CiteULike: jyuh bayes

Empirical Bayes analysis of single nucleotide polymorphisms

Holger Schwender — 2008-03-07T17:32:07-00:00

BMC Bioinformatics, Vol. 9 (06 March 2008), 144.

Empirical Bayes models for multiple probe type microarrays at the probe level

Magnus Astrand — 2008-03-21T05:49:07-00:00

BMC Bioinformatics, Vol. 9 (20 March 2008), 156.

Bayesian semiparametric regression for longitudinal binary processes with missing data.

L Su — 2008-06-26T02:33:27-00:00

Statistics in medicine, Vol. 27, No. 17. (30 July 2008), pp. 3247-3268.

Longitudinal studies with binary repeated measures are widespread in biomedical research. Marginal regression approaches for balanced binary data are well developed, whereas for binary process data, where measurement times are irregular and may differ by individuals, likelihood-based methods for marginal regression analysis are less well developed. In this article, we develop a Bayesian regression model for analyzing longitudinal binary process data, with emphasis on dealing with missingness. We focus on the settings where data are missing at random (MAR), which require a correctly specified joint distribution for the repeated measures in order to draw valid likelihood-based inference about the marginal mean. To provide maximum flexibility, the proposed model specifies both the marginal mean and serial dependence structures using nonparametric smooth functions. Serial dependence is allowed to depend on the time lag between adjacent outcomes as well as other relevant covariates. Inference is fully Bayesian. Using simulations, we show that adequate modeling of the serial dependence structure is necessary for valid inference of the marginal mean when the binary process data are MAR. Longitudinal viral load data from the HIV Epidemiology Research Study are analyzed for illustration. Copyright (c) 2008 John Wiley & Sons, Ltd.

High dimensional multivariate mixed models for binary questionnaire data

Fieuws — 2006-07-24T03:25:28-00:00

Journal of the Royal Statistical Society: Series C (Applied Statistics), Vol. 55, No. 4. (August 2006), pp. 449-460.

SEPARATE AND JOINT ANALYSIS OF LONGITUDINAL AND SURVIVAL DATA

2008-06-23T04:16:26-00:00

PubH 7440 Introduction to Bayesian Analysis-Spring 2008

2008-06-23T03:49:11-00:00

Hierarchical and Joint Longitudinal and Survival Modeling Using WinBUGS

2008-06-23T01:02:52-00:00

Generalized conjugate priors for Bayesian analysis of risk and survival regressions.

S Greenland — 2008-06-22T11:58:17-00:00

Biometrics, Vol. 59, No. 1. (March 2003), pp. 92-99.

Conjugate priors for Bayesian analyses of relative risks can be quite restrictive, because their shape depends on their location. By introducing a separate location parameter, however, these priors generalize to allow modeling of a broad range of prior opinions, while still preserving the computational simplicity of conjugate analyses. The present article illustrates the resulting generalized conjugate analyses using examples from case-control studies of the association of residential wire codes and magnetic fields with childhood leukemia.

Incorporating model uncertainty in cost-effectiveness analysis: A Bayesian model averaging approach.

Miguel A Negrín — 2008-06-16T03:41:37-00:00

Journal of health economics (12 April 2008)

Recently, several authors have proposed the use of linear regression models in cost-effectiveness analysis. In this paper, by modelling costs and outcomes using patient and Health Centre covariates, we seek to identify the part of the cost or outcome difference that is not attributable to the treatment itself, but to the patients' condition or to characteristics of the Centres. Selection of the covariates to be included as predictors of effectiveness and cost is usually assumed by the researcher. This behaviour ignores the uncertainty associated with model selection and leads to underestimation of the uncertainty about quantities of interest. We propose the use of Bayesian model averaging as a mechanism to account for such uncertainty about the model. Data from a clinical trial are used to analyze the effect of incorporating model uncertainty, by comparing two highly active antiretroviral treatments applied to asymptomatic HIV patients. The joint posterior density of incremental effectiveness and cost and cost-effectiveness acceptability curves are proposed as decision-making measures.

A Bayesian approach to retransformation bias in transformed regression.

CA Stow — 2008-06-13T12:16:23-00:00

Ecology, Vol. 87, No. 6. (June 2006), pp. 1472-1477.

Ecological data analysis often involves fitting linear or nonlinear equations to data after transforming either the response variable, the right side of the equation, or both, so that the standard suite of regression assumptions are more closely met. However, inference is usually done in the natural metric and it is well known that retransforming back to the original metric provides a biased estimator for the mean of the response variable. For the normal linear model, fit under a log-transformation, correction factors are available to reduce this bias, but these factors may not be generally applicable to all model forms or other transformations. We demonstrate that this problem is handled in a straightforward manner using a Bayesian approach, which is general for linear and nonlinear models and other transformations and model error structures. The Bayesian framework provides a predictive distribution for the response variable so that inference can be made at the mean, or over the entire distribution to incorporate the predictive uncertainty.

