Repeated confidence intervals for adaptive group sequential trials

This paper proposes a method for computing conservative confidence intervals for a group sequential test in which an adaptive design change is made one or more times over the course of the trial. The key idea, due to Müller and Schäfer (Biometrics 2001; 57:886-891), is that by preserving the null conditional rejection probability of the remainder of the trial at the time of each adaptive change, the overall type I error rate, taken unconditionally over all possible design modifications, is also preserved. We show how this principle may be extended to construct one-sided confidence intervals by applying the idea to a sequence of dual tests derived from the repeated confidence intervals (RCIs) proposed by Jennison and Turnbull (J. Roy. Statist. Soc. B 1989; 51:301-361). These adaptive RCIs, such as their classical counterparts, have the advantage that they preserve the desired coverage probability even if the pre-specified stopping rule is over-ruled. The statistical methodology is explored by simulations and is illustrated by an application to a clinical trial of deep brain stimulation for Parkinson's disease.