Hierarchical Negative Binomial Models Research Articles

Incorporating driving volatility measures in safety performance functions: Improving safety at signalized intersections

About 40 percent of motor vehicle crashes in the US are related to intersections. To deal with such crashes, Safety Performance Functions (SPFs) are vital elements of the predictive methods used in the Highway Safety Manual. The predictions of crash frequencies and potential reductions due to countermeasures are based on exposure and geometric variables. However, the role of driving behavior factors, e.g., hard accelerations and declarations at intersections, which can lead to crashes, are not explicitly treated in SPFs. One way to capture driving behavior is to harness connected vehicle data and quantify performance at intersections in terms of driving volatility measures, i.e., rapid changes in speed and acceleration. According to recent studies, driving volatility is typically associated with higher risk and safety-critical events and can serve as a surrogate for driving behavior. This study incorporates driving volatility measures in the development of SPFs for four-leg signalized intersections. The Safety Pilot Model Deployment (SPMD) data containing over 125 million Basic Safety Messages generated by over 2,800 connected vehicles are harnessed and linked with the crash, traffic, and geometric data belonging to 102 signalized intersections in Ann Arbor, Michigan. The results show that including driving volatility measures in SPFs can reduce model bias and significantly enhances the models' goodness-of-fit and predictive performance. Technically, the best results were obtained by applying Bayesian hierarchical Negative Binomial Models, which account for spatial correlation between signalized intersections. The results of this study have implications for practitioners and transportation agencies about incorporating driving behavior factors in the development of SPFs for greater accuracy and measures that can potentially reduce volatile driving.

Maternal and Child Health Care Service Disruptions and Recovery in Mozambique After Cyclone Idai: An Uncontrolled Interrupted Time Series Analysis.

Climate change-related extreme weather events have increased in frequency and intensity, threatening people's health, particularly in places with weak health systems. In March 2019, Cyclone Idai devastated Mozambique's central region, causing infrastructure destruction, population displacement, and death. We assessed the impact of Idai on maternal and child health services and recovery in the Sofala and Manica provinces. Using monthly district-level routine data from November 2016 to March 2020, we performed an uncontrolled interrupted time series analysis to assess changes in 10 maternal and child health indicators in all 25 districts before and after Idai. We applied a Bayesian hierarchical negative binomial model with district-level random intercepts and slopes to estimate Idai-related service disruptions and recovery. Of the 4.44 million people in Sofala and Manica, 1.83 (41.2%) million were affected. Buzi, Nhamatanda, and Dondo (all in Sofala province) had the highest proportion of people affected. After Idai, all 10 indicators showed an abrupt substantial decrease. First antenatal care visits per 100,000 women of reproductive age decreased by 23% (95% confidence interval [CI]=0.62, 0.96) in March and 11% (95% CI=0.75, 1.07) in April. BCG vaccinations per 1,000 children under age 5 years declined by 21% (95% CI=0.69, 0.90) and measles vaccinations decreased by 25% (95% CI=0.64, 0.87) in March and remained similar in April. Within 3 months post-cyclone, almost all districts recovered to pre-Idai levels, including Buzi, which showed a 22% and 13% relative increase in the number of first antenatal care visits and BCG, respectively. We found substantial health service disruptions immediately after Idai, with greater impact in the most affected districts. The findings suggest impressive recovery post-Idai, emphasizing the need to build resilient health systems to ensure quality health care during and after natural disasters.

Differential RNA methylation analysis for MeRIP-seq data under general experimental design.

RNA epigenetics is an emerging field to study the post-transcriptional gene regulation. The dynamics of RNA epigenetic modification have been reported to associate with many human diseases. Recently developed high-throughput technology named Methylated RNA Immunoprecipitation Sequencing (MeRIP-seq) enables the transcriptome-wide profiling of N6-methyladenosine (m6A) modification and comparison of RNA epigenetic modifications. There are a few computational methods for the comparison of mRNA modifications under different conditions but they all suffer from serious limitations. In this work, we develop a novel statistical method to detect differentially methylated mRNA regions from MeRIP-seq data. We model the sequence count data by a hierarchical negative binomial model that accounts for various sources of variations and derive parameter estimation and statistical testing procedures for flexible statistical inferences under general experimental designs. Extensive benchmark evaluations in simulation and real data analyses demonstrate that our method is more accurate, robust and flexible compared to existing methods. Our method TRESS is implemented as an R/Bioconductor package and is available at https://bioconductor.org/packages/devel/TRESS. Supplementary data are available at Bioinformatics online.