Why clinicians are natural bayesians.

CJ Gill — 2008-06-09T15:52:22-00:00

BMJ (Clinical research ed.), Vol. 330, No. 7499. (7 May 2005), pp. 1080-1083.

Use of Bayesian statistical approach in diagnosing secondary hypertension.

LJ Krzych — 2008-06-09T15:51:49-00:00

Polskie archiwum medycyny wewnȩtrznej, Vol. 118, No. 3. (March 2008), pp. 132-142.

Bayes's theorem is predominantly used in diagnosing based on the results of various diagnostic tests. This statistical approach is intuitive in differential diagnosis as it explicitly takes into consideration data from medical history, physical examination, laboratory findings and imaging. Bayes's theorem states that the probability of disease occurrence (or occurrence of other outcome) after new information is obtained, called a posteriori probability, depends directly on an a priori probability and the value of likelihood ratio associated with a given test result. This paper describes basic Bayesian analysis in relation to the diagnosis of two types of secondary hypertension; primary aldosteronism and pheochromocytoma. This choice is based on two facts; primary aldosteronism is believed to be the most common and the most commonly detected cause of symptomatic hypertension and pheochromocytoma is thought to have rapid progress and stormy clinical course. This article aims to draw physicians' attention to and increase the knowledge of Bayesian analysis, and to describe its use in everyday clinical decision making. On the basis of this theorem's foundations, the discussion in relation to the issue of differential diagnosis between physicians, their patients, and medical students should also improve. When used in practice, one should be aware, however, of Bayesian analysis limitations concerning the diagnostic test application and limited knowledge of diagnostic test accuracy, and insecure or faulty a priori probability estimates.

Bayesians and frequentists.

JM Bland — 2008-06-09T15:42:32-00:00

BMJ (Clinical research ed.), Vol. 317, No. 7166. (24 October 1998), pp. 1151-1160.

Innovations in bayes and empirical bayes methods: estimating parameters, populations and ranks.

TA Louis — 2008-06-09T15:39:48-00:00

Statistics in medicine, Vol. 18, No. 17-18. (0 1999), pp. 2493-2505.

By formalizing the relation among components and 'borrowing information' among them, Bayes and empirical Bayes methods can produce more valid, efficient and informative statistical evaluations than those based on traditional methods. In addition, Bayesian structuring of complicated models and goals guides development of appropriate statistical approaches and generates summaries which properly account for sampling and modelling uncertainty. Computing innovations enable implementation of complex and relevant models, thereby substantially increasing the role of Bayes/empirical Bayes methods in important statistical assessments. Policy-relevant statistical assessments involve synthesis of information from a set of related components such as medical clinics, geographic regions or research studies. Typical assessments include inference for individual parameters, synthesis over the collection of components (for example, the parameter histogram) and comparisons among parameters (for example, ranks). The relative importance of these goals depends on the context. Bayesian structuring provides a guide to valid inference. For example, while posterior means are the 'obvious' and optimal estimates for individual components under squared error loss, their empirical distribution function (EDF) is underdispersed and never valid for estimating the EDF of the true, underlying parameters. Effective histogram estimates result from optimizing a loss function based in a distance between the histogram and its estimate. Similarly, ranking observed data usually produces poor estimates and ranking posterior means can be inappropriate. Effective estimates should be based on a loss function that caters directly to ranks. Using examples of 'borrowing information', shrinkage and the variance/bias trade-off we motivate Bayes and empirical Bayes analysis. Then, we outline the formal approach and discuss 'triple-goal' estimates with values that when ranked produce optimal ranks, for which the EDF is an optimal estimate of the parameter EDF and such that the values themselves are effective estimates of co-ordinate-specific parameters. We use basic models and data analysis examples to highlight the conceptual and structural issues.

Bayesians, Frequentists, and Scientists

Bradley Efron — 2005-06-15T21:25:05-00:00

(2005)

Bayesian design and conduct of phase II single-arm clinical trials with binary outcomes: a tutorial.

S Zohar — 2008-06-08T01:00:14-00:00

Contemporary clinical trials, Vol. 29, No. 4. (July 2008), pp. 608-616.

