An assessment of empirical Bayes and composite estimators for small areas

We compare a set of empirical Bayes and composite estimators of the population means of the districts (small areas) of a country, and show that the natural modelling strategy of searching for a well fitting empirical Bayes model and using it for estimation of the area-level means can be inefficient.

From Empirical Bayes to Full Bayes: Methods for Analysing Traffice Safety Data, October 25, 2004

Traffic safety engineers are among the early adopters of Bayesian statistical tools for analyzing crash data. As in many other areas of application, empirical Bayes methods were their first choice, perhaps because they represent an intuitively appealing, yet relatively easy to implement alternative to purely classical approaches. With the enormous progress in numerical methods made in recent years and with the availability of free, easy to use software that permits implementing a fully Bayesian approach, however, there is now ample justification to progress towards fully Bayesian analyses of crash data. The fully Bayesian approach, in particular as implemented via multi-level hierarchical models, has many advantages over the empirical Bayes approach. In a full Bayesian analysis, prior information and all available data are seamlessly integrated into posterior distributions on which practitioners can base their inferences. All uncertainties are thus accounted for in the analyses and there is no need to pre-process data to obtain Safety Performance Functions and other such prior estimates of the effect of covariates on the outcome of interest. In this slight, fully Bayesian methods may well be less costly to implement and may result in safety estimates with more realistic standard errors. In this manuscript, we present the full Bayesian approach to analyzing traffic safety data and focus on highlighting the differences between the empirical Bayes and the full Bayes approaches. We use an illustrative example to discuss a step-by-step Bayesian analysis of the data and to show some of the types of inferences that are possible within the full Bayesian framework.

From Empirical Bayes to Full Bayes: Methods for Analyzubg Traffic Safey Data, October 25, 2004

Traffic safety engineers are among the early adopters of Bayesian statistical tools for analyzing crash data. As in many other areas of application, empirical Bayes methods were their first choice, perhaps because they represent an intuitively appealing, yet relatively easy to implement alternative to purely classical approaches. With the enormous progress in numerical methods made in recent years and with the availability of free, easy to use software that permits implementing a fully Bayesian approach, however, there is now ample justification to progress towards fully Bayesian analyses of crash data. The fully Bayesian approach, in particular as implemented via multi-level hierarchical models, has many advantages over the empirical Bayes approach. In a full Bayesian analysis, prior information and all available data are seamlessly integrated into posterior distributions on which practitioners can base their inferences. All uncertainties are thus accounted for in the analyses and there is no need to pre-process data to obtain Safety Performance Functions and other such prior estimates of the effect of covariates on the outcome of interest. In this light, fully Bayesian methods may well be less costly to implement and may result in safety estimates with more realistic standard errors. In this manuscript, we present the full Bayesian approach to analyzing traffic safety data and focus on highlighting the differences between the empirical Bayes and the full Bayes approaches. We use an illustrative example to discuss a step-by-step Bayesian analysis of the data and to show some of the types of inferences that are possible within the full Bayesian framework.

Empirical Bayes self-test quiz

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Development of safety performance functions for empirical Bayes estimation of crash reduction factors

Crash reduction factors (CRFs) are used to estimate the potential number of traffic crashes expected to be prevented from investment in safety improvement projects. The method used to develop CRFs in Florida has been based on the commonly used before-and-after approach. This approach suffers from a widely recognized problem known as regression-to-the-mean (RTM). The Empirical Bayes (EB) method has been introduced as a means to addressing the RTM problem. This method requires the information from both the treatment and reference sites in order to predict the expected number of crashes had the safety improvement projects at the treatment sites not been implemented. The information from the reference sites is estimated from a safety performance function (SPF), which is a mathematical relationship that links crashes to traffic exposure. The objective of this dissertation was to develop the SPFs for different functional classes of the Florida State Highway System. Crash data from years 2001 through 2003 along with traffic and geometric data were used in the SPF model development. SPFs for both rural and urban roadway categories were developed. The modeling data used were based on one-mile segments that contain homogeneous traffic and geometric conditions within each segment. Segments involving intersections were excluded. The scatter plots of data show that the relationships between crashes and traffic exposure are nonlinear, that crashes increase with traffic exposure in an increasing rate. Four regression models, namely, Poisson (PRM), Negative Binomial (NBRM), zero-inflated Poisson (ZIP), and zero-inflated Negative Binomial (ZINB), were fitted to the one-mile segment records for individual roadway categories. The best model was selected for each category based on a combination of the Likelihood Ratio test, the Vuong statistical test, and the Akaike's Information Criterion (AIC). The NBRM model was found to be appropriate for only one category and the ZINB model was found to be more appropriate for six other categories. The overall results show that the Negative Binomial distribution model generally provides a better fit for the data than the Poisson distribution model. In addition, the ZINB model was found to give the best fit when the count data exhibit excess zeros and over-dispersion for most of the roadway categories. While model validation shows that most data points fall within the 95% prediction intervals of the models developed, the Pearson goodness-of-fit measure does not show statistical significance. This is expected as traffic volume is only one of the many factors contributing to the overall crash experience, and that the SPFs are to be applied in conjunction with Accident Modification Factors (AMFs) to further account for the safety impacts of major geometric features before arriving at the final crash prediction. However, with improved traffic and crash data quality, the crash prediction power of SPF models may be further improved.

