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

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

Leveraging probe data to model speeding on urban limited access highway segments: Examining the impact of operational performance, roadway characteristics, and COVID-19 pandemic.

Stay-at-home orders - imposed to prevent the spread of COVID-19 - drastically changed the way highways operate. Despite lower traffic volumes during these times, the rate of fatal and serious injury crashes increased significantly across the United States due to increased speeding on roads with less traffic congestion and lower levels of speed enforcement. This paper uses a mixed effect binomial regression model to investigate the impact of stay-at-home orders on odds of speeding on urban limited access highway segments in Maine and Connecticut. This paper also establishes a link between traffic density and the odds of speeding. For this purpose, hourly speed and volume probe data were collected on limited access highway segments for the U.S. states of Maine and Connecticut to estimate the traffic density. The traffic density was then combined with the roadway geometric characteristics, speed limit, as well as dummy variables denoting the time of the week, time of the day, COVID-19 phases (before, during and after stay-at-home order), and the interactions between them. Density, represented in the model as Level of Service, was found to be associated with the odds of speeding, with better levels of service such as A, or B (low density) resulting in the higher odds that drivers would speed. We also found that narrower shoulder width could result in lower odds of speeding. Furthermore, we found that during the stay-at-home order, the odds of speeding by more than 10, 15, and 20 mph increased respectively by 54%, 71% and 85% in Connecticut, and by 15%, 36%, and 65% in Maine during evening peak hours. Additionally, one year after the onset of the pandemic, during evening peak hours, the odds of speeding greater than 10, 15, and 20 mph were still 35%, 29%, and 19% greater in Connecticut and 35% 35% and 20% greater in Maine compared to before pandemic.

Driver, roadway, and weather factors on severity of lane departure crashes in Maine.

INTRODUCTION: In Maine, lane departure crashes account for over 70% of roadway fatalities. The majority of roadways in Maine are rural. Moreover, Maine has aging infrastructure, houses the oldest population in the United States, and experiences the third coldest weather in the United States. METHODS: This study analyzes the impact of roadway, driver, and weather factors on the severity of single-vehicle lane departure crashes occurring from 2017 to 2019 on rural roadways in Maine. Rather than using police reported weather, weather station data were utilized. Four facility types: Interstates, minor arterials, major collectors, and minor collectors were considered for analysis. The Multinomial Logistic Regression model was used for the analysis. The property damage only (PDO) outcome was considered as the reference (or base) category. RESULTS: The modeling results show that the odds of a crash leading to major injury or fatality (KA outcome) increases by 330%, 150%, 243%, and 266% for older drivers (65 or above) compared to young drivers (29 or less) on Interstates, minor arterials, major collectors, and minor collectors, respectively. During the winter period (October to April), the odds of KA severity outcome (with respect to the PDO) decreases by 65%, 65%, 65%, and 48% on Interstates, minor arterials, major collectors, and minor collectors, respectively, presumably due to reduced speeds during winter weather events. CONCLUSION: In Maine, factors such as older drivers, operating under the influence, speeding, precipitation, and not wearing a seatbelt showed higher odds of leading to injury. PRACTICAL APPLICATIONS: This study provides safety analysts and practitioners in Maine a comprehensive study of factors that influence the severity of crashes in Maine at different facilities to improve maintenance strategies, enhance safety using proper safety countermeasures, or increase awareness across the state.

Modeling the impact of the COVID-19 pandemic on speeding at rural roadway facilities in Maine using short-term speed and traffic count data.

The COVID-19 pandemic caused a significant change in traffic operations and safety. For instance, various U.S. states reported an increase in the rate of fatal and severe injury crashes over this duration. In April and May of 2020, comprehensive stay-at-home orders were issued across the country, including in Maine. These orders resulted in drastic reductions in traffic volume. Additionally, there is anecdotal evidence that speed enforcement had been reduced during pandemic. Drivers responded to these changes by increasing their speed. More importantly, data show that speeding continues to occur, even one year after the onset of the pandemic. This study develops statistical models to quantify the impact of the pandemic on speeding in Maine. We developed models for three rural facility types (i.e., major collectors, minor arterials, and principal arterials) using a mixed effect Binomial regression model and short duration speed and traffic count data collected at continuous count stations in Maine. Our results show that the odds of speeding by more than 15 mph increased by 34% for rural major collectors, 32% for rural minor arterials, and 51% for rural principal arterials (non-Interstates) during the stay-at-home order in April and May of 2020 compared to the same months in 2019. In addition, the odds of speeding by more than 15 mph, in April and May of 2021, one year after the order, were still 27% higher on rural major collectors and 17% higher on rural principal arterials compared to the same months in 2019.

Finite mixture Negative Binomial-Lindley for modeling heterogeneous crash data with many zero observations.

