Exact confidence bounds following adaptive group sequential tests

We provide a method for obtaining confidence intervals, point estimates, and p-values for the primary effect size parameter at the end of a two-arm group sequential clinical trial in which adaptive changes have been implemented along the way. The method is based on applying the adaptive hypothesis testing procedure of Müller and Schäfer (2001, Biometrics 57, 886-891) to a sequence of dual tests derived from the stage-wise adjusted confidence interval of Tsiatis, Rosner, and Mehta (1984, Biometrics 40, 797-803). In the nonadaptive setting this confidence interval is known to provide exact coverage. In the adaptive setting exact coverage is guaranteed provided the adaptation takes place at the penultimate stage. In general, however, all that can be claimed theoretically is that the coverage is guaranteed to be conservative. Nevertheless, extensive simulation experiments, supported by an empirical characterization of the conditional error function, demonstrate convincingly that for all practical purposes the coverage is exact and the point estimate is median unbiased. No procedure has previously been available for producing confidence intervals and point estimates with these desirable properties in an adaptive group sequential setting. The methodology is illustrated by an application to a clinical trial of deep brain stimulation for Parkinson's disease.