Multiple Testing With an Empirical Alternative Hypothesis

An optimal multiple testing procedure is identified for linear hypotheses under the general linear model, maximizing the expected number of false null hypotheses rejected at any significance level. The optimal procedure depends on the unknown data-generating distribution, but can be consistently estimated. Drawing information together across many hypotheses, the estimated optimal procedure provides an empirical alternative hypothesis by adapting to underlying patterns of departure from the null. Proposed multiple testing procedures based on the empirical alternative are evaluated through simulations and an application to gene expression microarray data. Compared to a standard multiple testing procedure, it is not unusual for use of an empirical alternative hypothesis to increase by 50% or more the number of true positives identified at a given significance level.

Spatial distribution and socioeconomic context of tuberculosis in Rio de Janeiro, Brazil

OBJECTIVE To analyze the spatial distribution of risk for tuberculosis and its socioeconomic determinants in the city of Rio de Janeiro, Brazil.METHODS An ecological study on the association between the mean incidence rate of tuberculosis from 2004 to 2006 and socioeconomic indicators of the Censo Demográfico (Demographic Census) of 2000. The unit of analysis was the home district registered in the Sistema de Informação de Agravos de Notificação (Notifiable Diseases Information System) of Rio de Janeiro, Southeastern Brazil. The rates were standardized by sex and age group, and smoothed by the empirical Bayes method. Spatial autocorrelation was evaluated by Moran’s I. Multiple linear regression models were studied and the appropriateness of incorporating the spatial component in modeling was evaluated.RESULTS We observed a higher risk of the disease in some neighborhoods of the port and north regions, as well as a high incidence in the slums of Rocinha and Vidigal, in the south region, and Cidade de Deus, in the west. The final model identified a positive association for the variables: percentage of permanent private households in which the head of the house earns three to five minimum wages; percentage of individual residents in the neighborhood; and percentage of people living in homes with more than two people per bedroom.CONCLUSIONS The spatial analysis identified areas of risk of tuberculosis incidence in the neighborhoods of the city of Rio de Janeiro and also found spatial dependence for the incidence of tuberculosis and some socioeconomic variables. However, the inclusion of the space component in the final model was not required during the modeling process.

Spatial analysis of avoidable hospitalizations due to tuberculosis in Ribeirao Preto, SP, Brazil (2006-2012)

ABSTRACT OBJECTIVE To describe the spatial distribution of avoidable hospitalizations due to tuberculosis in the municipality of Ribeirao Preto, SP, Brazil, and to identify spatial and space-time clusters for the risk of occurrence of these events. METHODS This is a descriptive, ecological study that considered the hospitalizations records of the Hospital Information System of residents of Ribeirao Preto, SP, Southeastern Brazil, from 2006 to 2012. Only the cases with recorded addresses were considered for the spatial analyses, and they were also geocoded. We resorted to Kernel density estimation to identify the densest areas, local empirical Bayes rate as the method for smoothing the incidence rates of hospital admissions, and scan statistic for identifying clusters of risk. Softwares ArcGis 10.2, TerraView 4.2.2, and SaTScanTM were used in the analysis. RESULTS We identified 169 hospitalizations due to tuberculosis. Most were of men (n = 134; 79.2%), averagely aged 48 years (SD = 16.2). The predominant clinical form was the pulmonary one, which was confirmed through a microscopic examination of expectorated sputum (n = 66; 39.0%). We geocoded 159 cases (94.0%). We observed a non-random spatial distribution of avoidable hospitalizations due to tuberculosis concentrated in the northern and western regions of the municipality. Through the scan statistic, three spatial clusters for risk of hospitalizations due to tuberculosis were identified, one of them in the northern region of the municipality (relative risk [RR] = 3.4; 95%CI 2.7–4,4); the second in the central region, where there is a prison unit (RR = 28.6; 95%CI 22.4–36.6); and the last one in the southern region, and area of protection for hospitalizations (RR = 0.2; 95%CI 0.2–0.3). We did not identify any space-time clusters. CONCLUSIONS The investigation showed priority areas for the control and surveillance of tuberculosis, as well as the profile of the affected population, which shows important aspects to be considered in terms of management and organization of health care services targeting effectiveness in primary health care.