Beyond rates: time-varying dynamics of high frequency oscillations as a biomarker of the seizure onset zone

Objective. High frequency oscillations (HFOs) recorded by intracranial electrodes have generated excitement for their potential to help localize epileptic tissue for surgical resection. However, the number of HFOs per minute (i.e. the HFO ‘rate’) is not stable over the duration of intracranial recordings; for example, the rate of HFOs increases during periods of slow-wave sleep. Moreover, HFOs that are predictive of epileptic tissue may occur in oscillatory patterns due to phase coupling with lower frequencies. Therefore, we sought to further characterize between-seizure (i.e. ‘interictal’) HFO dynamics both within and outside the seizure onset zone (SOZ). Approach. Using long-term intracranial EEG (mean duration 10.3 h) from 16 patients, we automatically detected HFOs using a new algorithm. We then fit a hierarchical negative binomial model to the HFO counts. To account for differences in HFO dynamics and rates between sleep and wakefulness, we also fit a mixture model to the same data that included the ability to switch between two discrete brain states that were automatically determined during the fitting process. The ability to predict the SOZ by model parameters describing HFO dynamics (i.e. clumping coefficients and coefficients of variation) was assessed using receiver operating characteristic curves. Main results. Parameters that described HFO dynamics were predictive of SOZ. In fact, these parameters were found to be more consistently predictive than HFO rate. Using concurrent scalp EEG in two patients, we show that the model-found brain states corresponded to (1) non-REM sleep and (2) awake and rapid eye movement sleep. However the brain state most likely corresponding to slow-wave sleep in the second model improved SOZ prediction compared to the first model for only some patients. Significance. This work suggests that delineation of SOZ with interictal data can be improved by the inclusion of time-varying HFO dynamics.

1499Health behaviours as risk factors of COVID-19 incidence in South Korea

BackgroundPersonal health behaviours, which rely on community characteristics, could affect individual vulnerability on disease infection. Due to insufficient study to examine health behaviours as risk factors of COVID-19 infection, we conducted municipal level spatial analysis to investigate association between health behaviours and COVID-19 incidence.MethodsWe extracted cumulative COVID-19 incidence data from January 20th 2020 to February 25th 2021, health behaviours, health condition, socio-economic factors, and covariates in municipal level from publicly available dataset. We chose variables, which were standardized, considering multicollinearity (VIF<10). Further, we employed bayesian hierarchical negative binomial model with intrinsic conditional autoregressive (iCAR) and Besag, York and Mollié (BYM) model, and used deviance information criterion (DIC) for final model selection.ResultsThe mean cumulative COVID-19 incidence per 10,000 population among 229 municipality was 13.73 (Standard deviation=11.43). iCAR model (DIC=2,825.3) outperformed BYM model (DIC=14,009.4). The results of iCAR model highlighted that incidence was associated with dental hygiene practice (incidence risk ratios [IRR]=0.92, 95% Credible Interval [CI]=0.85–1.00), whether tried to be thin (IRR=1.10, 95% CI = 1.00–1.20), proportion of medical personnel (IRR=1.09, 95% CI = 1.01–1.17), and volume of public transportation (IRR=1.19, 95% CI = 1.05–1.35), even after adjusting for various confounding factors.ConclusionsMunicipality with lower cumulative incidence was likely to have more people who practiced to keep dental hygiene and less people who tried to be thin.Key messagesMunicipal level spatial analysis resulted that health behaviours were associated with COVID-19 incidence in South Korea.

