Background Bayesian 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. Objectives This 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. Methods The 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. Results Bayesian 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.

/pdf/bayesian-methods-in-health-technology-assessment-a-review-4j5dc5afcw.pdf

Bayesian methods in health technology assessment: a review.

The authors present an analysis of the choice of sample sizes for demonstrating cost-effectiveness of a new treatment or procedure, when data on both cost and efficacy will be collected in a clinical trial. The Bayesian approach to statistics is employed, as well as a novel Bayesian criterion that provides insight into the sample size problem and offers a very flexible formulation.

http://www.biostat.umn.edu/~ph7440/pubh7440/OHaganStevens2001.pdf

Bayesian assessment of sample size for clinical trials of cost-effectiveness.

BACKGROUND: Many decisions in health care aim to maximise health, requiring judgements about interventions that may have higher health effects but potentially incur additional costs (cost-effectiveness framework). The evidence used to establish cost-effectiveness is typically uncertain and it is important that this uncertainty is characterised. In situations in which evidence is uncertain, the experience of experts is essential. The process by which the beliefs of experts can be formally collected in a quantitative manner is structured expert elicitation. There is heterogeneity in the existing methodology used in health-care decision-making. A number of guidelines are available for structured expert elicitation; however, it is not clear if any of these are appropriate for health-care decision-making. OBJECTIVES: The overall aim was to establish a protocol for structured expert elicitation to inform health-care decision-making. The objectives are to (1) provide clarity on methods for collecting and using experts' judgements, (2) consider when alternative methodology may be required in particular contexts, (3) establish preferred approaches for elicitation on a range of parameters, (4) determine which elicitation methods allow experts to express uncertainty and (5) determine the usefulness of the reference protocol developed. METHODS: A mixed-methods approach was used: systemic review, targeted searches, experimental work and narrative synthesis. A review of the existing guidelines for structured expert elicitation was conducted. This identified the approaches used in existing guidelines (the 'choices') and determined if dominant approaches exist. Targeted review searches were conducted for selection of experts, level of elicitation, fitting and aggregation, assessing accuracy of judgements and heuristics and biases. To sift through the available choices, a set of principles that underpin the use of structured expert elicitation in health-care decision-making was defined using evidence generated from the targeted searches, quantities to elicit experimental evidence and consideration of constraints in health-care decision-making. These principles, including fitness for purpose and reflecting individual expert uncertainty, were applied to the set of choices to establish a reference protocol. An applied evaluation of the developed reference protocol was also undertaken. RESULTS: For many elements of structured expert elicitation, there was a lack of consistency across the existing guidelines. In almost all choices, there was a lack of empirical evidence supporting recommendations, and in some circumstances the principles are unable to provide sufficient justification for discounting particular choices. It is possible to define reference methods for health technology assessment. These include a focus on gathering experts with substantive skills, eliciting observable quantities and individual elicitation of beliefs. Additional considerations are required for decision-makers outside health technology assessment, for example at a local level, or for early technologies. Access to experts may be limited and in some circumstances group discussion may be needed to generate a distribution. LIMITATIONS: The major limitation of the work conducted here lies not in the methods employed in the current work but in the evidence available from the wider literature relating to how appropriate particular methodological choices are. CONCLUSIONS: The reference protocol is flexible in many choices. This may be a useful characteristic, as it is possible to apply this reference protocol across different settings. Further applied studies, which use the choices specified in this reference protocol, are required. FUNDING: This project was funded by the NIHR Health Technology Assessment programme and will be published in full in Health Technology Assessment; Vol. 25, No. 37. See the NIHR Journals Library website for further project information. This work was also funded by the Medical Research Council (reference MR/N028511/1).

https://njl-admin.nihr.ac.uk/document/download/2036808

Developing a reference protocol for structured expert elicitation in health-care decision-making: a mixed-methods study.