Drugs Associated with Hepatotoxicity and their Reporting Frequency of Liver Adverse Events in VigiBase (TM) Unified List Based on International Collaborative Work

BACKGROUND Challenges exist in the clinical diagnosis of drug-induced liver injury (DILI) and in obtaining information on hepatotoxicity in humans. OBJECTIVE (i) To develop a unified list that combines drugs incriminated in well vetted or adjudicated DILI cases from many recognized sources and drugs that have been subjected to serious regulatory actions due to hepatotoxicity; and (ii) to supplement the drug list with data on reporting frequencies of liver events in the WHO individual case safety report database (VigiBase). DATA SOURCES AND EXTRACTION (i) Drugs identified as causes of DILI at three major DILI registries; (ii) drugs identified as causes of drug-induced acute liver failure (ALF) in six different data sources, including major ALF registries and previously published ALF studies; and (iii) drugs identified as being subjected to serious governmental regulatory actions due to their hepatotoxicity in Europe or the US were collected. The reporting frequency of adverse events was determined using VigiBase, computed as Empirical Bayes Geometric Mean (EBGM) with 90% confidence interval for two customized terms, 'overall liver injury' and 'ALF'. EBGM of >or=2 was considered a disproportional increase in reporting frequency. The identified drugs were then characterized in terms of regional divergence, published case reports, serious regulatory actions, and reporting frequency of 'overall liver injury' and 'ALF' calculated from VigiBase. DATA SYNTHESIS After excluding herbs, supplements and alternative medicines, a total of 385 individual drugs were identified; 319 drugs were identified in the three DILI registries, 107 from the six ALF registries (or studies) and 47 drugs that were subjected to suspension or withdrawal in the US or Europe due to their hepatotoxicity. The identified drugs varied significantly between Spain, the US and Sweden. Of the 319 drugs identified in the DILI registries of adjudicated cases, 93.4% were found in published case reports, 1.9% were suspended or withdrawn due to hepatotoxicity and 25.7% were also identified in the ALF registries/studies. In VigiBase, 30.4% of the 319 drugs were associated with disproportionally higher reporting frequency of 'overall liver injury' and 83.1% were associated with at least one reported case of ALF. CONCLUSIONS This newly developed list of drugs associated with hepatotoxicity and the multifaceted analysis on hepatotoxicity will aid in causality assessment and clinical diagnosis of DILI and will provide a basis for further characterization of hepatotoxicity.

Safety Effectiveness of High-Speed Expressway Signals, 2005

The safety benefit of signalizing intersections of high-speed divided expressways is considered. Analyses were conducted on 50 and 55 mph and on 55 mph only intersections, comparing unsignalized and signalized intersections. Results of the 55 mph analysis are included in this report. Matched-pair analysis indicates that generally, signalized intersections have higher crash rate but lower costs per crash. On the other hand, before-and-after analysis (intersections signalized between 1994 and 2001) indicates lower crash rates (~30 percent) and total costs (~10 percent) after signalization. Empirical Bayes (EB) adjusted before-and-after analysis reduces estimates of safety benefit (crash rate) to about 20 percent. The study shows how commonly used analyses can differ in their results, and that there is great variability in the safety performance of individual signalized locations. This variability and the effect of EB adjustment are demonstrated through the use of innovative graphics.