The aim of phase II single-arm clinical trials of a new drug is to determine whether it has sufficient promising activity to warrant its further development. For the last several years Bayesian statistical methods have been proposed and used. Bayesian approaches are ideal for earlier phase trials as they take into account information that accrues during a trial. Predictive probabilities are then updated and so become more accurate as the trial progresses. Suitable priors can act as pseudo samples, which make small sample clinical trials more informative. Thus patients have better chances to receive better treatments. The goal of this paper is to provide a tutorial for statisticians who use Bayesian methods for the first time or investigators who have some statistical background. In addition, real data from three clinical trials are presented as examples to illustrate how to conduct a Bayesian approach for phase II single-arm clinical trials with binary outcomes.

A Bayesian approach to adjust for diagnostic misclassification between two mortality causes in Poisson regression.

JD Stamey — 2008-06-07T14:26:17-00:00

Statistics in medicine, Vol. 27, No. 13. (15 June 2008), pp. 2440-2452.

Response misclassification of counted data biases and understates the uncertainty of parameter estimators in Poisson regression models. To correct these problems, researchers have devised classical procedures that rely on asymptotic distribution results and supplemental validation data in order to estimate unknown misclassification parameters. We derive a new Bayesian Poisson regression procedure that accounts and corrects for misclassification for a count variable with two categories. Under the Bayesian paradigm, one can use validation data, expert opinion, or a combination of these two approaches to correct for the consequences of misclassification. The Bayesian procedure proposed here yields an operationally effective way to correct and account for misclassification effects in Poisson count regression models. We demonstrate the performance of the model in a simulation study. Additionally, we analyze two real-data examples and compare our new Bayesian inference method that adjusts for misclassification with a similar analysis that ignores misclassification. Copyright (c) 2007 John Wiley & Sons, Ltd.

Bayesian Nonparametric Estimation of Continuous Monotone Functions with Applications to Dose-Response Analysis.

Björn Bornkamp — 2008-06-06T14:06:22-00:00

Biometrics (28 May 2008)

In this article, we consider monotone nonparametric regression in a Bayesian framework. The monotone function is modeled as a mixture of shifted and scaled parametric probability distribution functions, and a general random probability measure is assumed as the prior for the mixing distribution. We investigate the choice of the underlying parametric distribution function and find that the two-sided power distribution function is well suited both from a computational and mathematical point of view. The model is motivated by traditional nonlinear models for dose-response analysis, and provides possibilities to elicitate informative prior distributions on different aspects of the curve. The method is compared with other recent approaches to monotone nonparametric regression in a simulation study and is illustrated on a data set from dose-response analysis.

Implementing a decision-theoretic design in clinical trials: why and how?

CR Palmer — 2008-06-06T13:07:24-00:00

Statistics in medicine, Vol. 26, No. 27. (30 November 2007), pp. 4939-4957.

This paper addresses two main questions: first, why should Bayesian and other innovative, data-dependent design models be put into practice and, secondly, given the past dearth of actual applications, how might one example of such a design be implemented in a genuine example trial? Clinical trials amalgamate theory, practice and ethics, but this last point has become relegated to the background, rather than taking often a more appropriate primary role. Trial practice has evolved but has its roots in R. A. Fisher's randomized agricultural field trials of the 1920s. Reasons for, and consequences of, this are discussed from an ethical standpoint, drawing on an under-used dichotomy introduced by French authors Lellouch and Schwartz (Int. Statist. Rev. 1971; 39:27-36). Plenty of ethically motivated designs for trials, including Bayesian designs have been proposed, but have found little application thus far. One reason for this is a lack of awareness of such alternative designs among trialists, while another reason is a lack of user-friendly software to allow study simulations. To encourage implementation, a new C++ program called 'Daniel' is introduced, offering much potential to assist the design of today's randomized controlled trials. Daniel evaluates a particular decision-theoretic method suitable for coping with either two or three Bernoulli response treatments with input features allowing user-specified choices of: patient horizon (number to be treated before and after the comparative stages of the trial); an arbitrary fixed trial truncation size (to allow ready comparison with traditional designs or to cope with practical constraints); anticipated success rates and a measure of their uncertainty (a matter ignored in standard power calculations); and clinically relevant, and irrelevant, differences in treatment effect sizes. Error probabilities and expected trial durations can be thoroughly explored via simulation, it being better by far to harm 'computer patients' instead of real ones. Suppose the objective in a clinical trial is to select between two treatments using a maximum horizon of 500 patients, when the truly superior treatment is expected to yield a 40 per cent success rate, but is believed to really range between 20 and 60 per cent. Simulation studies show that to detect a clinically relevant, absolute difference of 10 per cent between treatments, simulation studies show the decision-theoretic procedure would treat a mean 68 pairs of patients (SD 37) before correctly identifying the better treatment 96.7 per cent of the time, an error rate of 3.3 per cent. Having made a recommendation based on these patients, the remaining, on average 364 individuals, could either be given the indicated treatment, knowing its choice is optimal for the chosen horizon, or, alternatively, they could be entered into another, separate clinical trial. For comparison, a fixed sample size trial, with standard 5 per cent level of significance and 80 per cent power to detect a 10 per cent difference, requires treating over 700 patients in two groups, with the half allocated to inferior treatment considerably outnumbering the 68 expected under the decision-theoretic design, and the overall number simply too high for realistic application. In brief, the keys to answering the above 'why?' and 'how?' questions are ethics and software, respectively. Wider implications, both pros and cons, of implementing the particular method described will be discussed, with the overall conclusion that, where appropriate, clinical trials are now ready to undergo modernization from the agricultural age to the information age.

