Empirical Bayesian Methods Research Articles

Polymorphic variability in the exon 19 of the RB1 gene and its flanking intronic sequences in HPV16-associated precancerous lesions in the Greek population.

The tumour suppressor protein RB plays a decisive role in negative control of the cell cycle, inhibiting tumour development. The present analysis investigated the prevalence of the nucleotide polymorphism A153104G, which is located at intron 18 of the RB1 gene, and investigated the impact of the polymorphic variability in the exon 19 and its flanking intronic sequences on the severity of cervical disease in HPV16-positive Greek women. The nucleotide polymorphism A153104G was detected by PCR-RFLP assay, while the amplicons were further subjected to cloning and sequencing. Moreover, molecular evolutionary analysis was performed using the maximum-likelihood (ML) and empirical Bayesian (EB) methods in order to evaluate the selective pressure acting on exon 19 of the RB1 gene.Results/Key findings. The A153104G nucleotide polymorphism was only detected in one control case. Moreover, sequence analysis of the amplicons revealed that the polymorphic variability in the RB1 gene increased with the severity of the cervical dysplasia. The link between the observed polymorphic variability and the progress of cervical disease was reflected in the molecular evolutionary analysis that was performed on the exon 19 of the RB1 gene, since negative selective pressure was acting upon exon 19 in the control and low-grade squamous intraepithelial lesion (LSIL) cervical samples, while positive selective pressure was acting upon exon 19 in the high-grade squamous intraepithelial lesion (HSIL) specimens. The A153104G nucleotide polymorphism did not emerge as a potential biomarker for the development of precancerous lesions in the Greek patients, while the accumulation of sequence variations in RB1 gene might influence patients' susceptibility towards the progression of cervical neoplasia.

Patch-based survey methods for studying prehistoric human land-use in agriculturally modified landscapes: A case study from the Canal de Navarrés, eastern Spain

In landscapes whose surface has been modified by terracing and other agricultural land-use, the spatial and temporal patterning of prehistoric settlement can be difficult to detect using traditional, site-orientated archaeological survey methods, especially for small-scale societies. In these contexts, methods that can reveal occupational patterns at landscape scales, without the need to pinpoint specific sites of human occupation, can be especially useful. We employ a stratified, randomly selected patch-based survey strategy to examine socio-ecological dynamics from the Middle Paleolithic through Bell Beaker (Chalcolithic) periods within the Canal de Navarrés, eastern Spain. We divide the study region into survey strata according to differences in topography and vegetation communities and use a random selection of demarcated, terraced fields as data collection patches. All survey data is digitally recorded using tablets in the field, creating a streamlined and more accurate workflow, where observations of artifacts, soils, ground visibility, and photographs are georeferenced and ready for analysis in a GIS. Surface artifact densities, estimated from sampled patches, are used to generate prehistoric land-use maps and empirical Bayesian methods allow us to track shifts in occupational patterns through time. Regional reference collections of well-dated lithic artifacts provide the “prior knowledge” required to make estimates of the probability of prehistoric occupation in each sampled patch. This combination of field and analytical methods makes possible the study of regional-scale land-use dynamics in agriculturally modified landscapes.

Estimating the safety impacts in before–after studies using the Naïve Adjustment Method

ABSTRACTThe before–after study is the most popular approach for estimating the safety impacts of an intervention or treatment. Recent research, however, has shown that the most common before–after approaches can still provide a biased estimate when an entry criterion is used and when the characteristics of the treatment and control groups are dissimilar. Recently, a new simple method, referred to as the Naïve Adjustment Method (NAM), has been proposed to mitigate the limitations identified above. Unfortunately, the effectiveness of the NAM using ‘real’ data has not yet been properly investigated. Hence, this paper examined the accuracy of the NAM when the treatment group contains sites that have different mean values. Simulated and two observed datasets were used. The results show that the NAM outperforms the Naïve, the Control Group, and the empirical Bayesian methods. Furthermore, it can be used as a simpler alternative for adjusting the Naïve estimators documented in previous studies.

Effects of mergers on corporate performance: An empirical evaluation using OLS and the empirical Bayesian methods

In this paper, we empirically examine the impact of mergers on corporate financial performance in Pakistan using data on the deals occurred during the period 1995–2012. Ordinary least squares (OLS) and empirical Bayesian estimation methods are applied to carry out empirical analysis. The OLS regression results suggest that the merger deals do not have any significant impact on the profitability, liquidity, and leverage position of the firms. However, the estimates indicate that the merger deals have a negative and statistically significant impact on quick ratio of merged/acquirer firms. We show that the results of the empirical Bayesian method are largely consistent with the OLS results.