Estimating the effect of moving meat-free products to the meat aisle on sales of meat and meat-free products: A non-randomised controlled intervention study in a large UK supermarket chain

Reducing meat consumption could bring health and environmental benefits, but there is little research to date on effective interventions to achieve this. A non-randomised controlled intervention study was used to evaluate whether prominent positioning of meat-free products in the meat aisle was associated with a change in weekly mean sales of meat and meat-free products. Weekly sales data were obtained from 108 stores: 20 intervention stores that moved a selection of 26 meat-free products into a newly created meat-free bay within the meat aisle and 88 matched control stores. The primary outcome analysis used a hierarchical negative binomial model to compare changes in weekly sales (units) of meat products sold in intervention versus control stores during the main intervention period (Phase I: February 2019 to April 2019). Interrupted time series analysis was also used to evaluate the effects of the Phase I intervention. Moreover, 8 of the 20 stores enhanced the intervention from August 2019 onwards (Phase II intervention) by adding a second bay of meat-free products into the meat aisle, which was evaluated following the same analytical methods. During the Phase I intervention, sales of meat products (units/store/week) decreased in intervention (approximately -6%) and control stores (-5%) without significant differences (incidence rate ratio [IRR] 1.01 [95% CI 0.95-1.07]. Sales of meat-free products increased significantly more in the intervention (+31%) compared to the control stores (+6%; IRR 1.43 [95% CI 1.30-1.57]), mostly due to increased sales of meat-free burgers, mince, and sausages. Consistent results were observed in interrupted time series analyses where the effect of the Phase II intervention was significant in intervention versus control stores. Prominent positioning of meat-free products into the meat aisle in a supermarket was not effective in reducing sales of meat products, but successfully increased sales of meat-free alternatives in the longer term. A preregistered protocol (https://osf.io/qmz3a/) was completed and fully available before data analysis.

Spatial and temporal trends in social vulnerability and COVID-19 incidence and death rates in the United States.

BackgroundSocially vulnerable communities may be at higher risk for COVID-19 outbreaks in the US. However, no prior studies examined temporal trends and differential effects of social vulnerability on COVID-19 incidence and death rates. Therefore, we examined temporal trends among counties with high and low social vulnerability to quantify disparities in trends over time.MethodsWe conducted a longitudinal analysis examining COVID-19 incidence and death rates from March 15 to December 31, 2020, for each US county using data from USAFacts. We classified counties using the Social Vulnerability Index (SVI), a percentile-based measure from the Centers for Disease Control and Prevention, with higher values indicating more vulnerability. Using a Bayesian hierarchical negative binomial model, we estimated daily risk ratios (RRs) comparing counties in the first (lower) and fourth (upper) SVI quartiles, adjusting for rurality, percentage in poor or fair health, percentage female, percentage of smokers, county average daily fine particulate matter (PM2.5), percentage of primary care physicians per 100,000 residents, daily temperature and precipitation, and proportion tested for COVID-19.ResultsAt the outset of the pandemic, the most vulnerable counties had, on average, fewer cases per 100,000 than least vulnerable SVI quartile. However, on March 28, we observed a crossover effect in which the most vulnerable counties experienced higher COVID-19 incidence rates compared to the least vulnerable counties (RR = 1.05, 95% PI: 0.98, 1.12). Vulnerable counties had higher death rates starting on May 21 (RR = 1.08, 95% PI: 1.00,1.16). However, by October, this trend reversed and the most vulnerable counties had lower death rates compared to least vulnerable counties.ConclusionsThe impact of COVID-19 is not static but can migrate from less vulnerable counties to more vulnerable counties and back again over time.

A Bayesian joint model for zero-inflated integers and left-truncated event times with a time-varying association: Applications to senior health care.

Population aging in most industrialized societies has led to a dramatic increase in emergency medical demand among the elderly. In the context of private health care, an optimal allocation of the medical resources for seniors is commonly done by forecasting their life spans. Accounting for each subject's particularities is therefore indispensable, so the available data must be processed at an individual level. We use a large and unique dataset of insured parties aged 65 and older to appropriately relate the emergency care usage with mortality risk. Longitudinal and time-to-event processes are jointly modeled, and their underlying relationship can therefore be assessed. Such an application, however, requires some special features to also be considered. First, longitudinal demand for emergency services exhibits a nonnegative integer response with an excess of zeros due to the very nature of the data. These subject-specific responses are handled by a zero-inflated version of the hierarchical negative binomial model. Second, event times must account for the left truncation derived from the fact that policyholders must reach the age of 65 before they may begin to be observed. Consequently, a delayed entry bias arises for those individuals entering the study after this age threshold. Third, and as the main challenge of our analysis, the association parameter between both processes is expected to be age-dependent, with an unspecified association structure. This is well-approximated through a flexible functional specification provided by penalized B-splines. The parameter estimation of the joint model is derived under a Bayesian scheme.

