Bayesian Approaches to Clinical Trials and Health-Care Evaluation

"This is a terrific book and should be on the shelf of every professional that works in clinical trials or health-care evaluation. It gives a thorough pragmatic introduction to Bayesian methods for health-care interventions, provides many example along with data and software to reproduce the analyses, guides readers to areas where Bayesian methods are particularly valuable, and includes an excellent set of exercises." (Journal of the American Statistical Association, June 2009) "Bayesian Approaches to Clinical Trials and Health-Care Evaluation' is a clear and comprehensive text for biostatisticians who want to understand and apply Bayesian statistical methods to clinical research." (Journal of Clinical Best Practices, Nov 2008) "an indispensable resource for all students and investigators who plan to incorporate Bayesian methods into their research." (The Annals of Pharmacotherapy, January 2005) "...a valuable resource for libraries, and those who are involved in quantitative health care evaluation..." (Royal Statistical Society, Vol.168, No.1, January 2005) "...The technical material is presented in an accessible style, and the examples given clearly illustrate the principles under discussion..." (Short Book Reviews, Vol.24, No.3, December 2004) "...Bayesian analysis seems set to reach a wider audience with the publication of [this] introductory level text..." (Financial Times, 16 April 2004) "...very well laid-out and easy to follow...a very good resource for teaching students..." (Statistical Methods in Medical Research, Vol 14, 2005) "I would use with pleasure and interest this book as a textbook..." (Metron Journal, Vol.63, No.2, 2005) "...I can pay the authors no higher tribute than to say that I would be proud to have written this book. It is elegant and it is destined to becoming a classic in the field." (Statistics in Medicine, 15th July 2005) "...a generous supply of exercises...I recommend it very highly..." (Clinical Trials, No.1 2004) "...Bayesian analysis seems set to reach a wider audience with the publication of [this] introductory level text..." (Financial Times, 16 April 2004) "...a generous supply of exercises...I recommend it very highly..." (Clinical Trials, No.1 2004)

Sir David John Spiegelhalter, OBE FRS, is a British statistician and Winton Professor of the Public Understanding of Risk in the Statistical Laboratory at the University of Cambridge and a Fellow of Churchill College, Cambridge. Spiegelhalter is an ISI highly cited researcher. Keith R. Abrams is the author of Bayesian Approaches to Clinical Trials and Health-Care Evaluation, published by Wiley. Jonathan P. Myles is the author of Bayesian Approaches to Clinical Trials and Health-Care Evaluation, published by Wiley.

Preface. List of examples. 1. Introduction. 1.1 What are Bayesian methods? 1.2 What do we mean by health-care evaluation? 1.3 A Bayesian approach to evaluation. 1.4 The aim of this book and the intended audience. 1.5 Structure of the book. 2. Basic Concepts from Traditional Statistical Analysis. 2.1 Probability. 2.1.1 What is probability? 2.1.2 Odds and log-odds. 2.1.3 Bayes theorem for simple events. 2.2 Random variables, parameters and likelihood. 2.2.1 Random variables and their distributions. 2.2.2 Expectation, variance, covariance and correlation. 2.2.3 Parametric distributions and conditional independence. 2.2.4 Likelihoods. 2.3 The normal distribution. 2.4 Normal likelihoods. 2.4.1 Normal approximations for binary data. 2.4.2 Normal likelihoods for survival data. 2.4.3 Normal likelihoods for count responses. 2.4.4 Normal likelihoods for continuous responses. 2.5 Classical inference. 2.6 A catalogue of useful distributions*. 2.6.1 Binomial and Bernoulli. 2.6.2 Poisson. 2.6.3 Beta. 2.6.4 Uniform. 2.6.5 Gamma. 2.6.6 Root-inverse-gamma. 2.6.7 Half-normal. 2.6.8 Log-normal. 2.6.9 Students t. 2.6.10 Bivariate normal. 2.7 Key points. Exercises. 3. An Overview of the Bayesian Approach. 3.1 Subjectivity and context. 3.2 Bayes theorem for two hypotheses. 3.3 Comparing simple hypotheses: likelihood ratios and Bayes factors. 3.4 Exchangeability and parametric modelling*. 3.5 Bayes theorem for general quantities. 3.6 Bayesian analysis with binary data. 3.6.1 Binary data with a discrete prior distribution. 3.6.2 Conjugate analysis for binary data. 3.7 Bayesian analysis with normal distributions. 3.8 Point estimation, interval estimation and interval hypotheses. 3.9 The prior distribution. 3.10 How to use Bayes theorem to interpret trial results. 3.11 The credibility of significant trial results*. 3.12 Sequential use of Bayes theorem*. 3.13 Predictions. 3.13.1 Predictions in the Bayesian framework. 3.13.2 Predictions for binary data*. 3.13.3 Predictions for normal data. 3.14 Decision-making. 3.15 Design. 3.16 Use of historical data. 3.17 Multiplicity, exchangeability and hierarchical models. 3.18 Dealing with nuisance parameters*. 3.18.1 Alternative methods for eliminating nuisance parameters*. 3.18.2 Profile likelihood in a hierarchical model*. 3.19 Computational issues. 3.19.1 Monte Carlo methods. 3.19.2 Markov chain Monte Carlo methods. 3.19.3 WinBUGS. 3.20 Schools of Bayesians. 3.21 A Bayesian checklist. 3.22 Further reading. 3.23 Key points. Exercises. 4. Comparison of Alternative Approaches to Inference. 4.1 A structure for alternative approaches. 4.2 Conventional statistical methods used in health-care evaluation. 4.3 The likelihood principle, sequential analysis and types of error. 4.3.1 The likelihood principle. 4.3.2 Sequential analysis. 4.3.3 Type I and Type II error. 4.4 P-values and Bayes factors*. 4.4.1 Criticism of P-values. 4.4.2 Bayes factors as an alternative to P-values: simple hypotheses. 4.4.3 Bayes factors as an alternative to P-values: composite hypotheses. 4.4.4 Bayes factors in preference studies. 4.4.5 Lindleys paradox. 4.5 Key points. Exercises. 5. Prior Distributions. 5.1 Introduction. 5.2 Elicitation of opinion: a brief review. 5.2.1 Background to elicitation. 5.2.2 Elicitation techniques. 5.2.3 Elicitation from multiple experts. 5.3 Critique of prior elicitation. 5.4 Summary of external evidence*. 5.5 Default priors. 5.5.1 Non-informative or reference priors: 5.5.2 Sceptical priors. 5.5.3 Enthusiastic priors. 5.5.4 Priors with a point mass at the null hypothesis (lump-and-smear priors)*. 5.6 Sensitivity analysis and robust priors. 5.7 Hierarchical priors. 5.7.1 The judgement of exchangeability. 5.7.2 The form for the random-effects distribution. 5