Interim monitoring of group sequential trials using spending functions for the type I and type II error probabilities

Lan and DeMets (1) introduced a flexible procedure for the analysis of sequential trials based on the discretization of the Brownian motion. In this paper we consider an extension of this strategy that preserves both the desired significance level and the power of any group sequential trial. We propose a procedure that allows for any number and timing of interim analyses. This entails the derivation of boundaries at the monitoring stage by means of two spending functions, one for the type I and one for the type II error probabilities, as well as the adjustment of the target maximum information as the trial progresses. The general solution to the problem is provided together with a discussion of implementation strategies. The procedure is intended for group sequential designs that allow early stopping in favor of both the null and the alternative hypotheses, and an example is presented for this case. However its application,is also easily extended for designs where there is no early stopping in flavor of the null.