Sample size of thorough QTc clinical trial adjusted for multiple comparisons

A thorough QT trial is typically designed to test for two sets of hypotheses. The primary set of hypotheses is for demonstrating that the test treatment will not prolong QT interval. The second set of hypotheses is to demonstrate the assay sensitivity of the positive control treatment in the study population. Both analyses require multiple comparisons by testing the treatment difference measured repeatedly at multiple selected time points. Tsong and Zhong (2010) indicated that for prolongation testing, this involves an intersection-union test that leads to the reduction of study power. It requires type II error rate adjustment in order to maintain proper sample size and power of the test. Tsong et al. (2010) indicated also that the assay sensitivity analysis is carried out using a union-intersection test that leads to the inflation of the family-wise type I error rate. Type I error rate adjustment is required to control the family-wise type I error rate. Zhang and Machado (2008) proposed the sample size calculation of test-placebo QT response difference based on simulation with a multivariate normal distribution model. Even though the results are generally used as guidance for sample size determination for balanced arm TQT trials, they are limited in generalization to various advanced and adaptive designs of TQT trials (Zhang, 2011 ; Tsong, 2013). In this article, we propose a power equation based on multivariate normal distribution of TQT trials. Sample sizes of various TQT designs can be obtained through numerical iteration of the equation.