INTERIM ANALYSIS OF CLINICAL TRIALS: SIMULATION STUDIES OF CONDITIONAL POWER UNDER FRACTIONAL BROWNIAN MOTION

Abstract

Classical Brownian motion (BM) techniques for statistical monitoring of clinical trials have been widely used. The conditional power (CP) and [Formula: see text]-spending function-based boundary crossing probabilities are popular procedures for statistical hypothesis testing under the assumption of BM. However, in some clinical trials, the assumptions of BM may not be fully met for the design and data analysis. Therefore, a more general class of stochastic processes, fractional Brownian motion (FBM), was proposed in the literature to model the test statistics derived from interim analysis of clinical trials. To investigate the properties of FBM, in this paper, we simulated a wide range of FBM data, e.g. [Formula: see text] (BM) versus [Formula: see text] (FBM), with treatment effects versus without treatment effects. Then the performance of CP-based interim analysis was compared by assuming that the data follow BM or FBM. Our simulation study suggested that CP under the FBM assumptions was generally higher than that under the BM assumptions when [Formula: see text] and also matched well with the empirical results.