Bayesian change-point analyses in ecology

Beckage — 2007-03-24T18:36:26-00:00

New Phytologist, Vol. 174, No. 2. (April 2007), pp. 456-467.

Bayesian analysis of logistic regression with an unknown change point and covariate measurement error.

C Gössl — 2008-06-06T13:18:12-00:00

Statistics in medicine, Vol. 20, No. 20. (30 October 2001), pp. 3109-3121.

We discuss Bayesian estimation of a logistic regression model with an unknown threshold limiting value (TLV). In these models it is assumed that there is no effect of a covariate on the response under a certain unknown TLV. The estimation of these models in a Bayesian context by Markov chain Monte Carlo (MCMC) methods is considered with focus on the TLV. We extend the model by accounting for measurement error in the covariate. The Bayesian solution is compared with the likelihood solution proposed by Küchenhoff and Carroll using a data set concerning the relationship between dust concentration in the working place and the occurrence of chronic bronchitis.

Bayesian sample size for exploratory clinical trials incorporating historical data.

J Whitehead — 2008-06-06T13:10:04-00:00

Statistics in medicine, Vol. 27, No. 13. (15 June 2008), pp. 2307-2327.

This paper presents a simple Bayesian approach to sample size determination in clinical trials. It is required that the trial should be large enough to ensure that the data collected will provide convincing evidence either that an experimental treatment is better than a control or that it fails to improve upon control by some clinically relevant difference. The method resembles standard frequentist formulations of the problem, and indeed in certain circumstances involving 'non-informative' prior information it leads to identical answers. In particular, unlike many Bayesian approaches to sample size determination, use is made of an alternative hypothesis that an experimental treatment is better than a control treatment by some specified magnitude. The approach is introduced in the context of testing whether a single stream of binary observations are consistent with a given success rate p(0). Next the case of comparing two independent streams of normally distributed responses is considered, first under the assumption that their common variance is known and then for unknown variance. Finally, the more general situation in which a large sample is to be collected and analysed according to the asymptotic properties of the score statistic is explored. Copyright (c) 2007 John Wiley & Sons, Ltd.

A Bayesian Estimator of Protein-Protein Association Probabilities

JM Gilmore — 2008-06-03T03:00:58-00:00

Bioinformatics (22 May 2008), btn238.

Summary: The Bayesian Estimator of Protein-Protein Association Probabilities (BEPro3) is a software tool for estimating probabilities of protein-protein association between bait and prey protein pairs using data from multiple-bait, multiple-replicate, protein LC-MS/MS affinity isolation experiments. Availability: BEPro3 is public domain software, has been tested on Windows XP and version 10.4 or newer of the Mac OS 10.4, and is freely available from http://www.pnl.gov/statistics/BEPro3. Contact: ds.daly@pnl.gov Supplementary Information: A user guide, example dataset with analysis and additional documentation are included with the BEPro3 download 10.1093/bioinformatics/btn238

Multivariate hierarchical Bayesian model for differential gene expression analysis in microarray experiments.

H Zhao — 2008-05-16T08:44:23-00:00

BMC bioinformatics, Vol. 9 Suppl 1 (2008)

BACKGROUND: Identification of differentially expressed genes is a typical objective when analyzing gene expression data. Recently, Bayesian hierarchical models have become increasingly popular to solve this type of problems. These models show good performance in accommodating noise, variability and low replication of microarray data. However, the correlation between different fluorescent signals measured from a gene spot is ignored, which can diversely affect the data analysis step. In fact, the intensities of the two signals are significantly correlated across samples. The larger the log-transformed intensities are, the smaller the correlation is. RESULTS: Motivated by the complicated error relations in microarray data, we propose a multivariate hierarchical Bayesian framework for data analysis in the replicated microarray experiments. Gene expression data are modelled by a multivariate normal distribution, parameterized by the corresponding mean vectors and covariance matrixes with a conjugate prior distribution. Within the Bayesian framework, a generalized likelihood ratio test (GLRT) is also developed to infer the gene expression patterns. Simulation studies show that the proposed approach presents better operating characteristics and lower false discovery rate (FDR) than existing methods, especially when the correlation coefficient is large. The approach is illustrated with two examples of microarray analysis. The proposed method successfully detects significant genes closely related to the experimental states, which are verified by the biological information. CONCLUSIONS: The multivariate Bayesian model, compatible with the dependence between mean and variance in the univariate Bayesian model, relaxes the constant coefficient of variation assumption between measurements by adding a covariance structure. This model improves the identification of differentially expressed genes significantly since the Bayesian model fit well with the microarray data.

