A flexible futility monitoring method with time-varying conditional power boundary

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Abstract
In an ongoing multi-center randomized control clinical trial, the Carotid Occlusion Surgery Study (COSS), the study protocol specifies multiple interim analyses whose results will be reviewed by an independent DSMB to determine if the trial needs to be stopped early due to either efficacy or futility. Conditional power is used as the decision rule for the DSMB to recommend stopping the trial for futility. An aggressive rule for futility stopping sets a relatively high threshold for the conditional power which may result in significant loss of overall power of the study. A conservative rule using a lower threshold may not be able to stop the trial early when there is indeed no treatment efficacy. The goal of this article is to develop a flexible futility monitoring plan with a time-varying conditional power boundary that maintains the overall power of the study well, but has a better chance to stop the trial earlier for futility compared to a futility stopping rule with a fixed value for the minimum conditional power to continue. The conditional power boundary for futility is developed using the β-spending function method for sequential test statistics and assuming no interim analysis for efficacy. It is then modified to account for the repeated interim analyses for efficacy. Simulation studies that mirror the design of the COSS trial show that the proposed method with sample size calculated without considering interim analyses will maintain the designed size and power well when the designed effect size holds, but will have a better chance to exit the trial earlier if the true effect size is smaller than the designed size such that it is not clinically meaningful to conduct the trial. The method is valid for sequential test statistics that constitute of a stochastic process which approximates the Brownian motion. It is not applicable to the monitored process that behaves quire differently from the Brownian motion. The proposed conditional power method facilitates a flexible futility monitoring plan that can be easily implemented in long-term clinical trials where multiple interim analyses are required. It provides the DSMB an objective guideline to use in considering early stopping for futility.