Generalized empirical Bayesian methods for discovery of differential data in high-throughput biology.

High-throughput data are now commonplace in biological research. Rapidly changing technologies and application mean that novel methods for detecting differential behaviour that account for a 'large P, small n' setting are required at an increasing rate. The development of such methods is, in general, being done on an ad hoc basis, requiring further development cycles and a lack of standardization between analyses. We present here a generalized method for identifying differential behaviour within high-throughput biological data through empirical Bayesian methods. This approach is based on our baySeq algorithm for identification of differential expression in RNA-seq data based on a negative binomial distribution, and in paired data based on a beta-binomial distribution. Here we show how the same empirical Bayesian approach can be applied to any parametric distribution, removing the need for lengthy development of novel methods for differently distributed data. Comparisons with existing methods developed to address specific problems in high-throughput biological data show that these generic methods can achieve equivalent or better performance. A number of enhancements to the basic algorithm are also presented to increase flexibility and reduce computational costs. The methods are implemented in the R baySeq (v2) package, available on Bioconductor http://www.bioconductor.org/packages/release/bioc/html/baySeq.html. tjh48@cam.ac.uk Supplementary data are available at Bioinformatics online.

Preparation for global introduction of inactivated poliovirus vaccine: safety evidence from the US Vaccine Adverse Event Reporting System, 2000–12

Safety data from countries with experience in the use of inactivated poliovirus vaccine (IPV) are important for the global polio eradication strategy to introduce IPV into the immunisation schedules of all countries. In the USA, IPV has been included in the routine immunisation schedule since 1997. We aimed to analyse adverse events after IPV administration reported to the US Vaccine Adverse Event Reporting System (VAERS). We analysed all VAERS data associated with IPV submitted between Jan 1, 2000, and Dec 31, 2012, either as individual or as combination vaccines, for all age and sex groups. We analysed the number and event type (non-serious, non-fatal serious, and death reports) of individual reports, and explored the most commonly coded event terms to describe the adverse event. We classified death reports according to previously published body-system categories (respiratory, cardiovascular, neurological, gastrointestinal, other infectious, and other non-infectious) and reviewed death reports to identify the cause of death. We classified sudden infant death syndrome as a separate cause of death considering previous concerns about sudden infant syndrome after vaccines. We used empirical Bayesian data mining methods to identify disproportionate reporting of adverse events for IPV compared with other vaccines. Additional VAERS data from 1991 to 2000 were analysed to compare the safety profiles of IPV and oral poliovirus vaccine (OPV). Of the 41,792 adverse event reports submitted, 39,568 (95%) were for children younger than 7 years. 38,381 of the reports for children in this age group (97%) were for simultaneous vaccination with IPV and other vaccines (most commonly pneumococcal and acellular pertussis vaccines), whereas standalone IPV vaccines accounted for 0·5% of all reports. 34,880 reports were for non-serious events (88%), 3905 reports were for non-fatal serious events (10%), and 783 reports were death reports (2%). Injection-site erythema was the most commonly coded term for non-serious events (29%), and pyrexia for non-fatal serious events (38%). Most deaths (96%) were in children aged 12 months or younger; most (52%) had sudden infant death syndrome as the reported cause of death. The safely profiles of combined IPV and whole-cell pertussis vaccines, OPV and whole-cell pertussis vaccines, and OPV and acellular pertussis vaccines were similar. We noted no indication of disproportionate reporting of adverse events after immunisation with IPV-containing vaccines compared with other vaccines between 1990 and 2013. Fairly few adverse events were reported for the more than 250 million IPV doses distributed between 2000 and 2012. Sudden infant death syndrome reports after IPV were consistent with reporting patterns for other vaccines. No new or unexpected vaccine safety problems were identified for fatal, non-fatal serious, and non-serious reports in this assessment of adverse events after IPV. None.

Signal detection in FDA AERS database using Dirichlet process.

In the recent two decades, data mining methods for signal detection have been developed for drug safety surveillance, using large post-market safety data. Several of these methods assume that the number of reports for each drug-adverse event combination is a Poisson random variable with mean proportional to the unknown reporting rate of the drug-adverse event pair. Here, a Bayesian method based on the Poisson-Dirichlet process (DP) model is proposed for signal detection from large databases, such as the Food and Drug Administration's Adverse Event Reporting System (AERS) database. Instead of using a parametric distribution as a common prior for the reporting rates, as is the case with existing Bayesian or empirical Bayesian methods, a nonparametric prior, namely, the DP, is used. The precision parameter and the baseline distribution of the DP, which characterize the process, are modeled hierarchically. The performance of the Poisson-DP model is compared with some other models, through an intensive simulation study using a Bayesian model selection and frequentist performance characteristics such as type-I error, false discovery rate, sensitivity, and power. For illustration, the proposed model and its extension to address a large amount of zero counts are used to analyze statin drugs for signals using the 2006-2011 AERS data.