A Bayesian measure of the probability of false discovery in genetic epidemiology studies.

J Wakefield — 2008-05-07T08:18:29-00:00

American journal of human genetics, Vol. 81, No. 2. (August 2007), pp. 208-227.

In light of the vast amounts of genomic data that are now being generated, we propose a new measure, the Bayesian false-discovery probability (BFDP), for assessing the noteworthiness of an observed association. BFDP shares the ease of calculation of the recently proposed false-positive report probability (FPRP) but uses more information, has a noteworthy threshold defined naturally in terms of the costs of false discovery and nondiscovery, and has a sound methodological foundation. In addition, in a multiple-testing situation, it is straightforward to estimate the expected numbers of false discoveries and false nondiscoveries. We provide an in-depth discussion of FPRP, including a comparison with the q value, and examine the empirical behavior of these measures, along with BFDP, via simulation. Finally, we use BFDP to assess the association between 131 single-nucleotide polymorphisms and lung cancer in a case-control study.

Robust Bayesian sample size determination in clinical trials.

Pierpaolo Brutti — 2008-05-03T09:53:04-00:00

Statistics in medicine (18 January 2008)

This article deals with determination of a sample size that guarantees the success of a trial. We follow a Bayesian approach and we say an experiment is successful if it yields a large posterior probability that an unknown parameter of interest (an unknown treatment effect or an effects-difference) is greater than a chosen threshold. In this context, a straightforward sample size criterion is to select the minimal number of observations so that the predictive probability of a successful trial is sufficiently large. In the paper we address the most typical criticism to Bayesian methods-their sensitivity to prior assumptions-by proposing a robust version of this sample size criterion. Specifically, instead of a single distribution, we consider a class of plausible priors for the parameter of interest. Robust sample sizes are then selected by looking at the predictive distribution of the lower bound of the posterior probability that the unknown parameter is greater than a chosen threshold. For their flexibility and mathematical tractability, we consider classes of epsilon-contamination priors. As specific applications we consider sample size determination for a Phase III trial. Copyright (c) 2008 John Wiley & Sons, Ltd.

Data augmentation priors for Bayesian and semi-Bayes analyses of conditional-logistic and proportional-hazards regression.

S Greenland — 2008-04-03T10:13:49-00:00

Statistics in medicine, Vol. 20, No. 16. (30 August 2001), pp. 2421-2428.

Data augmentation priors have a long history in Bayesian data analysis. Formulae for such priors have been derived for generalized linear models, but their accuracy depends on two approximation steps. This note presents a method for using offsets as well as scaling factors to improve the accuracy of the approximations in logistic regression. This method produces an exceptionally simple form of data augmentation that allows it to be used with any standard package for conditional-logistic or proportional-hazards regression to perform Bayesian and semi-Bayes analyses of matched and survival data. The method is illustrated with an analysis of a matched case-control study of diet and breast cancer.

Bayesian Ranking of Biochemical System Models.

Vladislav Vyshemirsky — 2007-12-10T11:27:47-00:00

Bioinformatics (5 December 2007)

MOTIVATION: There often are many alternative models of a biochemical system. Distinguishing models and finding the most suitable ones is an important challenge in Systems Biology, as such model ranking, by experimental evidence, will help to judge the support of the working hypotheses forming each model. Bayes factors are employed as a measure of evidential preference for one model over another. Marginal likelihood is a key component of Bayes factors, however computing the marginal likelihood is a difficult problem, as it involves integration of nonlinear functions in multidimensional space. There are a number of methods available to compute the marginal likelihood approximately. A detailed investigation of such methods is required to find ones that perform appropriately for biochemical modelling. RESULTS: We assess four methods for estimation of the marginal likelihoods required for computing Bayes factors. The Prior Arithmetic Mean estimator, the Posterior Harmonic Mean estimator, the Annealed Importance Sampling and the Annealing-Melting Integration methods are investigated and compared on a typical case study in Systems Biology. This allows us to understand the stability of the analysis results and make reliable judgements in uncertain context. We investigate the variance of Bayes factor estimates, and highlight the stability of the Annealed Importance Sampling and the Annealing-Melting Integration methods for the purposes of comparing nonlinear models. AVAILABILITY: Models used in this study are available in SBML format as the supplementary material to this paper. CONTACT: vvv@dcs.gla.ac.uk.

