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Estimating and Adjusting for Publication Bias Using Data Augmentation in Bayesian MetaAnalysis
, 1995
"... We introduce a Bayesian approach which estimates and adjusts for selection bias in a set of studies used in a metaanalysis. We use a hierarchical model for study outcome, and propose an additional model component to account for publication bias, which is the possibility that studies of interest are ..."
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We introduce a Bayesian approach which estimates and adjusts for selection bias in a set of studies used in a metaanalysis. We use a hierarchical model for study outcome, and propose an additional model component to account for publication bias, which is the possibility that studies of interest are not equally likely to be published and hence observed studies are not a random sample. Estimation is based on the data augmentation principle and the number and outcomes of unobserved studies are simulated using Gibbs sampling methods. After examining simulation performance, we apply our techniques to a metaanalysis of 35 studies of the relationship between lung cancer and spousal exposure to environmental tobacco smoke. We find that the 95% posterior probability interval for relative risk is shifted downward after allowing for this. These results are consistent with earlier, ad hoc, approaches to this problem. Keywords and phrases: Metaanalysis, publication bias, missing studies, Markov...
Comparing Survival Data For Two Therapies: Nonhierarchical And Hierarchical Bayesian Approaches
, 1994
"... The problem of comparing two therapies with survival data is considered from a Bayesian point of view. Survival times on each therapy are assumed to have an exponential distribution. The posterior distribution of the log hazard ratio of the experimental therapy to the standard therapy is the basis o ..."
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The problem of comparing two therapies with survival data is considered from a Bayesian point of view. Survival times on each therapy are assumed to have an exponential distribution. The posterior distribution of the log hazard ratio of the experimental therapy to the standard therapy is the basis of inference. Two models are proposed in this dissertation. The first assumes center homogeneity and the second uses a Bayesian hierarchical model for heterogeneity of therapy effects among different centers in...
Decision Models in Clinical Recommendations Development: the Stroke Prevention Policy Model
 in Bayesian Biostatistics
, 1996
"... The goal of this chapter is to give a general overview and a practical illustration of the role of Bayesian methods in large interdisciplinary studies for clinical recommendation development. These studies have a strongly decisionoriented nature, they draw from several sources of information, and t ..."
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The goal of this chapter is to give a general overview and a practical illustration of the role of Bayesian methods in large interdisciplinary studies for clinical recommendation development. These studies have a strongly decisionoriented nature, they draw from several sources of information, and they require a probabilistic assessment of the uncertainty of the answers. These are among the features that make them an ideal terrain for the application of Bayesian methods. The chapter consists of two parts. The first is a broad overview of issues, with pointers to some of the relevant literature. The second is an illustration in the context of the Stroke Prevention Policy Model, being developed by the Stroke Prevention Patient Outcome Research Team (PORT). We discuss in detail selected aspects of the study. We focus on: general goals and structure of the decision model; computing framework for predictive distributions of the outcomes of interest; combining information by simulation and r...
Assessing Sensitivity to Data Problems in Epidemiological Metaanalyses
"... this paper we restrict comment to the following specific issues, although there are many more to which similar approaches will apply: (i) the problem of comparability of data and study design, since for the metaanalysis to be meaningfully interpreted, we must not combine "apples and oranges"; (ii) ..."
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this paper we restrict comment to the following specific issues, although there are many more to which similar approaches will apply: (i) the problem of comparability of data and study design, since for the metaanalysis to be meaningfully interpreted, we must not combine "apples and oranges"; (ii) the effect of "publication bias", recognising that failure to obtain all relevant studies, both published and unpublished, may result in a quite distorted metaanalysis; (iii) the possible existence of systematic errors in individual studies, since these flow to bias in the overall analysis, and some account must be taken of them. Clearly all of these (and many other problems) are of concern in principle in any metaanalysis, but it is not obvious whether they will cause real problems in any one specific application. Our theme in this paper is that, by using sensitivity analyses based on the collection of real data and comparison of more and less sophisticated models, one can develop useful information on the extent and effect of such problems, rather than merely expressing concern about their existence. We shall see that for each of (i)(iii), we can develop approaches based on data which describe the best and worst case scenarios (and the intermediate ones also), and use these to quantify whether further steps must be taken to protect the metaanalysis from incorrect inferences. Although other measures of relationship are possible, in epidemiology it is common to consider the effect of the relationship to be measured by the relative risk (RR), given conceptually as the ratio
Model Discrimination in MetaAnalysis  A Bayesian Perspective
"... In wanting to summarise evidence from a number of studies a variety of statistical methods have been proposed. Of these the most widely used is the socalled fixed effect model in which the individual studies are estimating a single, but unknown, overall population effect. When there is `considerabl ..."
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In wanting to summarise evidence from a number of studies a variety of statistical methods have been proposed. Of these the most widely used is the socalled fixed effect model in which the individual studies are estimating a single, but unknown, overall population effect. When there is `considerable' heterogeneity, in terms of the effect sizes, between the studies the use of a random effect model has been advocated in which each individual study is assumed to be estimating its own, unknown, true effect. Discrimination between fixed and random effect models has been advocated by means of a Ø 2 test for heterogeneity, which it is accepted has low statistical power. Recent interest has been shown in the use of Bayes Factors as an alternative. The use of Bayes factors is illustrated using a number of previously published metaanalyses in which there are varying degrees of heterogeneity. It is shown how the use of Bayes Factors leads to a more intuitive assessment of the evidence in favo...
