Optimality, sample size, and power calculations for the sequential parallel comparison design

The sequential parallel comparison design (SPCD) has been proposed to increase the likelihood of success of clinical trials in therapeutic areas where high-placebo response is a concern. The trial is run in two stages, and subjects are randomized into three groups: (i) placebo in both stages; (ii) placebo in the first stage and drug in the second stage; and (iii) drug in both stages. We consider the case of binary response data (response/no response). In the SPCD, all first-stage and second-stage data from placebo subjects who failed to respond in the first stage of the trial are utilized in the efficacy analysis. We develop 1 and 2 degree of freedom score tests for treatment effect in the SPCD. We give formulae for asymptotic power and for sample size computations and evaluate their accuracy via simulation studies. We compute the optimal allocation ratio between drug and placebo in stage 1 for the SPCD to determine from a theoretical viewpoint whether a single-stage design, a two-stage design with placebo only in the first stage, or a two-stage design is the best design for a given set of response rates. As response rates are not known before the trial, a two-stage approach with allocation to active drug in both stages is a robust design choice.