Bayesian hypothesis testing-use in interpretation of measurements.

G Miller — 2008-03-09T01:22:22-00:00

Health Phys, Vol. 94, No. 3. (March 2008), pp. 248-254.

Bayesian hypothesis testing may be used to qualitatively interpret a dataset as indicating something "detected" or not. Hypothesis testing is shown to be equivalent to testing the posterior distribution for positive true amounts by redefining the prior to be a mixture of the original prior and a delta-function component at 0 representing the null hypothesis that nothing is truly present. The hypothesis-testing interpretation of the data is based on the posterior probability of the usual modeling hypothesis relative to the null hypothesis. Real numerical examples are given and discussed, including the distribution of the non-null hypothesis probability over 4,000 internal dosimetry cases. Currently used comparable methods based on classical statistics are discussed.

Elicitation of a Beta Prior for Bayesian Inference in Clinical Trials.

Yujun Wu — 2008-02-12T04:41:32-00:00

Biom J (12 December 2007)

When making Bayesian inferences we need to elicit an expert's opinion to set up the prior distribution. For applications in clinical trials, we study this problem with binary variables. A critical and often ignored issue in the process of eliciting priors in clinical trials is that medical investigators can seldom specify the prior quantities with precision. In this paper, we discuss several methods of eliciting beta priors from clinical information, and we use simulations to conduct sensitivity analyses of the effect of imprecise assessment of the prior information. These results provide useful guidance for choosing methods of eliciting the prior information in practice. ((c) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim).

Bayesian multivariate logistic regression.

SM O'Brien — 2008-01-30T08:12:54-00:00

Biometrics, Vol. 60, No. 3. (September 2004), pp. 739-746.

Bayesian analyses of multivariate binary or categorical outcomes typically rely on probit or mixed effects logistic regression models that do not have a marginal logistic structure for the individual outcomes. In addition, difficulties arise when simple noninformative priors are chosen for the covariance parameters. Motivated by these problems, we propose a new type of multivariate logistic distribution that can be used to construct a likelihood for multivariate logistic regression analysis of binary and categorical data. The model for individual outcomes has a marginal logistic structure, simplifying interpretation. We follow a Bayesian approach to estimation and inference, developing an efficient data augmentation algorithm for posterior computation. The method is illustrated with application to a neurotoxicology study.

Sensitivity analysis of misclassification: a graphical and a Bayesian approach.

H Chu — 2008-01-30T07:28:37-00:00

Ann Epidemiol, Vol. 16, No. 11. (November 2006), pp. 834-841.

PURPOSE: Misclassification can produce bias in measures of association. Sensitivity analyses have been suggested to explore the impact of such bias, but do not supply formally justified interval estimates. METHODS: To account for exposure misclassification, recently developed Bayesian approaches were extended to incorporate prior uncertainty and correlation of sensitivity and specificity. Under nondifferential misclassification, a contour plot is used to depict relations among the corrected odds ratio, sensitivity, and specificity. RESULTS: Methods are illustrated by application to a case-control study of cigarette smoking and invasive pneumococcal disease while varying the distributional assumptions about sensitivity and specificity. Results are compared with those of conventional methods, which do not account for misclassification, and a sensitivity analysis, which assumes fixed sensitivity and specificity. CONCLUSION: By using Bayesian methods, investigators can incorporate uncertainty about misclassification into probabilistic inferences.

A Bayesian approach estimating treatment effects on biomarkers containing zeros with detection limits.

Haitao Chu — 2008-01-09T06:20:55-00:00

Stat Med (2 January 2008)

Often in randomized clinical trials and observational studies in occupational and environmental health, a non-negative continuously distributed response variable denoting some metabolites of environmental toxicants is measured in treatment and control groups. When observations occur in both unexposed and exposed subjects, the biomarker measurement can be bimodally distributed with an extra spike at zero reflecting those unexposed. In the presence of left censoring due to values falling below biomarker assay detection limits, those unexposed with true zeros are indistinguishable from those exposed with left-censored values. Since interventions usually do not enhance or eliminate exposure, they do not have any impact on those unexposed. Thus, only the subset of individuals who are exposed should be used to make comparisons to estimate the effect of interventions. In this article, we present Bayesian approaches using non-standard mixture distributions to account for true zeros. The performance of the proposed Bayesian methods is compared with the maximum likelihood methods presented in Chu et al. (Stat. Med. 2005; 24:2053-2067) through simulation studies and a randomized chemoprevention trial conducted in Qidong, People's Republic of China. Copyright (c) 2007 John Wiley & Sons, Ltd.