Bayesian hierarchical negative binomial models for multivariable analyses with applications to human microbiome count data.

The analyses of large volumes of metagenomic data extracted from aggregate populations of microscopic organisms residing on and in the human body are advancing contemporary understandings of the integrated participation of microbes in human health and disease. Next generation sequencing technology facilitates said analyses in terms of diversity, community composition, and differential abundance by filtering and binning microbial 16S rRNA genes extracted from human tissues into operational taxonomic units. However, current statistical tools restrict study designs to investigations of limited numbers of host characteristics mediated by limited numbers of samples potentially yielding a loss of relevant information. This paper presents a Bayesian hierarchical negative binomial model as an efficient technique capable of compensating for multivariable sets including tens or hundreds of host characteristics as covariates further expanding analyses of human microbiome count data. Simulation studies reveal that the Bayesian hierarchical negative binomial model provides a desirable strategy by often outperforming three competing negative binomial model in terms of type I error while simultaneously maintaining consistent power. An application of the Bayesian hierarchical negative binomial model using subsets of the open data published by the American Gut Project demonstrates an ability to identify operational taxonomic units significantly differentiable among persons diagnosed by a medical professional with either inflammatory bowel disease or irritable bowel syndrome that are consistent with contemporary gastrointestinal literature.

Risk-standardized Acute Admission Rates Among Patients With Diabetes and Heart Failure as a Measure of Quality of Accountable Care Organizations: Rationale, Methods, and Early Results.

Population-based measures of admissions among patients with chronic conditions are important quality indicators of Accountable Care Organizations (ACOs), yet there are challenges in developing measures that enable fair comparisons among providers. On the basis of consensus standards for outcome measure development and with expert and stakeholder input on methods decisions, we developed and tested 2 models of risk-standardized acute admission rates (RSAARs) for patients with diabetes and heart failure using 2010-2012 Medicare claims data. Model performance was assessed with deviance R; score reliability was tested with intraclass correlation coefficient. We estimated RSAARs for 114 Shared Savings Program ACOs in 2012 and we assigned ACOs to 3 performance categories: no different, worse than, and better than the national rate. The diabetes and heart failure cohorts included 6.5 and 2.6 million Medicare Fee-For-Service beneficiaries aged 65 years and above, respectively. Risk-adjustment variables were age, comorbidities, and condition-specific severity variables, but not socioeconomic status or other contextual factors. We selected hierarchical negative binomial models with the outcome of acute, unplanned hospital admissions per 100 person-years. For the diabetes and heart failure measures, respectively, the models accounted for 22% and 12% of the deviance in outcomes and score reliability was 0.89 and 0.81. For the diabetes measure, 51 (44.7%) ACOs were no different, 45 (39.5%) were better, and 18 (15.8%) were worse than the national rate. The distribution of performance for the heart failure measure was 61 (53.5%), 37 (32.5%), and 16 (14.0%), respectively. Measures of RSAARs for patients with diabetes and heart failure meet criteria for scientific soundness and reveal important variation in quality across ACOs.

Empirical Bayes analysis of RNA-seq data for detection of gene expression heterosis.

An important type of heterosis, known as hybrid vigor, refers to the enhancements in the phenotype of hybrid progeny relative to their inbred parents. Although hybrid vigor is extensively utilized in agriculture, its molecular basis is still largely unknown. In an effort to understand phenotypic heterosis at the molecular level, researchers are measuring transcript abundance levels of thousands of genes in parental inbred lines and their hybrid offspring using RNA sequencing (RNA-seq) technology. The resulting data allow researchers to search for evidence of gene expression heterosis as one potential molecular mechanism underlying heterosis of agriculturally important traits. The null hypotheses of greatest interest in testing for gene expression heterosis are composite null hypotheses that are difficult to test with standard statistical approaches for RNA-seq analysis. To address these shortcomings, we develop a hierarchical negative binomial model and draw inferences using a computationally tractable empirical Bayes approach to inference. We demonstrate improvements over alternative methods via a simulation study based on a maize experiment and then analyze that maize experiment with our newly proposed methodology. This article has supplementary material online.