Full Bayesian evaluation of the safety effects of reducing the posted speed limit in urban residential area

Full Bayesian (FB) before–after evaluation is a newer approach than the empirical Bayesian (EB) evaluation in traffic safety research. While a number of earlier studies have conducted univariate and multivariate FB before–after safety evaluations and compared the results with the EB method, often contradictory conclusions have been drawn. To this end, the objectives of the current study were to (i) perform a before–after safety evaluation using both the univariate and multivariate FB methods in order to enhance our understanding of these methodologies, (ii) perform the EB evaluation and compare the results with those of the FB methods and (iii) apply the FB and EB methods to evaluate the safety effects of reducing the urban residential posted speed limit (PSL) for policy recommendation. In addition to three years of crash data for both the before and after periods, traffic volume, road geometry and other relevant data for both the treated and reference sites were collected and used. According to the model goodness-of-fit criteria, the current study found that the multivariate FB model for crash severities outperformed the univariate FB models. Moreover, in terms of statistical significance of the safety effects, the EB and FB methods led to opposite conclusions when the safety effects were relatively small with high standard deviation. Therefore, caution should be taken in drawing conclusions from the EB method. Based on the FB method, the PSL reduction was found effective in reducing crashes of all severities and thus is recommended for improving safety on urban residential collector roads.

Effect of reporting bias in the analysis of spontaneous reporting data.

It is well-known that a spontaneous reporting system suffers from significant under-reporting of adverse drug reactions from the source population. The existing methods do not adjust for such under-reporting for the calculation of measures of association between a drug and the adverse drug reaction under study. Often there is direct and/or indirect information on the reporting probabilities. This work incorporates the reporting probabilities into existing methodologies, specifically to Bayesian confidence propagation neural network and DuMouchel's empirical Bayesian methods, and shows how the two methods lead to biased results in the presence of under-reporting. Considering all the cases to be reported, the association measure for the source population can be estimated by using only exposure information through a reference sample from the source population.

A note on hotspot identification for urban expressways

Hotspot identification (HSID) is of great importance to land transport authorities (e.g. the Land Transport Authority (LTA) of Singapore) in their efforts to improve the safety of highways. According to a survey of experienced engineers at the LTA of Singapore, we draw the conclusion that the severity of crashes should not be neglected in the HSID process. Accordingly, in this technical note, societal risk-based simple ranking and empirical Bayesian methods are proposed to identify the hotspots in a Singapore expressway on the basis of the detailed three-year casualty data in the Historical Crash Damage (HCD) database. We further conduct a consistency analysis to compare the societal risk-based method and the conventional frequency-based method. The consistency analysis reports that (1) the frequency-based method is more consistent than the societal risk-based method, and (2) the empirical Bayesian method is more consistent than the simple ranking method.

SPATIAL DISTRIBUTION OF NEW CASES OF TUBERCULOSIS IN THE STATE OF RIO GRANDE DO NORTE, BRAZIL.

This study presents the results of an ecological analysis of the spatial distribution of 4,739 new cases of tuberculosis in Rio Grande do Norte, Brazil, between 2006 and 2010. Global and Local empirical Bayesian methods were used in the analysis. Tuberculosis was found to be homogenously distributed and present at low incidence; additionally, incidence was underestimated in 17.96% of the municipalities.

Comparison of Sichel and Negative Binomial Models in Hot Spot Identification

Identification of crash hot spots is the critical component of the highway safety management process. Errors in hot spot identification (HSID) may result in the inefficient use of resources for safety improvements. One HSID method that is based on the empirical Bayesian (EB) method has been widely used as an effective approach for identifying crash-prone sites. For the EB method, the negative binomial (NB) model is usually needed to obtain the EB estimates. Recently, some studies have shown that the Sichel (SI) model can be easily used in the EB modeling framework and potentially yield better EB estimates. The objective of this study was to compare the performance of the two crash prediction (SI and NB) models in identifying hot spots with the EB method. To accomplish the objective of this study, empirical crash data collected at highway segments in Texas were used to generate simulated crash counts. Three commonly used HSID methods (simple ranking, confidence interval, and EB) were applied with the use of simulated data. False positives, false negatives, and false identifications were calculated and compared across the methods. The simulation results in this study suggested that the SI-based EB method could consistently provide a better HSID result than the NB-based EB method. Moreover, EB methods yielded the lowest error percentage of the three HSID methods. This study confirmed that the EB technique was an effective method for identifying hazardous sites. On the basis of the findings in this study, it is recommended that transportation safety researchers consider the SI model as an alternative crash prediction model when the EB approach is used.