Bayesian sensitivity analysis for unmeasured confounding in observational studies.

LC McCandless — 2008-01-03T14:25:20-00:00

Stat Med, Vol. 26, No. 11. (20 May 2007), pp. 2331-2347.

We consider Bayesian sensitivity analysis for unmeasured confounding in observational studies where the association between a binary exposure, binary response, measured confounders and a single binary unmeasured confounder can be formulated using logistic regression models. A model for unmeasured confounding is presented along with a family of prior distributions that model beliefs about a possible unknown unmeasured confounder. Simulation from the posterior distribution is accomplished using Markov chain Monte Carlo. Because the model for unmeasured confounding is not identifiable, standard large-sample theory for Bayesian analysis is not applicable. Consequently, the impact of different choices of prior distributions on the coverage probability of credible intervals is unknown. Using simulations, we investigate the coverage probability when averaged with respect to various distributions over the parameter space. The results indicate that credible intervals will have approximately nominal coverage probability, on average, when the prior distribution used for sensitivity analysis approximates the sampling distribution of model parameters in a hypothetical sequence of observational studies. We motivate the method in a study of the effectiveness of beta blocker therapy for treatment of heart failure.

Prior data for non-normal priors.

S Greenland — 2008-01-03T14:19:48-00:00

Stat Med, Vol. 26, No. 19. (30 August 2007), pp. 3578-3590.

Data augmentation priors facilitate contextual evaluation of prior distributions and the generation of Bayesian outputs from frequentist software. Previous papers have presented approximate Bayesian methods using 2x2 tables of 'prior data' to represent lognormal relative-risk priors in stratified and regression analyses. The present paper describes extensions that use the tables to represent generalized-F prior distributions for relative risks, which subsume lognormal priors as a limiting case. The method provides a means to increase tail-weight or skew the prior distribution for the log relative risk away from normality, while retaining the simple 2x2 table form of the prior data. When prior normality is preferred, it also provides a more accurate lognormal relative-risk prior in for the 2x2 table format. For more compact representation in regression analyses, the prior data can be compressed into a single data record. The method is illustrated with historical data from a study of electronic foetal monitoring and neonatal death.

Bayes and diagnostic testing.

E Lesaffre — 2008-01-03T14:18:26-00:00

Vet Parasitol, Vol. 148, No. 1. (19 August 2007), pp. 58-61.

Interpretation of the result of a diagnostic test depends not only on the actual test result(s) but also on information external to this result, namely the test's sensitivity and specificity. This external information (also called prior information) must be combined with the data to yield the so-called updated, posterior estimates of the true prevalence and the test characteristics. The Bayesian approach offers a natural, intuitive framework in which to carry out this estimation process. The influence of the prior information on the final result may not be ignored. Guidance for the choice of prior information not in conflict with the data can be obtained from a set of statistics and indices (DIC, p(D), Bayes-p).

Bayesian statistics in medicine: a 25 year review.

D Ashby — 2008-01-02T15:59:12-00:00

Stat Med, Vol. 25, No. 21. (15 November 2006), pp. 3589-3631.

This review examines the state of Bayesian thinking as Statistics in Medicine was launched in 1982, reflecting particularly on its applicability and uses in medical research. It then looks at each subsequent five-year epoch, with a focus on papers appearing in Statistics in Medicine, putting these in the context of major developments in Bayesian thinking and computation with reference to important books, landmark meetings and seminal papers. It charts the growth of Bayesian statistics as it is applied to medicine and makes predictions for the future. From sparse beginnings, where Bayesian statistics was barely mentioned, Bayesian statistics has now permeated all the major areas of medical statistics, including clinical trials, epidemiology, meta-analyses and evidence synthesis, spatial modelling, longitudinal modelling, survival modelling, molecular genetics and decision-making in respect of new technologies.

Clinical judgement in the interpretation of evidence: a Bayesian approach

Harbison — 2006-11-22T08:27:43-00:00

Journal of Clinical Nursing, Vol. 15, No. 12. (December 2006), pp. 1489-1497.

Semiparametric Bayesian analysis of structural equation models with fixed covariates.

