Sequential parallel comparison design with binary and time-to-event outcomes

Sequential parallel comparison design (SPCD) has been proposed to increase the likelihood of success of clinical trials especially trials with possibly high placebo effect. Sequential parallel comparison design is conducted with 2 stages. Participants are randomized between active therapy and placebo in stage 1. Then, stage 1 placebo nonresponders are rerandomized between active therapy and placebo. Data from the 2 stages are pooled to yield a single P value. We consider SPCD with binary and with time-to-event outcomes. For time-to-event outcomes, response is defined as a favorable event prior to the end of follow-up for a given stage of SPCD. We show that for these cases, the usual test statistics from stages 1 and 2 are asymptotically normal and uncorrelated under the null hypothesis, leading to a straightforward combined testing procedure. In addition, we show that the estimators of the treatment effects from the 2 stages are asymptotically normal and uncorrelated under the null and alternative hypothesis, yielding confidence interval procedures with correct coverage. Simulations and real data analysis demonstrate the utility of the binary and time-to-event SPCD.