Bayesian Biostatistics

Emmanuel Lesaffre, Professor of Statistics, Biostatistical Centre, Catholic University of Leuven, Leuven, Belgium. Dr Lesaffre has worked on and studied various areas of biostatistics for 25 years. He has taught a variety of courses to students from many disciplines, from medicine and pharmacy, to statistics and engineering, teaching Bayesian statistics for the last 5 years. Having published over 200 papers in major statistical and medical journals, he has also Co-Edited the book Disease Mapping and Risk Assessment for Public Health, and was the Associate Editor for Biometrics. He is currently Co-Editor of the journal "Statistical Modelling: An International Journal", Special Editor of two volumes on Statistics in Dentistry in Statistical Methods in Medical Research, and a member of the Editorial Boards of numerous journals.
 
Andrew Lawson, Professor of Statistics, Dept of Epidemiology & Biostatistics, University of South Carolina, USA. Dr Lawson has considerable and wide ranging experience in the development of statistical methods for spatial and environmental epidemiology. He has solid experience in teaching Bayesian statistics to students studying biostatistics and has also written two books and numerous journal articles in the biostatistics area. Dr Lawson has also guest edited two special issues of "Statistics in Medicine" focusing on Disease Mapping. He is a member of the editorial boards of the journals: Statistics in Medicine and .

The growth of biostatistics has been phenomenal in recent years and has been marked by considerable technical innovation in both methodology and computational practicality. One area that has experienced significant growth is Bayesian methods. The growing use of Bayesian methodology has taken place partly due to an increasing number of practitioners valuing the Bayesian paradigm as matching that of scientific discovery. In addition, computational advances have allowed for more complex models to be fitted routinely to realistic data sets.
 
Through examples, exercises and a combination of introductory and more advanced chapters, this book provides an invaluable understanding of the complex world of biomedical statistics illustrated via a diverse range of applications taken from epidemiology, exploratory clinical studies, health promotion studies, image analysis and clinical trials.
 
Key Features:
* Provides an authoritative account of Bayesian methodology, from its most basic elements to its practical implementation, with an emphasis on healthcare techniques.
* Contains introductory explanations of Bayesian principles common to all areas of application.
* Presents clear and concise examples in biostatistics applications such as clinical trials, longitudinal studies, bioassay, survival, image analysis and bioinformatics.
* Illustrated throughout with examples using software including WinBUGS, OpenBUGS, SAS and various dedicated R programs.
* Highlights the differences between the Bayesian and classical approaches.
* Supported by an accompanying website hosting free software and case study guides.
 
Bayesian Biostatistics introduces the reader smoothly into the Bayesian statistical methods with chapters that gradually increase in level of complexity. Master students in biostatistics, applied statisticians and all researchers with a good background in classical statistics who have interest in Bayesian methods will find this book useful.

This book provides an authoritative account of Bayesian methodology, from its most basic elements to its practical implementations, with an emphasis on healthcare techniques. Contains introductory explanations of Bayesian principles common to all areas.

Preface xiii
 
Notation, terminology and some guidance for reading the book xvii
 
Part I BASIC CONCEPTS IN BAYESIAN METHODS
 
1 Modes of statistical inference 3
1.1 The frequentist approach: A critical reflection 4
1.2 Statistical inference based on the likelihood function 10
1.3 The Bayesian approach: Some basic ideas 14
1.4 Outlook 18
 
2 Bayes theorem: Computing the posterior distribution 20
2.1 Introduction 20
2.2 Bayes theorem - the binary version 20
2.3 Probability in a Bayesian context 21
2.4 Bayes theorem - the categorical version 22
2.5 Bayes theorem - the continuous version 23
2.6 The binomial case 24
2.7 The Gaussian case 30
2.8 The Poisson case 36
2.9 The prior and posterior distribution of h(theta) 40
2.10 Bayesian versus likelihood approach 40
2.11 Bayesian versus frequentist approach 41
2.12 The different modes of the Bayesian approach 41
2.13 An historical note on the Bayesian approach 42
2.14 Closing remarks 44
 
3 Introduction to Bayesian inference 46
 
3.1 Introduction 46
3.2 Summarizing the posterior by probabilities 46
3.3 Posterior summary measures 47
3.4 Predictive distributions 51
3.5 Exchangeability 58
3.6 A normal approximation to the posterior 60
3.7 Numerical techniques to determine the posterior 63
3.8 Bayesian hypothesis testing 72
3.9 Closing remarks 78
 
4 More than one parameter 82
4.1 Introduction 82
4.2 Joint versus marginal posterior inference 83
4.3 The normal distribution with mu and sigma2 unknown 83
4.4 Multivariate distributions 89
4.5 Frequentist properties of Bayesian inference 92
4.6 Sampling from the posterior distribution: The Method of Composition 93
4.7 Bayesian linear regression models 96
4.8 Bayesian generalized linear models 101
4.9 More complex regression models 102
4.10 Closing remarks 102
 
5 Choosing the prior distribution 104
5.1 Introduction 104
5.2 The sequential use of Bayes theorem 104
5.3 Conjugate prior distributions 106
5.4 Noninformative prior distributions 113
5.5 Informative prior distributions 121
5.6 Prior distributions for regression models 129
5.7 Modeling priors 134
5.8 Other regression models 136
5.9 Closing remarks 136
 
6 Markov chain Monte Carlo sampling 139
6.1 Introduction 139
6.2 The Gibbs sampler 140
6.3 The Metropolis(-Hastings) algorithm 154
6.4 Justification of the MCMC approaches* 162
6.5 Choice of the sampler 165
6.6 The Reversible Jump MCMC algorithm* 168
6.7 Closing remarks 172
 
7 Assessing and improving convergence of the Markov chain 175
7.1 Introduction 175
7.2 Assessing convergence of a Markov chain 176
7.3 Accelerating convergence 189
7.4 Practical guidelines for assessing and accelerating convergence 194
7.5 Data augmentation 195
7.6 Closing remarks 200
 
8 Software 202
8.1 WinBUGS and related software 202
8.2 Bayesian analysis using SAS 215
8.3 Additional Bayesian software and comparisons 221
8.4 Closing remarks 222
 
Part II BAYESIAN TOOLS FOR STATISTICAL MODELING
 
9 Hierarchical models 227
9.1 Introduction 227
9.2 The Poisson-gamma hierarchical model 228
9.3 Full versus empirical Bayesian approach 238
9.4 Gaussian hierarchical models 240
9.5 Mixed models 244
9.6 Propriety of the posterior 260
9.7 Assessing and accelerating convergence 261
9.8 Comparison of Bayesian and frequentist hierarchical models 263
9.9 Closing remarks 265
 
10 Model building and assessment 267
10.1 Introduction 267
10.2 Measures for model selection 268
10.3 Model checking 288
10.4 Closing remarks 316
 
11 Variable selection 319
11.1 Introduction 319
11.2 Classical variable selection 320
11.3 Bayesian variable selection: Concepts and questions 325
11.4 Introduction