Statisticians have long argued that randomized controlled trials should be sufficiently large to achieve their purpose, and for common diseases with major public health implications this has brought many benefits. However, there are many instances where it is unrealistic to expect clinicians to provide the information on which sample sizes are calculated and undue emphasis on trial size can be counterproductive. Examples of such trials are given and some general issues discussed, including the unhelpful contribution of hypothesis testing, the need for replication and the role of the statistician.

Small clinical trials: are they all bad?

Small but important therapeutic effects of new treatments can be most efficiently detected through the study of large randomized prospective series of patients. Such large scale clinical trials are nowadays commonplace. The alternative is years of polemic and debate surrounding several trials each too small to detect plausible differences with any certainty. Such trials produce equivocal and contradictory results, which could be predicted from power calculations based upon sensible pre-trial estimates of treatment differences. Unfortunately such calculations often lead to sample sizes of several thousands. It is not surprising that investigators tend to be over-optimistic in their estimation of treatment effects (which are necessarily uncertain) especially when the sample size requirements are so stark. In this paper a method is outlined for incorporating into the sample size calculations the uncertainty of the estimate made at the design stage of a clinical trial. In particular a formal scheme is described for deciding how many interim analyses should be performed to satisfy ethical and pragmatic requirements of large clinical trial design. Although the argument will be 'Bayesian', the criteria for assessment and comparison will be strictly of a Neyman-Pearson (i.e. significance testing) kind.

On choosing the number of interim analyses in clinical trials.

The design of scientific studies is a significant part of statistics, an important aspect of which is considering the number of experimental units required. The formulae used in classical statistics assume that the sample size should be determined by controlling the variance of the parameters of interest or the type I and type II error rates for testing hypotheses. A Bayesian approach is based on considering prior distributions and the desired properties of the posterior distributions. Four methods for calculating sample sizes using a Bayesian philosophy are presented. As these methods are particularly relevant when there are precise but conflicting prior distributions, a study of professional's beliefs about indicators of child sexual abuse is used to illustrate the methods. All applied statisticians are aware of the need for careful design of scientific studies. Although, unfortunately, advice is often requested only about the number of experimental subjects needed, the calculation of sample sizes is important. Classical methods require the scientists to know or estimate the value and the variance of the parameters of interest, and specify the type I error rate, in order to use formulae for the number of units necessary to obtain a given precision. The type II error rate must also be specified if a significance test comparing parameters is considered. Instead of requiring a specified value and a variance, a Bayesian approach attempts to quantify the scientist's knowledge by defining a prior distribution for the parameter of interest. The sample size required to estimate a parameter is then determined by requiring the posterior distribution to have particular properties. Comparison of different possible values of a parameter is dealt with by specifying relationships between the posterior distributions for the parameter, given different prior distributions. We consider four cases with respect to the probability of success in a Bernoulli trial: first, the implications of the classical sample size calculation given an individual's prior distribution; second, requiring the posterior credible interval to include a specific value; third, requiring the posterior credible interval for an individual to include a parameter with an alternative prior distribution; and, finally, requiring the posterior credible intervals for two extreme prior distributions to touch. Although there is now considerable interest in using Bayesian methods in the analysis of health-related studies, there has been relatively little discussion of the use of Bayesian ideas in the design of studies. Herson (1979) considers the sensitivity of a Bayesian stopping rule for phase II clinical trials to different prior distributions, but assumes that one prior distribution will be specified. McPherson (1982) also considers the effects of different prior distributions, in this case the effect of the prior distribution of the treatment difference on the choice of the number of interim analyses in clinical trials. He comments in passing that the prior distribution could be obtained by averaging over experts' priors. Freedman and Spiegelhalter (1983) describe a study which uses McPherson's methods. They suggest either an average prior distribution or the use of two or three consensus prior distributions, rather than attempting to use divergent prior distributions. Spiegelhalter and Freedman (1986) use a consensus prior to calculate the probabilities of reaching the correct or

Bayesian Sample Size Calculations and Prior Beliefs About Child Sexual Abuse

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Bayesian Sample Size Calculations and Prior Beliefs About Child Sexual Abuse