Bayesian Approaches to Clinical Trials and Health-Care Evaluation (Statistics in Practice)

Bayesian Approaches 
to Clinical Trials and 
Health-Care Evaluation......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 13
List of Examples......Page 15
1.1 WHAT ARE BAYESIAN METHODS?......Page 17
1.2 WHATDOWEMEAN BY ¡® HEALTH- CARE EVALUATION¡¯?......Page 18
1.4 THE AIM OF THIS BOOK AND THE INTENDED AUDIENCE......Page 19
1.5 STRUCTURE OF THE BOOK......Page 20
2 Basic Concepts from Traditional Statistical Analysis......Page 25
2.1.1 What is probability?......Page 26
2.1.2 Odds and log- odds......Page 28
2.1.3 Bayes theorem for simple events......Page 29
2.2.1 Random variables and their distributions......Page 30
2.2.2 Expectation, variance, covariance and correlation......Page 32
2.2.3 Parametric distributions and conditional independence......Page 33
2.2.4 Likelihoods......Page 34
2.3 THE NORMAL DISTRIBUTION......Page 36
2.4 NORMAL LIKELIHOODS......Page 38
2.4.1 Normal approximations for binary data......Page 39
2.4.2 Normal likelihoods for survival data......Page 43
2.4.3 Normal likelihoods for count responses......Page 46
2.5 CLASSICAL INFERENCE......Page 47
2.6.1 Binomial and Bernoulli......Page 50
2.6.2 Poisson......Page 51
2.6.3 Beta......Page 52
2.6.4 Uniform......Page 54
2.6.5 Gamma......Page 55
2.6.6 Root- inverse- gamma......Page 56
2.6.7 Half- normal......Page 57
2.6.8 Log- normal......Page 58
2.6.9 Student¡¯s t......Page 59
2.6.10 Bivariate normal......Page 60
EXERCISES......Page 62
3.1 SUBJECTIVITY AND CONTEXT......Page 65
3.2 BAYES THEOREM FOR TWO HYPOTHESES......Page 67
3.3 Comparing simple hypotheses: likelihood ratios and Bayes factors......Page 70
3.4 EXCHANGEABILITY AND PARAMETRIC MODELLING*......Page 72
3.6 BAYESIAN ANALYSIS WITH BINARY DATA......Page 73
3.6.1 Binary data with a discrete prior distribution......Page 74
3.6.2 Conjugate analysis for binary data......Page 75
3.7 Bayesian analysis with normal distributions......Page 78
3.8 Point estimation, interval estimation and interval hypotheses......Page 80
3.9 THE PRIOR DISTRIBUTION......Page 89
3.10 How to use Bayes theorem to interpret trial results......Page 90
3.11 The ‘credibility’ of significant trial results*......Page 91
3.12 SEQUENTIAL USE OF BAYES THEOREM*......Page 95
3.13.1 Predictions in the Bayesian framework......Page 96
3.13.2 Predictions for binary data*......Page 97
3.13.3 Predictions for normal data......Page 99
3.14 DECISION- MAKING......Page 101
3.16 USE OF HISTORICAL DATA......Page 106
3.17 Multiplicity, exchangeability and hierarchical models......Page 107
3.18.1 Alternative methods for eliminating nuisance parameters*......Page 116
3.19 COMPUTATIONAL ISSUES......Page 118
3.19.1 Monte Carlo methods......Page 119
3.19.2 Markov chain Monte Carlo methods......Page 121
3.19.3 WinBUGS......Page 123
3.20 SCHOOLS OF BAYESIANS......Page 128
3.21 A BAYESIAN CHECKLIST......Page 129
3.22 FURTHER READING......Page 131
3.23 KEY POINTS......Page 132
EXERCISES......Page 133
4.1 A STRUCTURE FOR ALTERNATIVE APPROACHES......Page 137
4.2 CONVENTIONAL STATISTICAL METHODS USED IN HEALTH- CARE EVALUATION......Page 138
4.3.1 The likelihood principle......Page 140
4.3.2 Sequential analysis......Page 142
4.4.1 Criticism of P- values......Page 143
4.4.2 Bayes factors as an alternative to P- values: simple hypotheses......Page 144
4.4.3 Bayes factors as an alternative to P- values: composite hypotheses......Page 146
4.4.4 Bayes factors in preference studies......Page 149
4.4.5 Lindley¡¯s paradox......Page 151
EXERCISES......Page 152
5.1 INTRODUCTION......Page 155
5.2.1 Background to elicitation......Page 156
5.2.2 Elicitation techniques......Page 157
5.2.3 Elicitation from multiple experts......Page 158
5.3 CRITIQUE OF PRIOR ELICITATION......Page 163
5.4 SUMMARY OF EXTERNAL EVIDENCE*......Page 164
5.5.1 ¡® Non- informative¡¯ or ¡® reference¡¯ priors......Page 173