Variation in treatment of neonatal abstinence syndrome in US children's hospitals, 2004-2011.

Neonatal abstinence syndrome (NAS) is a drug withdrawal syndrome experienced by opioid-exposed infants. There is no standard treatment for NAS and surveys suggest wide variation in pharmacotherapy for NAS. Our objective was to determine whether different pharmacotherapies for NAS are associated with differences in outcomes and to determine whether pharmacotherapy and outcome vary by hospital. We used the Pediatric Health Information System Database from 2004 to 2011 to identify a cohort of infants with NAS requiring pharmacotherapy. Mixed effects hierarchical negative binomial models evaluated the association between pharmacotherapy and hospital with length of stay (LOS), length of treatment (LOT) and hospital charges, after adjusting for socioeconomic variables and comorbid clinical conditions. Our cohort included 1424 infants with NAS from 14 children's hospitals. Among hospitals in our sample, six used morphine, six used methadone and two used phenobarbital as primary initial treatment for NAS. In multivariate analysis, when compared with NAS patients initially treated with morphine, infants treated with methadone had shorter LOT (incidence rate ratio (IRR) = 0.55; P < 0.0001) and LOS (IRR = 0.60; P < 0.0001). Phenobarbital as a second-line agent was associated with increased LOT (IRR = 2.09; P<0.0001), LOS (IRR = 1.78; P < 0.0001) and higher hospital charges (IRR = 1.84; P < 0.0001). After controlling for case-mix, hospitals varied in LOT, LOS and hospital charges. We found variation in hospital in treatment for NAS among major US children's hospitals. In analyses controlling for possible confounders, methadone as initial treatment was associated with reduced LOT and hospital stay.

A Genetic Analysis of Mortality in Pigs

An analysis of mortality is undertaken in two breeds of pigs: Danish Landrace and Yorkshire. Zero-inflated and standard versions of hierarchical Poisson, binomial, and negative binomial Bayesian models were fitted using Markov chain Monte Carlo (MCMC). The objectives of the study were to investigate whether there is support for genetic variation for mortality and to study the quality of fit and predictive properties of the various models. In both breeds, the model that provided the best fit to the data was the standard binomial hierarchical model. The model that performed best in terms of the ability to predict the distribution of stillbirths was the hierarchical zero-inflated negative binomial model. The best fit of the binomial hierarchical model and of the zero-inflated hierarchical negative binomial model was obtained when genetic variation was included as a parameter. For the hierarchical binomial model, the estimate of the posterior mean of the additive genetic variance (posterior standard deviation in brackets) at the level of the logit of the probability of a stillbirth was 0.173(0.039) in Landrace and 0.202(0.048) in Yorkshire. The implications of these results from a breeding perspective are briefly discussed.

Evidence of Alaskan Trumpeter Swan Population Growth Using Bayesian Hierarchical Models

ABSTRACT Alaska (USA) contains a large proportion of the breeding population of trumpeter swans (Cygnus buccinator) in the United States. However, tracking population trends in Alaska trumpeter swans is complicated by variables such as an increase in survey effort over time, periodic surveys (1968 and every 5 yr after 1975), and missing data. We therefore constructed Bayesian hierarchical negative binomial models to account for nuisance variables and to estimate population size of trumpeter swans using aerial survey data from all known breeding habitats in Alaska, 1968–2005. We also performed an augmented analysis, where we entered zeroes for missing data. This approach differed from the standard (nonaugmented) analysis where we generated estimates for missing data through simulation. We estimated that adult swan populations in Alaska increased at an average rate of 5.9% annually (95% credibility interval = 5.2–6.6%) and cygnet production increased at 5.3% annually (95% credibility interval = 2.2–8.0%). We also found evidence that cygnet production exhibited higher rates of increase at higher latitudes in later years, which may be a response to warmer spring temperatures. Augmented analyses always produced higher swan population estimates than the nonaugmented estimates and likely overestimate true population abundance. Our results provide evidence that trumpeter swan populations are increasing in Alaska, especially at northern latitudes. Changes in population size and distribution could negatively affect tundra swans (Cygnus columbianus) breeding in Alaska, and biologists should monitor these interactions. We recommend using nonaugmented Bayesian hierarchical analyses to estimate wildlife populations when missing survey data occur.