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Bayesian Approaches to Clinical Trials and Health-Care Evaluation



Bayesian Approaches to Clinical Trials and Health-Care Evaluation

David J. Spiegelhalter, Keith R. Abrams, Jonathan P. Myles

ISBN: 978-0-470-09259-0 May 2004 406 Pages

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David Spiegelhalter has recently joined the ranks of Isaac Newton, Charles Darwin and Stephen Hawking by becoming a fellow of the Royal Society. Originating from the Medical Research Council’s biostatistics unit, David has played a leading role in the Bristol heart surgery and Harold Shipman inquiries.  

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The Bayesian approach involves synthesising data and judgement in order to reach conclusions about unknown quantities and make predictions. Bayesian methods have become increasingly popular in recent years, notably in medical research, and although there are a number of books on Bayesian analysis, few cover clinical trials and biostatistical applications in any detail. Bayesian Approaches to Clinical Trials and Health-Care Evaluation provides a valuable overview of this rapidly evolving field, including basic Bayesian ideas, prior distributions, clinical trials, observational studies, evidence synthesis and cost-effectiveness analysis.
Covers a broad array of essential topics, building from the basics to more advanced techniques.

  • Illustrated throughout by detailed case studies and worked examples
  • Includes exercises in all chapters
  • Accessible to anyone with a basic knowledge of statistics
  • Authors are at the forefront of research into Bayesian methods in medical research
  • Accompanied by a Web site featuring data sets and worked examples using Excel and WinBUGS - the most widely used Bayesian modelling package

Bayesian Approaches to Clinical Trials and Health-Care Evaluation is suitable for students and researchers in medical statistics, statisticians in the pharmaceutical industry, and anyone involved in conducting clinical trials and assessment of health-care technology.


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 Student’s t.

2.6.10 Bivariate normal.

2.7 Key points.


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.


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 Lindley’s paradox.

4.5 Key points.


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.

5.7.3 The prior for the standard deviation of the random effects*.

5.8 Empirical criticism of priors.

5.9 Key points.


6. Randomised Controlled Trials.

6.1 Introduction.

6.2 Use of a loss function: is a clinical trial for inference or decision?

6.3 Specification of null hypotheses.

6.4 Ethics and randomisation: a brief review.

6.4.1 Is randomisation necessary?

6.4.2 When is it ethical to randomise?

6.5 Sample size of non-sequential trials.

6.5.1 Alternative approaches to sample-size assessment.

6.5.2 ‘Classical power’: hybrid classical-Bayesian methods assuming normality.

6.5.3 ‘Bayesian power’.

6.5.4 Adjusting formulae for different hypotheses.

6.5.5 Predictive distribution of power and necessary sample size.

6.6 Monitoring of sequential trials.

6.6.1 Introduction.

6.6.2 Monitoring using the posterior distribution.

6.6.3 Monitoring using predictions: ‘interim power’.

6.6.4 Monitoring using a formal loss function.

6.6.5 Frequentist properties of sequential Bayesian methods.

6.6.6 Bayesian methods and data monitoring committees.

6.7 The role of ‘scepticism’ in confirmatory studies.

6.8 Multiplicity in randomised trials.

6.8.1 Subset analysis.

6.8.2 Multi-centre analysis.

6.8.3 Cluster randomization.

6.8.4 Multiple endpoints and treatments.

6.9 Using historical controls*.

6.10 Data-dependent allocation.

6.11 Trial designs other than two parallel groups.

6.12 Other aspects of drug development.

6.13 Further reading.

6.14 Key points.


7. Observational Studies.

7.1 Introduction.

7.2 Alternative study designs.

7.3 Explicit modelling of biases.

7.4 Institutional comparisons.

7.5 Key points.


8. Evidence Synthesis.

8.1 Introduction.

8.2 ‘Standard’ meta-analysis.

8.2.1 A Bayesian perspective.

8.2.2 Some delicate issues in Bayesian meta-analysis.

8.2.3 The relationship between treatment effect and underlying risk.

8.3 Indirect comparison studies.

8.4 Generalised evidence synthesis.

8.5 Further reading.

8.6 Key points.


9. Cost-effectiveness, Policy-Making and Regulation.

9.1 Introduction.

9.2 Contexts.

9.3 ‘Standard’ cost-effectiveness analysis without uncertainty.

9.4 ‘Two-stage’ and integrated approaches to uncertainty in cost-effectiveness modeling.

9.5 Probabilistic analysis of sensitivity to uncertainty about parameters: two-stage approach.

9.6 Cost-effectiveness analyses of a single study: integrated approach.

9.7 Levels of uncertainty in cost-effectiveness models.

9.8 Complex cost-effectiveness models.

9.8.1 Discrete-time, discrete-state Markov models.

9.8.2 Micro-simulation in cost-effectiveness models.

9.8.3 Micro-simulation and probabilistic sensitivity analysis.

9.8.4 Comprehensive decision modeling.

9.9 Simultaneous evidence synthesis and complex cost-effectiveness modeling.

9.9.1 Generalised meta-analysis of evidence.

9.9.2 Comparison of integrated Bayesian and two-stage approach.

9.10 Cost-effectiveness of carrying out research: payback models.

9.10.1 Research planning in the public sector.

9.10.2 Research planning in the pharmaceutical industry.

9.10.3 Value of information.

9.11 Decision theory in cost-effectiveness analysis, regulation and policy.

9.12 Regulation and health policy.

9.12.1 The regulatory context.

9.12.2 Regulation of pharmaceuticals.

9.12.3 Regulation of medical devices.

9.13 Conclusions.

9.14 Key points.


10. Conclusions and Implications for Future Research.

10.1 Introduction.

10.2 General advantages and problems of a Bayesian approach.

10.3 Future research and development.

Appendix: Websites and Software.

A.1 The site for this book.

A.2 Bayesian methods in health-care evaluation.

A.3 Bayesian software.

A.4 General Bayesian sites.



"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)  

>Bayesian Approaches to Clinical Trials and Health-Care Evaluation Visit this site to see fully worked examples in WINBUGS, and other programs referred to in the text.