Sample size calculation for the sequential parallel comparison design with binary endpoint using exact methods

High placebo responses in clinical trial could reduce the treatment effect leading to the failure of a promising drug. Several strategies have been developed to minimize high placebo responses, including the sequential parallel comparison design (SPCD). For a study with binary outcome, the existing statistical methods to test the drug effectiveness always rely on the asymptotic limiting distribution. When a study's sample size is small to medium, the asymptotic approaches do not have satisfactory performance with regard to type I error rate and statistical power. For that reason, we propose utilizing exact conditional approach to calculate sample size based on the existing test statistics to order the sample space. The proposed method controls the type I error rate under the unconditional framework. We compare the proposed exact sample sizes using different test statistics and the sample size for a randomized parallel study. We would recommend using exact sample sizes for the SPCD with small- to medium sample sizes and the SPCD with extreme response rates.