Sik-Yum Lee — 2007-12-12T06:36:43-00:00

Stat Med (16 November 2007)

Latent variables play the most important role in structural equation modeling. In almost all existing structural equation models (SEMs), it is assumed that the distribution of the latent variables is normal. As this assumption is likely to be violated in many biomedical researches, a semiparametric Bayesian approach for relaxing it is developed in this paper. In the context of SEMs with covariates, we provide a general Bayesian framework in which a semiparametric hierarchical modeling with an approximate truncation Dirichlet process prior distribution is specified for the latent variables. The stick-breaking prior and the blocked Gibbs sampler are used for efficient simulation in the posterior analysis. The developed methodology is applied to a study of kidney disease in diabetes patients. A simulation study is conducted to reveal the empirical performance of the proposed approach. Supplementary electronic material for this paper is available in Wiley InterScience at http://www.mrw.interscience.wiley.com/suppmat/1097-0258/suppmat/. Copyright (c) 2007 John Wiley & Sons, Ltd.

Bayesian isotonic regression and trend analysis.

B Neelon — 2007-12-11T15:27:35-00:00

Biometrics, Vol. 60, No. 2. (June 2004), pp. 398-406.

In many applications, the mean of a response variable can be assumed to be a nondecreasing function of a continuous predictor, controlling for covariates. In such cases, interest often focuses on estimating the regression function, while also assessing evidence of an association. This article proposes a new framework for Bayesian isotonic regression and order-restricted inference. Approximating the regression function with a high-dimensional piecewise linear model, the nondecreasing constraint is incorporated through a prior distribution for the slopes consisting of a product mixture of point masses (accounting for flat regions) and truncated normal densities. To borrow information across the intervals and smooth the curve, the prior is formulated as a latent autoregressive normal process. This structure facilitates efficient posterior computation, since the full conditional distributions of the parameters have simple conjugate forms. Point and interval estimates of the regression function and posterior probabilities of an association for different regions of the predictor can be estimated from a single MCMC run. Generalizations to categorical outcomes and multiple predictors are described, and the approach is applied to an epidemiology application.

Generalized monotonic regression using random change points.

CC Holmes — 2007-12-11T15:27:47-00:00

Stat Med, Vol. 22, No. 4. (28 February 2003), pp. 623-638.

We introduce a procedure for generalized monotonic curve fitting that is based on a Bayesian analysis of the isotonic regression model. Conventional isotonic regression fits monotonically increasing step functions to data. In our approach we treat the number and location of the steps as random. For each step level we adopt the conjugate prior to the sampling distribution of the data as if the curve was unconstrained. We then propose to use Markov chain Monte Carlo simulation to draw samples from the unconstrained model space and retain only those samples for which the monotonic constraint holds. The proportion of the samples collected for which the constraint holds can be used to provide a value for the weight of evidence in terms of Bayes factors for monotonicity given the data. Using the samples, probability statements can be made about other quantities of interest such as the number of change points in the data and posterior distributions on the location of the change points can be provided. The method is illustrated throughout by a reanalysis of the leukaemia data studied by Schell and Singh.

Bayesian methods for proteomics

Gil Alterovitz — 2007-07-28T00:16:33-00:00

PROTEOMICS, Vol. 9999, No. 9999. (2007), NA.

Biological and medical data have been growing exponentially over the past several years [1, 2]. In particular, proteomics has seen automation dramatically change the rate at which data are generated [3]. Analysis that systemically incorporates prior information is becoming essential to making inferences about the myriad, complex data [4-6]. A Bayesian approach can help capture such information and incorporate it seamlessly through a rigorous, probabilistic framework. This paper starts with a review of the background mathematics behind the Bayesian methodology: from parameter estimation to Bayesian networks. The article then goes on to discuss how emerging Bayesian approaches have already been successfully applied to research across proteomics, a field for which Bayesian methods are particularly well suited [7-9]. After reviewing the literature on the subject of Bayesian methods in biological contexts, the article discusses some of the recent applications in proteomics and emerging directions in the field.

Bayesians in clinical trials: Asleep at the switch.

Lemuel A Moyé — 2007-07-04T01:55:36-00:00

Stat Med (15 June 2007)

The refreshing Bayes perspective has much to offer biostatistics. Yet, from its 225-year-old roots sprung difficulties that blocked its growth at the beginning of the 20th century. Computational obstacles in concert with an inability to identify the best indifferent prior revealed a weakness on which frequentists capitalized. It took Bayesians 40 years to recover, allowing the infant field of biostatistics to fall firmly in the hands of the frequentists. Recent disillusionment with the frequentist perspective, and its hegemony of p-values, has produced a second opportunity for the Bayesian philosophy to make solid contributions to clinical trials.However, difficulty with the applicability of the likelihood principle, problems with prevalent prior 'disinformation' in clinical medicine, in concert with the complexity of truly representative loss functions threaten again to thwart the Bayesian march into biostatistics. Seven suggestions are offered to the Bayesians to help them adapt to the rigors of clinical research. Copyright (c) 2007 John Wiley & Sons, Ltd.