An Adaptive Futility Monitoring Method with Time-Varying Conditional Power Boundary

For a long-term randomized clinical trial, it has become a well-accepted practice to include interim analyses in trial protocols. In addition to design an efficacy monitoring plan, investigators often develop a futility monitoring plan as well to prevent continuing a trial that has little chance to demonstrate treatment efficacy. Conditional power is the probability that the final analysis will result in rejection of the null hypothesis given data accumulated at interim analysis and a prespecified effect size. Because of its nice interpretation of the projection to the end of study, the conditional power is often built in decision rules to stop the trial for futility at interim analysis. An aggressive rule for futility stopping sets a relatively large threshold for the conditional power which may result in significant loss of overall power of the study. On the contrast, a conservative rule using small threshold may not be able to stop the trial early when there is indeed no treatment efficacy or the treatment is even inferior to the control. An adaptive futility monitoring plan with a time-varying conditional power boundary is developed in this paper. This method maintains the overall size and power very well but has better chance to stop the trial earlier for futility compared to a conservative futility stopping rule of the conditional power. The method is illustrated using simulation studies for the one-sided two-sample proportion test which is motivated by the ongoing multi-center randomized control clinical trial, the Carotid Occlusion Surgical Study (COSS). Some key words: B-value; Brownian motion; Conditional power; Group sequential test; Interim analysis; Randomized clinical trial; Stochastic curtailment;