Dependence, hyper-dependence and hypothesis testing in clinical trials

While investigators designing clinical trials face the important issue of endpoint selection, an equally troublesome concern can be the a priori selection of the endpoint analysis. In this latter circumstance, there may be only one endpoint of interest in the clinical trial, but several competing endpoint analyses are available (e.g., an analysis of the endpoint that is adjusted for clinical center versus an analysis that is adjusted for geographic region versus an unadjusted analysis). An example that demonstrates the unsatisfactory conclusions that ambiguous choices can produce is offered. A procedure utilizing conditional probability is provided that permits the conservation of type I error when the investigators have one endpoint and several worthy competitor endpoint analyses that are each prospectively identified and carried out at the trial's conclusion. When the high levels of dependence among these analyses are taken into account, it is possible to carry out the hypothesis tests in a way that 1) provides practicable type I error levels for each analysis, and 2) conserves the familywise type I error. In circumstances in which the endpoint and all members of the family of analyses are selected during the design phase of the trial, this procedure provides confirmatory conclusions as opposed to exploratory findings.