies about reducing face-to-face bullying.

Powered two wheelers in a changing world : challenges and opportunities

Powered two wheelers (PTWs) come in diverse forms and are used for a range of purposes in very different parts of the world. In many parts of the world, the forms and uses of PTWs are changing, influenced by social, economic and demographic changes. Most of the challenges associated with PTWs relate to safety, while the majority of the opportunities relate to mobility. The challenges for improving safety relate to the PTW user, other road users, the road environment, the vehicle, data and research, and socio-political dimensions. The relative importance of particular challenges varies between developed and developing countries, and among developing countries according to whether PTWs are largely used for recreation or for transport. PTWs present a range of psychological, transport, economic and environmental opportunities to individuals and societies. The fun and excitement of riding PTWs is a major motivator for their purchase and use for recreational purposes, both off-road and on-road. The transport and economic advantages to the individual also need to be considered. At a societal level, research has examined the potential for increasing PTW volumes to reduce fossil fuel use and traffic congestion in busy cities. The future of PTWs may differ greatly between countries and environmental and technological changes are leading to an evolution in the form of PTWs to encompass new modes of personal transportation.