Statistical Inference in Adaptive Group Sequential Trials with the Standardized Mean Difference as Effect Size

Abstract

We consider the standardized difference of normal means as the outcome measure for comparing two independent groups, say experimental E and control C. This scale- and translation-invariant effect measure enables a convenient specification of a noninferiority margin in applications. Starting with a family of null hypotheses, we derive adaptive group sequential confidence intervals keeping the predefined confidence coefficient. The interval at the end of the trial determines whether and which null hypotheses can be rejected. During the course of the trial, the sample size can be calculated in a completely adaptive way based on the unblinded data of previously performed stages. Concrete rules for sample size updating are provided. Moreover, in each interim analysis, it is possible to change the planning from showing noninferiority to showing superiority or vice versa without affecting the overall type I error. A real data example is worked out in detail and the change in the sample size planning from showing noninferiority to showing superiority is considered during the ongoing trial. In Monte Carlo simulations, we investigate the practical properties of the proposed intervals.