Safety Effect of Missouri's Strategic Highway Safety Plan

This study systematically evaluated the changes in motor vehicle crashes that occurred on the Missouri Interstate highway system following the implementation of the Missouri Strategic Highway Safety Plan (MSHSP) between 2004 and 2007. The MSHSP implemented crash injury reduction strategies in enforcement, education, engineering, and public policy. Empirical Bayesian methods were commonly used to evaluate the effects of any change in safety as a result of countermeasures. This paper presents a simple new approach to evaluating the effects of Missouri's safety plans on roadway crashes. For crash data associated with traffic and roadway characteristics, negative binomial regression models were developed for the before-through-change conditions using a variable that was set to zero for preimplementation years and gradually increased over the implementation years to reach a plateau at the conclusion of the safety plans. The models developed for the various collision types and crash severities were used to estimate the expected number of crashes at roadway segments in 2008, assuming with and without the implementation of MSHSP. This procedure estimated significant reductions of 10% in the overall number of crashes and a 30% reduction for fatal crashes. Reductions in the number of collision types were estimated to be 18% to 37%. The theoretical results indicated that the MSHSP was a successful policy in reducing the number of crashes and decreasing fatalities by reducing the most severe collision types such as head-on crashes. The results are also consistent with many international studies and suggested that the safety strategic plans should be promoted as an effective treatment for highways.

Bayesian Estimation Dating of Lithic Surface Collections

Surface assemblages represent the most accessible, representative sample of the archaeological record for the study of human socio-ecological systems at regional scales. However, the difficulty in developing suitable chronological frameworks from surface assemblages has limited their use. Additionally, surface scatters are composed of artifacts that can accumulate across multiple occupational episodes. A challenge to chronology building in such surface contexts is the necessity to assess the probability of occupation during each time period. We describe a new method of dating surface lithic assemblages using empirical Bayesian methods, with an example from northeastern Spain. We use Bayesian methods to estimate the probability of occupation during 11 temporal periods (ca. 13,000–4,200 cal BP) for a sample of 25 lithic surface assemblages. A Bayesian approach allows us to combine prior knowledge, with different degrees of uncertainty, about the temporal sensitivity of projectile forms statistically derived from a regional calibration data set of 35 dated assemblages to estimate the age of each surface collections probabilistically. This approach provides new insight into the settlement history of the Maestrat in the first half of the Holocene, during the transition from foraging to food production, and offers a powerful tool to archaeologists for the dating of surface collections.

Estimation of stationary autoregressive models with the Bayesian LASSO

This article explores the problem of estimating stationary autoregressive models from observed data using the Bayesian least absolute shrinkage and selection operator (LASSO). By characterizing the model in terms of partial autocorrelations, rather than coefficients, it becomes straightforward to guarantee that the estimated models are stationary. The form of the negative log‐likelihood is exploited to derive simple expressions for the conditional likelihood functions, leading to efficient algorithms for computing the posterior mode by coordinate‐wise descent and exploring the posterior distribution by Gibbs sampling. Both empirical Bayes and Bayesian methods are proposed for the estimation of the LASSO hyper‐parameter from the data. Simulations demonstrate that the Bayesian LASSO performs well in terms of prediction when compared with a standard autoregressive order selection method.

Estimation of stationary autoregressive models with the Bayesian LASSO

This article explores the problem of estimating stationary autoregressive models from observed data using the Bayesian least absolute shrinkage and selection operator (LASSO). By characterizing the model in terms of partial autocorrelations, rather than coefficients, it becomes straightforward to guarantee that the estimated models are stationary. The form of the negative log-likelihood is exploited to derive simple expressions for the conditional likelihood functions, leading to efficient algorithms for computing the posterior mode by coordinate-wise descent and exploring the posterior distribution by Gibbs sampling. Both empirical Bayes and Bayesian methods are proposed for the estimation of the LASSO hyper-parameter from the data. Simulations demonstrate that the Bayesian LASSO performs well in terms of prediction when compared with a standard autoregressive order selection method.

