Original ArticleSeven items were identified for inclusion when reporting a Bayesian analysis of a clinical study
Introduction
The vast majority of studies in the biomedical literature are analyzed using classical statistical inference (also called frequentist inference), which relies on P-values and confidence intervals to draw conclusions from the study results. Frequentist statistical methods have several limitations, however, including the inability to determine the probability that an intervention is effective, sensitivity to the number of analyses performed, and inability to incorporate prior information [1], [2].
Analysis using Bayesian methods is an alternative that overcomes many of the limitations of frequentist analysis [1], [2]. In essence, a Bayesian analysis determines how the results of a study change the opinion held before the study was conducted. As a consequence, a Bayesian analysis requires an explicit mathematical expression of what is known before the study is conducted; this information is called the prior probability distribution. The data from the clinical study are represented by the likelihood. The prior probability distribution is then updated using the likelihood and the outcome is expressed as a posterior probability distribution. From this distribution, one can readily determine the probability that two treatments differ by some clinically meaningful amount.
Up until recently, Bayesian analysis has not been used widely in clinical research, in part because it is computationally complex [1]. However, since the recent advent of readily available software for Bayesian analysis [3], there has been increased interest in Bayesian methods [4] and increased use of such analyses in the biomedical literature [5], [6], [7]. Nonetheless, little attention has been paid to how such analyses should be reported, and there has been considerable variation in the reporting of individual items of these analyses [8]. Standardization of reporting is important; Bayesian analyses contain many elements foreign to most clinical readers, and thus clinical researchers using Bayesian methods may be tempted to omit virtually all details of the analysis. Some description of the analysis is required, however, for the reader to be able to interpret the analysis and to have some confidence that the approach was appropriate.
Although there are two sets of guidelines for reporting of Bayesian analysis in biomedical research (BayesWatch [9] and Bayesian Standards in Science, or BaSiS [8]), we felt that their content and format are not conducive toward use as a checklist for the purpose of publication. Consequently, we saw a need for the development of a list of items that should be reported when a Bayesian analysis is performed—a list that should be easy to use and specifically intended for publication of clinical research. If such a list could be developed, it would afford an opportunity to describe the extent to which these items are reported in the current medical literature and to identify factors related to the number of these items in an individual report.
Our objectives were to (1) generate a list of the items that experts consider to be most important when reporting a Bayesian analysis of a clinical study, (2) report on the extent to which we found these items in the current medical literature, and (3) identify factors related to the number of items in a report.
Section snippets
Item generation
The items potentially important in reporting a Bayesian analysis were developed by reviewing the two existing guidelines (BayesWatch and BaSiS) with input by the authors. Twenty-one items were identified (Table 1). Only items most pertinent to the analysis were included. We did not include items related to study design, such as randomization and concealment, because these are unique to specific study designs and because methodological criteria have already been developed for some designs (e.g.,
Development of ROBUST
The 24 experts were geographically distributed with representation from North America, Europe, and the Middle East. Half of the experts (12 of 24) resided in the United States and 6 of 24 (25%) resided in the United Kingdom. Responses were obtained from all 24 experts (100%) but one declined to participate further because of unfamiliarity with newer computational techniques; our results are therefore based on input from 23 experts.
Outside of the 21 items we proposed, no single additional item
Discussion
We succeeded in developing criteria for reporting of Bayesian analysis, drawing opinions from an international group of experts. The development and accessibility of such criteria directed toward clinical research is important, given the expected increase in the number of Bayesian analyses appearing in clinical journals. We showed that more of the ROBUST items were found in articles published in journals with a low impact factor and journals with a methodological focus. In addition to
Acknowledgments
L.S. and J.H. are supported by Canadian Institutes of Health Research (CIHR) Post-doctoral Fellowships; L.S. is also supported by a Hospital for Sick Children Clinician Scientist Fellowship; M.G. holds the POGO Chair in Childhood Cancer Control; G.K. is a senior scientist at CIHR; and B.M.F. holds the Canada Research Chair in Childhood Arthritis. We wish to thank James G. Wright, MD, MPH, FRCSC, for his review and constructive criticism of an early draft of this manuscript. We also wish to
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