Two-stage winner designs for non-inferiority trials with pre-specified non-inferiority margin

Abstract In drug development, a two-stage winner design (Lan et al. 2005, Shun et al. 2008) can be cost-effective when the best treatment is to be determined from multiple experimental treatments in superiority trials. However, the statistical methods assessing non-inferiority in a two-stage winner design have not yet been studied, for which the complexity arises in determining the critical value when parameter space is not a single point under the null hypothesis. Because the maximum error may not occur at the vertex of the null space, it is unclear if naive use of critical values and distributional results from the test for superiority remains correct. In this paper, we provided rigorous justifications to determine the critical value for testing non-inferiority hypothesis, with a pre-specified non-inferiority margin, in a two-stage winner design with two experimental treatments and an active control. We studied the distribution of the test statistics, critical values, sample size and power calculations using the exact distribution of the test statistics as well as using normal approximations. Theoretical justifications and extensive numerical assessments were conducted to calculate the design parameters and evaluate the performance of our methods.