Crash data are often highly dispersed; it may also include a large amount of zero observations or have a long tail. The traditional Negative Binomial (NB) model cannot model these data properly. To overcome this issue, the Negative Binomial-Lindley (NB-L) model has been proposed as an alternative to the NB to analyze data with these characteristics. Research studies have shown that the NB-L model provides a superior performance compared to the NB when data include numerous zero observations or have a long tail. In addition, crash data are often collected from sites with different spatial or temporal characteristics. Therefore, it is not unusual to assume that crash data are drawn from multiple subpopulations. Finite mixture models are powerful tools that can be used to account for underlying subpopulations and capture the population heterogeneity. This research documents the derivations and characteristics of the Finite mixture NB-L model (FMNB-L) to analyze data generated from heterogeneous subpopulations with many zero observations and a long tail. We demonstrated the application of the model to identify subpopulations with a simulation study. We then used the FMNB-L model to estimate statistical models for Texas four-lane freeway crashes. These data have unique characteristics; it is highly dispersed, have many locations with very large number of crashes, as well as significant number of locations with zero crash. We used multiple goodness-of-fit metrics to compare the FMNB-L model with the NB, NB-L, and the finite mixture NB models. The FMNB-L identified two subpopulations in datasets. The results show a significantly better fit by the FMNB-L compared to other analyzed models.

Derivation of the Empirical Bayesian method for the Negative Binomial-Lindley generalized linear model with application in traffic safety.

The expected crash frequency is the long-term average crash count for a specific site. It is extensively used to systematically evaluate the crash risk associated with roadway elements. To estimate the expected crashes, the Empirical Bayesian (EB) approach is typically employed. The EB method is a computationally convenient approximation to the Full Bayesian (FB) method, which gained popularity due to its simple interpretation, computational efficiency, and the ability to account for the regression to the mean bias. However, the common EB method used in traffic safety analysis is only applicable when the traditional Negative Binomial (NB) model is used. The NB model, however, is not a suitable choice when data is highly dispersed, skewed, or has a large number of zero observations. The Negative Binomial-Lindley (NB-L) model is a mixture of the NB and Lindley distributions and has shown superior fit compared to the NB model, especially when the dataset is characterized by excess zero observations. Even though several studies have used the NB-L in developing crash prediction models, the application of the NB-L in other safety-related tasks (e.g., hot spot identification) is largely neglected. This study proposed a framework to develop the EB method for the NB-L model and subsequently estimate the expected crash values. A comparison between the EB and FB estimates was performed to validate the approximation framework in general. The results indicated that the proposed EB framework is able to estimate expected crashes with comparable precision to the FB estimate, but with much less computational cost. In addition, a site ranking analysis using the EB estimates was conducted to validate the proposed approximation method in safety studies. However, it should be noted that any other type of safety analysis that requires access to the expected crashes can benefit from the proposed EB method. This study concluded that the proposed EB framework can properly approximate the underlying FB approach and can reasonably be considered as an alternative to the traditional EB formula derived from the NB model. The results of this study can help to extend the application of the advanced predictive models beyond predicting crashes to other safety-related tasks, with no additional computational efforts.

Iranian Society of Cardiac Surgeons COVID-19 task force version II, restarting elective surgeries.

Given the nature of heart disease and the importance of continuing heart surgery during the pandemic and its aftermath and in order to provide adequate safety for the surgical team and achieve the desired result for patients, as well as the optimal use of ICU beds, the medical team, blood, blood products, and personal protective equipment, it is essential to change the usual approach during the pandemic. There are still a lot of evidences and experiences needed to produce the perfect protocol. Some centers may have a special program for their centers during this period of epidemics that can be respected and performed. Generally, in pandemic conditions, the use of non-surgical approaches is preferred if similar outcomes can be obtained.

Differentiation of pain levels by deploying various electroencephalogram synchronization features and a dynamic ensemble selection mechanism.

Objective: The aim of this study was to measure pain intensity in an objective manner by analyzing electroencephalogram (EEG) signals. Although this problem has attracted the attention of researchers, increasing the resolution of this measurement by increasing the number of pain states significantly decreases the accuracy of pain level classification.Approach: To overcome this drawback, we adopt state-of-the-art synchronization schemes to measure the linear, nonlinear and generalized synchronization between different EEG channels. Thirty-two subjects executed the cold pressor task and experienced five defined levels of pain while their EEGs were recorded. Due to the large number of synchronization features from 34 channels, the most discriminative features were selected using the greedy overall relevancy method. The selected features were applied to a dynamic ensemble selection system.Main results: Our experiment provides 85.6% accuracy over the five classes, which significantly improves upon the results of past research. Moreover, we observed that the selected features belong to the channels placed over the ridge of the cortex, the area responsible for processing somatic sensation arising from nociceptive temperature. As expected, we noted that continuation of the painful stimulus for minutes engaged regions beyond the sensorimotor cortex (e.g. the prefrontal cortex).Significance: We conclude that the amount of synchronization between scalp EEG channels is an informative tool in revealing the pain sensation.

A methodology to design heuristics for model selection based on the characteristics of data: Application to investigate when the Negative Binomial Lindley (NB-L) is preferred over the Negative Binomial (NB).

