On choosing the number of interim analyses in clinical trials.

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.