Abstract:
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For a clinical trial incorporating a group sequential design that allows early stopping for efficacy or futility (GSDEF), the two main frequentist methods of monitoring for futility are conditional power (CP) and type II error spending. There is a long history of interest in their relationship; specifically, determining the type II error properties of CP. We show the equivalence of the methods for evaluating futility when power is aligned on the type II error probability of GSDE, utilizing the full type II error probability model for GSDEF obtained by Dobbins (2013). With power aligned, futility monitoring is an add-in to GSDE for both methods, with non-binding futility boundaries, and there is a 1:1 link between CP and the type II error probability of the tests of futility. This result provides a rationale for the choice of theta with CP based on the type II error probability of the tests of futility. We use an example trial to illustrate that a monitoring rule based on a specified (low) CP yields substantially different type II error properties depending on the chosen theta assumption, and discuss the implications of this result for monitoring for futility with CP.
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