A Transportation Safety Planning Tool for the City of Ames, August 2011

The historically-reactive approach to identifying safety problems and mitigating them involves selecting black spots or hot spots by ranking locations based on crash frequency and severity. The approach focuses mainly on the corridor level without taking the exposure rate (vehicle miles traveled) and socio-demographics information of the study area, which are very important in the transportation planning process, into consideration. A larger study analysis unit at the Transportation Analysis Zone (TAZ) level or the network planning level should be used to address the needs of development of the community in the future and incorporate safety into the long-range transportation planning process. In this study, existing planning tools (such as the PLANSAFE models presented in NCHRP Report 546) were evaluated for forecasting safety in small and medium-sized communities, particularly as related to changes in socio-demographics characteristics, traffic demand, road network, and countermeasures. The research also evaluated the applicability of the Empirical Bayes (EB) method to network-level analysis. In addition, application of the United States Road Assessment Program (usRAP) protocols at the local urban road network level was investigated. This research evaluated the applicability of these three methods for the City of Ames, Iowa. The outcome of this research is a systematic process and framework for considering road safety issues explicitly in the small and medium-sized community transportation planning process and for quantifying the safety impacts of new developments and policy programs. More specifically, quantitative safety may be incorporated into the planning process, through effective visualization and increased awareness of safety issues (usRAP), the identification of high-risk locations with potential for improvement, (usRAP maps and EB), countermeasures for high-risk locations (EB before and after study and PLANSAFE), and socio-economic and demographic induced changes at the planning-level (PLANSAFE).

Safety and Mobility Impacts of Winter Weather --Phase 3, SPR RB01-012, 2014

Highway agencies spend millions of dollars to ensure safe and efficient winter travel. However, the effectiveness of winter-weather maintenance practices on safety and mobility are somewhat difficult to quantify. Safety and Mobility Impacts of Winter Weather - Phase 1 investigated opportunities for improving traffic safety on state-maintained roads in Iowa during winter-weather conditions. In Phase 2, three Iowa Department of Transportation (DOT) high-priority sites were evaluated and realistic maintenance and operations mitigation strategies were also identified. In this project, site prioritization techniques for identifying roadway segments with the potential for safety improvements related to winter-weather crashes, were developed through traditional naïve statistical methods by using raw crash data for seven winter seasons and previously developed metrics. Additionally, crash frequency models were developed using integrated crash data for four winter seasons, with the objective of identifying factors that affect crash frequency during winter seasons and screening roadway segments using the empirical Bayes technique. Based on these prioritization techniques, 11 sites were identified and analyzed in conjunction with input from Iowa DOT district maintenance managers and snowplow operators and the Iowa DOT Road Weather Information System (RWIS) coordinator.

Predição em modelos de tempo de falha acelerado com efeito aleatório para avaliação de riscos de falha em poços petrolíferos

We considered prediction techniques based on models of accelerated failure time with random e ects for correlated survival data. Besides the bayesian approach through empirical Bayes estimator, we also discussed about the use of a classical predictor, the Empirical Best Linear Unbiased Predictor (EBLUP). In order to illustrate the use of these predictors, we considered applications on a real data set coming from the oil industry. More speci - cally, the data set involves the mean time between failure of petroleum-well equipments of the Bacia Potiguar. The goal of this study is to predict the risk/probability of failure in order to help a preventive maintenance program. The results show that both methods are suitable to predict future failures, providing good decisions in relation to employment and economy of resources for preventive maintenance.

Propriedades e aspectos geométricos de estimadores tipo James-Stein e do estimador de Hartigan

The James-Stein estimator is a biased shrinkage estimator with uniformly smaller risk than the risk of the sample mean estimator for the mean of multivariate normal distribution, except in the one-dimensional or two-dimensional cases. In this work we have used more heuristic arguments and intensified the geometric treatment of the theory of James-Stein estimator. New type James-Stein shrinking estimators are proposed and the Mahalanobis metric used to address the James-Stein estimator. . To evaluate the performance of the estimator proposed, in relation to the sample mean estimator, we used the computer simulation by the Monte Carlo method by calculating the mean square error. The result indicates that the new estimator has better performance relative to the sample mean estimator.

The Optimal Confidence Region for a Random Parameter

Under a two-level hierarchical model, suppose that the distribution of the random parameter is known or can be estimated well. Data are generated via a fixed, but unobservable realization of this parameter. In this paper, we derive the smallest confidence region of the random parameter under a joint Bayesian/frequentist paradigm. On average this optimal region can be much smaller than the corresponding Bayesian highest posterior density region. The new estimation procedure is appealing when one deals with data generated under a highly parallel structure, for example, data from a trial with a large number of clinical centers involved or genome-wide gene-expession data for estimating individual gene- or center-specific parameters simultaneously. The new proposal is illustrated with a typical microarray data set and its performance is examined via a small simulation study.