Permission and Disclaimer
 MRC Biostatistics Unit, Institute of Public Health
, 1996
"... and produce answers that are wrong, which is even worse. Please let us know of any successes or failures. Beware  Gibbs sampling can be dangerous!. BUGS c flcopyright MRC Biostatistics Unit 1995. ALL RIGHTS RESERVED. The support of the Economic and Social Research Council (UK) is gratefully ackno ..."
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and produce answers that are wrong, which is even worse. Please let us know of any successes or failures. Beware  Gibbs sampling can be dangerous!. BUGS c flcopyright MRC Biostatistics Unit 1995. ALL RIGHTS RESERVED. The support of the Economic and Social Research Council (UK) is gratefully acknowledged. The work was funded in part by ESRC (UK) Award Number H519 25 5023. 1 2 Contents 1 Introduction 5 1.1 What is BUGS? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 For what kind of problems is BUGS best suited? . . . . . . . . . . . . . . . . . . . . . 5 1.3 Markov Chain Monte Carlo (MCMC) techniques . . . . . . . . . . . . . . . . . . . . 5 1.4 A simple example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Hardware platforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Confidence Intervals in the OneWay Random Effects Model for MetaAnalytic Applications
, 1996
"... this paper we investigate interval estimation of both the mean and heterogeneity variance ..."
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this paper we investigate interval estimation of both the mean and heterogeneity variance
Hierarchical Bivariate Time Series Models: A Combined Analysis of the Effects of Particulate Matter on Morbidity and Mortality
"... In this paper we develop a hierarchical bivariate time series model to characterize the relationship between particulate matter less than 10 microns in aerodynamic diameter (P M10) and both mortality and hospital admissions for cardiovascular diseases. The model is applied to time series data on mor ..."
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In this paper we develop a hierarchical bivariate time series model to characterize the relationship between particulate matter less than 10 microns in aerodynamic diameter (P M10) and both mortality and hospital admissions for cardiovascular diseases. The model is applied to time series data on mortality and morbidity for 10 metropolitan areas in the United States from 1986 to 1993. We postulate that these time series should be related through a shared relationship with P M10. At the first stage of the hierarchy, we fit two seemingly unrelated Poisson regression models to produce cityspecific estimates of the log relative rates of mortality and morbidity associated with exposure to P M10 within each location. The sample covariance matrix of the estimated log relative rates is obtained using a novel generalized estimating equation approach that takes into account the correlation between the mortality and morbidity time series. At the second stage, we combine information across locations to estimate overall log relative rates of mortality and morbidity and variation of the rates across cities. Using the combined information across the 10 locations we find that a 10 µg/m3 increase in average P M10 at the current day and previous day is associated with a 0.26 % increase in mortality
Estimation of Bayes Factors in a Class of Hierarchical Random Effects Models using a Geometrically Ergodic MCMC Algorithm
"... We consider a Bayesian random effects model that is commonly used in metaanalysis, in which the random effects have a t distribution, with degrees of freedom parameter to be estimated. We develop a Markov chain Monte Carlo algorithm for estimating the posterior distribution in this model, and estab ..."
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We consider a Bayesian random effects model that is commonly used in metaanalysis, in which the random effects have a t distribution, with degrees of freedom parameter to be estimated. We develop a Markov chain Monte Carlo algorithm for estimating the posterior distribution in this model, and establish geometric convergence of the algorithm. The geometric convergence rate has important theoretical and practical ramifications. Indeed, it implies that, under standard second moment conditions, the ergodic averages used to estimate posterior quantities of interest satisfy central limit theorems. Moreover, it guarantees the consistency of a batch means estimate of the asymptotic variance in the CLT, which in turn allows for the construction of asymptotically valid standard errors. We show how our Markov chain can be used, in conjunction with an importance sampling method, to carry out an empirical Bayes approach for estimating the degrees of freedom parameter. To illustrate our methodology we consider a metaanalysis of studies that link intake of nonsteroidal antiinflammatory drugs to a reduction in colon cancer risk, in which some of the studies are outliers. To model the distribution of the study effects we consider the family of t distributions, as well as a family
MetaAnalysis of Candidate Gene Effects Using Bayesian Parametric and NonParametric Approaches
"... licenses/byncnd/3.0/). Reproduction is permitted for personal, noncommercial use, provided that the article is in whole, unmodified, and properly cited. Received: 2012.10.20; Accepted: 2012.12.16; Published: 2013.01.01 Candidate gene (CG) approaches provide a strategy for identification and charac ..."
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licenses/byncnd/3.0/). Reproduction is permitted for personal, noncommercial use, provided that the article is in whole, unmodified, and properly cited. Received: 2012.10.20; Accepted: 2012.12.16; Published: 2013.01.01 Candidate gene (CG) approaches provide a strategy for identification and characterization of major genes underlying complex phenotypes such as production traits and susceptibility to diseases, but the conclusions tend to be inconsistent across individual studies. Metaanalysis approaches can deal with these situations, e.g., by pooling effectsize estimates or combining P values from multiple studies. In this paper, we evaluated the performance of two types of statistical models, parametric and nonparametric, for metaanalysis of CG effects using simulated data. Both models estimated a “central ” effect size while taking into account heterogeneity over individual studies. The empirical distribution of studyspecific CG effects was multimodal. The parametric model assumed a normal distribution for the studyspecific CG effects whereas the nonparametric model relaxed this assumption by posing a more general distribution with a Dirichlet process prior (DPP). Results indicated that the metaanalysis approaches could reduce false positive or false negative rates by pooling strengths from multiple studies, as compared to individual