Bayesian subset analysis: application to studying treatment‐by‐gender interactions

Evaluating treatment effects within subsets of patients plays a major part of the analysis of many major clinical trials. Clinicians are often impressed by the heterogeneity of patient populations in clinical trials and hence are interested in examining subset effects. Statisticians generally discourage subset analysis or suggest that clinicians 'do subset analysis but do not believe it'. This advice, however, is a sign of the inadequacy of the analytic methods generally used for subset analysis. Separate analysis of many subsets, and basing conclusions on whether the observed treatment difference achieves significance at the 0.05 level, is likely to yield erroneous conclusions. Making the separate analysis of subsets dependent on demonstration of a statistically significant treatment-by-subset interaction is also not an effective analytic strategy because of the limited power of interaction tests. This paper describes a Bayesian approach to subset analysis developed by Simon, Dixon and Freidlin. The method avoids many of the problems of subset analysis because it is not 'separate' analysis of subsets. Instead, subset-specific treatment effects are estimated as an average of observed within-subset differences and overall differences; the two components are weighted by the a priori estimate of the likelihood of qualitative treatment by subset interactions. Hence, the Bayesian method proposed permits subset analyses incorporating the assumption that qualitative interactions are unlikely. The methodology is applied to the problem of designing and analysing clinical trials to estimate treatment effects for males and females.