Safety analysts usually use post-modeling methods, such as the Goodness-of-Fit statistics or the Likelihood Ratio Test, to decide between two or more competitive distributions or models. Such metrics require all competitive distributions to be fitted to the data before any comparisons can be accomplished. Given the continuous growth in introducing new statistical distributions, choosing the best one using such post-modeling methods is not a trivial task, in addition to all theoretical or numerical issues the analyst may face during the analysis. Furthermore, and most importantly, these measures or tests do not provide any intuitions into why a specific distribution (or model) is preferred over another (Goodness-of-Logic). This paper ponders into these issues by proposing a methodology to design heuristics for Model Selection based on the characteristics of data, in terms of descriptive summary statistics, before fitting the models. The proposed methodology employs two analytic tools: (1) Monte-Carlo Simulations and (2) Machine Learning Classifiers, to design easy heuristics to predict the label of the 'most-likely-true' distribution for analyzing data. The proposed methodology was applied to investigate when the recently introduced Negative Binomial Lindley (NB-L) distribution is preferred over the Negative Binomial (NB) distribution. Heuristics were designed to select the 'most-likely-true' distribution between these two distributions, given a set of prescribed summary statistics of data. The proposed heuristics were successfully compared against classical tests for several real or observed datasets. Not only they are easy to use and do not need any post-modeling inputs, but also, using these heuristics, the analyst can attain useful information about why the NB-L is preferred over the NB - or vice versa- when modeling data.

A Monte-Carlo simulation analysis for evaluating the severity distribution functions (SDFs) calibration methodology and determining the minimum sample-size requirements.

Severity distribution functions (SDFs) are used in highway safety to estimate the severity of crashes and conduct different types of safety evaluations and analyses. Developing a new SDF is a difficult task and demands significant time and resources. To simplify the process, the Highway Safety Manual (HSM) has started to document SDF models for different types of facilities. As such, SDF models have recently been introduced for freeway and ramps in HSM addendum. However, since these functions or models are fitted and validated using data from a few selected number of states, they are required to be calibrated to the local conditions when applied to a new jurisdiction. The HSM provides a methodology to calibrate the models through a scalar calibration factor. However, the proposed methodology to calibrate SDFs was never validated through research. Furthermore, there are no concrete guidelines to select a reliable sample size. Using extensive simulation, this paper documents an analysis that examined the bias between the 'true' and 'estimated' calibration factors. It was indicated that as the value of the true calibration factor deviates further away from '1', more bias is observed between the 'true' and 'estimated' calibration factors. In addition, simulation studies were performed to determine the calibration sample size for various conditions. It was found that, as the average of the coefficient of variation (CV) of the 'KAB' and 'C' crashes increases, the analyst needs to collect a larger sample size to calibrate SDF models. Taking this observation into account, sample-size guidelines are proposed based on the average CV of crash severities that are used for the calibration process.

Sample-size guidelines for recalibrating crash prediction models: Recommendations for the highway safety manual.

The Highway Safety Manual (HSM) prediction models are fitted and validated based on crash data collected from a selected number of states in the United States. Therefore, for a jurisdiction to be able to fully benefit from applying these models, it is necessary to calibrate or recalibrate them to local conditions. The first edition of the HSM recommends calibrating the models using a one-size-fits-all sample-size of 30-50 locations with total of at least 100 crashes per year. However, the HSM recommendation is not fully supported by documented studies. The objectives of this paper are consequently: (1) to examine the required sample size based on the characteristics of the data that will be used for the calibration or recalibration process; and, (2) propose revised guidelines. The objectives were accomplished using simulation runs for different scenarios that characterized the sample mean and variance of the data. The simulation results indicate that as the ratio of the standard deviation to the mean (i.e., coefficient of variation) of the crash data increases, a larger sample-size is warranted to fulfill certain levels of accuracy. Taking this observation into account, sample-size guidelines were prepared based on the coefficient of variation of the crash data that are needed for the calibration process. The guidelines were then successfully applied to the two observed datasets. The proposed guidelines can be used for all facility types and both for segment and intersection prediction models.

A semiparametric negative binomial generalized linear model for modeling over-dispersed count data with a heavy tail: Characteristics and applications to crash data.

Crash data can often be characterized by over-dispersion, heavy (long) tail and many observations with the value zero. Over the last few years, a small number of researchers have started developing and applying novel and innovative multi-parameter models to analyze such data. These multi-parameter models have been proposed for overcoming the limitations of the traditional negative binomial (NB) model, which cannot handle this kind of data efficiently. The research documented in this paper continues the work related to multi-parameter models. The objective of this paper is to document the development and application of a flexible NB generalized linear model with randomly distributed mixed effects characterized by the Dirichlet process (NB-DP) to model crash data. The objective of the study was accomplished using two datasets. The new model was compared to the NB and the recently introduced model based on the mixture of the NB and Lindley (NB-L) distributions. Overall, the research study shows that the NB-DP model offers a better performance than the NB model once data are over-dispersed and have a heavy tail. The NB-DP performed better than the NB-L when the dataset has a heavy tail, but a smaller percentage of zeros. However, both models performed similarly when the dataset contained a large amount of zeros. In addition to a greater flexibility, the NB-DP provides a clustering by-product that allows the safety analyst to better understand the characteristics of the data, such as the identification of outliers and sources of dispersion.