5.5.2 ¡® Sceptical¡¯ priors......Page 174
5.5.3 ¡® Enthusiastic¡¯ priors......Page 176
5.5.4 Priors with a point mass at the null hypothesis(‘ lump- and- smear’ priors)*......Page 177
5.6 SENSITIVITY ANALYSIS AND ¡® ROBUST¡¯ PRIORS......Page 181
5.7.1 The judgement of exchangeability......Page 183
effects*......Page 184
5.8 EMPIRICAL CRITICISM OF PRIORS......Page 190
5.9 KEY POINTS......Page 192
EXERCISES......Page 193
6.1 INTRODUCTION......Page 197
6.2 USE OF A LOSS FUNCTION: IS A CLINICAL TRIAL FOR INFERENCE OR DECISION?......Page 198
6.3 SPECIFICATION OF NULL HYPOTHESES......Page 200
6.4.2 When is it ethical to randomise?......Page 203
6.5.1 Alternative approaches to sample- size assessment......Page 205
6.5.2 ‘Classical power’: hybrid classical-Bayesian methods 
assuming normality......Page 209
6.5.3 ¡® Bayesian power¡¯......Page 210
6.5.4 Adjusting formulae for different hypotheses......Page 212
6.5.5 Predictive distribution of power and necessary sample size......Page 217
6.6.1 Introduction......Page 218
6.6.2 Monitoring using the posterior distribution......Page 220
6.6.3 Monitoring using predictions: ¡® interim power¡¯......Page 227
6.6.4 Monitoring using a formal loss function......Page 236
6.6.5 Frequentist properties of sequential Bayesian methods......Page 237
6.6.6 Bayesian methods and data monitoring committees......Page 238
6.7 The role of ‘scepticism’ in confirmatory studies......Page 240
6.8.3 Cluster randomisation......Page 243
6.9 USING HISTORICAL CONTROLS*......Page 244
6.10 DATA- DEPENDENT ALLOCATION......Page 251
6.11 TRIAL DESIGNS OTHER THAN TWO PARALLEL GROUPS......Page 253
6.12 OTHER ASPECTS OF DRUG DEVELOPMENT......Page 258
6.13 FURTHER READING......Page 260
6.14 KEY POINTS......Page 261
EXERCISES......Page 263
7.1 INTRODUCTION......Page 267
7.2 ALTERNATIVE STUDY DESIGNS......Page 268
7.3 EXPLICIT MODELLING OF BIASES......Page 269
7.4 INSTITUTIONAL COMPARISONS......Page 274
7.5 KEY POINTS......Page 278
EXERCISES......Page 279
8.1 INTRODUCTION......Page 283
8.2.1 A Bayesian perspective......Page 284
8.2.2 Some delicate issues in Bayesian meta- analysis......Page 290
8.2.3 The relationship between treatment effect and underlying risk......Page 294
8.3 INDIRECT COMPARISON STUDIES......Page 298
8.4 GENERALISED EVIDENCE SYNTHESIS......Page 301
8.5 FURTHER READING......Page 314
EXERCISES......Page 315
9.1 INTRODUCTION......Page 321
9.2 CONTEXTS......Page 322
9.3 ‘Standard’ cost-effectiveness analysis without uncertainty......Page 324
9.4 ‘Two-stage’ and integrated approaches to uncertainty in cost-effectiveness
 modelling......Page 326
9.5 Probabilistic analysis of sensitivity to uncertainty about parameters:
two-stage approach......Page 328
9.6 COST- EFFECTIVENESS ANALYSES OF A SINGLE STUDY: INTEGRATED APPROACH......Page 331
9.7 LEVELS OF UNCERTAINTY IN COST- EFFECTIVENESS MODELS......Page 336
9.8.1 Discrete- time, discrete- state Markov models......Page 338
9.8.2 Micro- simulation in cost- effectiveness models......Page 339
9.8.3 Micro- simulation and probabilistic sensitivity analysis......Page 340
9.8.4 Comprehensive decision modelling......Page 344
9.9.1 Generalised meta- analysis of evidence......Page 345
9.10.1 Research planning in the public sector......Page 351
9.10.2 Research planning in the pharmaceutical industry......Page 352
9.10.3 Value of information......Page 353
9.11 DECISION THEORY IN COST- EFFECTIVENESS ANALYSIS, REGULATION AND POLICY......Page 357
9.12.2 Regulation of pharmaceuticals......Page 359
9.13 CONCLUSIONS......Page 360
EXERCISES......Page 361
10.2 GENERAL ADVANTAGES AND PROBLEMS OF A BAYESIAN APPROACH......Page 365
10.3 FUTURE RESEARCH AND DEVELOPMENT......Page 366
A. 2 BAYESIAN METHODS IN HEALTH- CARE EVALUATION......Page 369
A. 3 BAYESIAN SOFTWARE......Page 370
A. 4 GENERAL BAYESIAN SITES......Page 371
References......Page 373
Index......Page 397
Statistics in Practice......Page 408