Reaching first Bayes

Abstract

Bayesian methods of statistical analysis have been advocated for many years,1-7 but most of the articles using Bayesian methods seem to have done so as an afterthought, or perhaps as a demonstration, not as the primary way of designing the study or analyzing the data.2 The study by Young et al8 in this issue of Annals is a welcome exception. The authors designed the study to use a Bayesian decision-theoretic method of examining the results as they were accumulated, as a way of affording early termination of the trial if the data were conclusive. Because interim analyses are possible with more traditional statistical methods, the authors took some risk in using a design and analytic plan that is likely to be unfamiliar to grant and journal reviewers.9 However, Bayesian methods have several important advantages over classical statistical methods. A Bayesian design allows more frequent monitoring of the data as they are accumulated. In principle, the data could be reanalyzed after each new outcome is known. More importantly, the decision-theoretic model allows a more informed decision to be made about whether to collect more data or to stop the trial and draw a conclusion. Collecting more data would be economically costly and could be clinically costly because, if one treatment were actually superior to the other, continuing the trial would increase the number of patients assigned the inferior therapy. Stopping the trial and drawing a conclusion about efficacy or the lack thereof could also be clinically costly because, if the trial were stopped too early, the probability of the wrong decision (a false positive or false negative conclusion) would be high. The decision-theoretic model allows the analyst to include those costs explicitly in the decision to continue or stop the trial and can even incorporate the likely magnitude of the effect into the decision. For example, the clinical cost of continuing a trial when one treatment is far superior to the other would usually be higher than when the difference is close to the threshold of clinical insignificance. In addition, the analyst could, in principle, use different costs for different kinds of decision errors, if for example, false negative conclusions about effect were much worse than false positive, or vice versa. Bayesian analyses, whether they use the decisiontheoretic model or not, have the additional advantage that the results can be analyzed validly at any point, even if the designed sample size is not reached. This cannot be done with classical methods, even though it probably occurs often. Finally, simulation studies have shown that Bayesian decision-theoretic designs have smaller average expected sample sizes than classical designs when the costs are set to produce the same levels of type I and type II errors.10 With all these advantages, why are Bayesian methods the exception and not the rule?11 There are at least 3 barriers to more widespread use. First, there are objections to the subjective nature of the prior probabilities that must be specified in the Bayesian world. This problem is more apparent than real, however, particularly in medicine. Physicians are highly empirical and will happily ignore theoretical considerations if they think they can get useful answers to their questions. In addition, if the data are strong, the results will not change much even if dramatically different priors are used. A more serious impediment is the computational difficulty of Bayesian methods and the lack of good software tools. This is beginning to yield as sophisticated resampling algorithms are implemented in software,12 enabling what were formerly computationally intractable problems to be tackled.13,14 However, at present such tools are still considered somewhat experimental and are more difficult to use than traditional statistical packages, which are not known for their user-friendliness. P E D I A T R I C S / E D I T O R I A L