Constrained Bayes and Empirical Bayes Estimator Applications in Insurance Pricing

Bayesian and empirical Bayesian methods have become quite popular in the theory and practice of statistics. However, the objective is to often produce an ensemble of parameter estimates as well as to produce the histogram of the estimates. For example, in insurance pricing, the accurate point estimates of risk for each group is necessary and also proper dispersion estimation should be considered. Well-known Bayes estimates (which is the posterior means under quadratic loss) are underdispersed as an estimate of the histogram of parameters. The adjustment of Bayes estimates to correct this problem is known as constrained Bayes estimators, which are matching the first two empirical moments. In this paper, we propose a way to apply the constrained Bayes estimators in insurance pricing, which is required to estimate accurately both location and dispersion. Also, the benefit of the constrained Bayes estimates will be discussed by analyzing real insurance accident data.

Estimation of the stress–strength reliability for the generalized logistic distribution

Ragab [A. Ragab, Estimation and predictive density for the generalized logistic distribution, Microelectronics and Reliability 31 (1991) 91–95] described the Bayesian and empirical Bayesian methods for estimation of the stress–strength parameter R=P(Y<X), when X and Y are independent random variables from two generalized logistic (GL) distributions having the same known scale but different shape parameters. In this current paper, we consider the estimation of R, when X and Y are both two-parameter GL distribution with the same unknown scale but different shape parameters or with the same unknown shape but different scale parameters. We also consider the general case when the shape and scale parameters are different. The maximum likelihood estimator of R and its asymptotic distribution are obtained and it is used to construct the asymptotic confidence interval of R. We also implement Gibbs and Metropolis samplings to provide a sample-based estimate of R and its associated credible interval. Finally, analyzes of real data set and Monte Carlo simulation are presented for illustrative purposes.

Detection of site-specific positive Darwinian selection on pandemic influenza A/H1N1 virus genome: integrative approaches

In the twenty-first century, the first pandemic novel human influenza A/H1N1virus (NIV) outbreak was reported at Mexico and USA on March and early April, 2009 respectively. The outbreak occurred among human populations due to the presence of meager or no immune response against newly emerged viruses. The success of vaccines and drugs depends on their low susceptibility to the formation of escape mutants in virus. Identification of excess, non-synonymous substitutions over synonymous ones is a main indicator of positive Darwinian selection in protein-coding genes of NIVs. The positive Darwinian selection operating on each site of proteins were inferred by computing ω, the ratio of the non-synonymous/synonymous substitutions [dN/dS (or) Ka/Ks], which was calculated by three different methods in terms of codon-based maximum likelihood, branch-site and empirical Bayesian methods under various models. Totally, nine sites from PB2, PB1, HA, M2 and NS1 are inferred as positively selected. The function for amino acid sites of NIVs proteins under positive selection are inferred by comparing the sites with experimentally determined functionally known amino acid sites. Completely 4 positively selected sites of PB1, HA and M2 are found to be involved in B-cell epitopes (BCEs). Interestingly, most of these sites are also involving in T-cell epitopes (TCEs). However, more sites under positive selection forces are involved in TCEs than those of BCEs. Amino acid sites engaged in both BCEs and TCEs should be measured as highly suitable targets, because these sites could induce the strong humoral and cellular immune responses against targets.

EBSeq: an empirical Bayes hierarchical model for inference in RNA-seq experiments

Messenger RNA expression is important in normal development and differentiation, as well as in manifestation of disease. RNA-seq experiments allow for the identification of differentially expressed (DE) genes and their corresponding isoforms on a genome-wide scale. However, statistical methods are required to ensure that accurate identifications are made. A number of methods exist for identifying DE genes, but far fewer are available for identifying DE isoforms. When isoform DE is of interest, investigators often apply gene-level (count-based) methods directly to estimates of isoform counts. Doing so is not recommended. In short, estimating isoform expression is relatively straightforward for some groups of isoforms, but more challenging for others. This results in estimation uncertainty that varies across isoform groups. Count-based methods were not designed to accommodate this varying uncertainty, and consequently, application of them for isoform inference results in reduced power for some classes of isoforms and increased false discoveries for others. Taking advantage of the merits of empirical Bayesian methods, we have developed EBSeq for identifying DE isoforms in an RNA-seq experiment comparing two or more biological conditions. Results demonstrate substantially improved power and performance of EBSeq for identifying DE isoforms. EBSeq also proves to be a robust approach for identifying DE genes. An R package containing examples and sample datasets is available at http://www.biostat.wisc.edu/kendzior/EBSEQ/. Supplementary data are available at Bioinformatics online.