Minimax two-stage-designs with applications to tissue banking case-control studies.

Abstract

'Tissue banks' are created, at least in part, to help medical scientists learn about disease biology on the basis of samples provided by patients on treatment protocols that were competed years earlier. The bank inventory consists of precious non-renewable patient material (such as frozen diagnostic blood or bone marrow), which can be linked to both clinical data and long term follow-up information. Case-control studies, where cases represent clinical failures and controls clinical successes, are ideal for rapidly learning if a laboratory marker might have prognostic significance. While group sequential (multi-stage) methods are widely used in clinical trials, they have rarely been applied in case-control studies. Further, unlike clinical trials where safety and efficiency may actually be in conflict, case-control studies can focus on efficiency. Hence, minimizing the expected sample size is a desirable goal in such a setting. Since the true effect size is never known, and since no prior distribution can be postulated for the effect size, we have opted for the minimax solution. A strategy is developed to determine amongst all two-stage designs with given type I and type II errors, the one for which the maximum expected sample size is minimized. The user is provided with simple tables, whereby one can determine everything necessary to conduct the study from the corresponding calculation for a single-stage design. A matched pair example is given where the suggested design can be modified, to obtain a superior 'two-plus' stage design. The basic idea is to conduct the first stage as planned, but use the estimate of variance to redesign the study, without using the estimate of effect size in the redesign.