• D J Spiegelhalter, J P Myles, D R Jones, and K R Abrams.
• MRC Biostatistics Unit, Institute of Public Health, Cambridge, UK.
• Health Technol Assess. 2000 Jan 1;4(38):1-130.

BackgroundBayesian methods may be defined as the explicit quantitative use of external evidence in the design, monitoring, analysis, interpretation and reporting of a health technology assessment. In outline, the methods involve formal combination through the use of Bayes's theorem of: 1. a prior distribution or belief about the value of a quantity of interest (for example, a treatment effect) based on evidence not derived from the study under analysis, with 2. a summary of the information concerning the same quantity available from the data collected in the study (known as the likelihood), to yield 3. an updated or posterior distribution of the quantity of interest. These methods thus directly address the question of how new evidence should change what we currently believe. They extend naturally into making predictions, synthesising evidence from multiple sources, and designing studies: in addition, if we are willing to quantify the value of different consequences as a 'loss function', Bayesian methods extend into a full decision-theoretic approach to study design, monitoring and eventual policy decision-making. Nonetheless, Bayesian methods are a controversial topic in that they may involve the explicit use of subjective judgements in what is conventionally supposed to be a rigorous scientific exercise.ObjectivesThis report is intended to provide: 1. a brief review of the essential ideas of Bayesian analysis 2. a full structured review of applications of Bayesian methods to randomised controlled trials, observational studies, and the synthesis of evidence, in a form which should be reasonably straightforward to update 3. a critical commentary on similarities and differences between Bayesian and conventional approaches 4. criteria for assessing the reporting of a Bayesian analysis 5. a comprehensive list of published 'three-star' examples, in which a proper prior distribution has been used for the quantity of primary interest 6. tutorial case studies of a variety of types 7. recommendations on how Bayesian methods and approaches may be assimilated into health technology assessments in a variety of contexts and by a variety of participants in the research process.MethodsThe BIDS ISI database was searched using the terms 'Bayes' or 'Bayesian'. This yielded almost 4000 papers published in the period 1990-98. All resultant abstracts were reviewed for relevance to health technology assessment; about 250 were so identified, and used as the basis for forward and backward searches. In addition EMBASE and MEDLINE databases were searched, along with websites of prominent authors, and available personal collections of references, finally yielding nearly 500 relevant references. A comprehensive review of all references describing use of 'proper' Bayesian methods in health technology assessment (those which update an informative prior distribution through the use of Bayes's theorem) has been attempted, and around 30 such papers are reported in structured form. There has been very limited use of proper Bayesian methods in practice, and relevant studies appear to be relatively easily identified.ResultsBayesian methods in the health technology assessment context 1. Different contexts may demand different statistical approaches. Prior opinions are most valuable when the assessment forms part of a series of similar studies. A decision-theoretic approach may be appropriate where the consequences of a study are reasonably predictable. 2. The prior distribution is important and not unique, and so a range of options should be examined in a sensitivity analysis. Bayesian methods are best seen as a transformation from initial to final opinion, rather than providing a single 'correct' inference. 3. The use of a prior is based on judgement, and hence a degree of subjectivity cannot be avoided. However, subjective priors tend to show predictable biases, and archetypal priors may be useful for identifying a reasonable range of prior opinion.

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