![Sample our Bioscience journals, sign in here to start your access, Latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5925/TOC-Subject-Sample-2021-Bioscience.jpg"})
Abstract
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 (Citation2008) 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, Citation2011; Tsong, Citation2013). 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.
ACKNOWLEDGMENTS
This project evolved through many discussions with our colleagues in Food and Drug Administration (FDA) and the National Health Research Institute in Taiwan. Here are a few that we want to acknowledge: Drs. Joanne Zhang, Xiaoyu Dong, and Hsiao Hui Tsou. We also thank Dr. Jie Chen of Merck Serono (Beijing) for his careful reading and constructive comments of the original article. The article is greatly improved based on the comments.
Notes
(1) Trial-wise type I error α = 0.05.
(2) Trial-wise power 1 − β = 0.90.
(3) Assume a simple compound symmetry structure for the variance-covariance matrix, ρ TP = 0.1.
O* Sample size based on formula (4) with β′ = 1 − (1 − β*)1/K .
(1) Trial-wise type I error α = 0.05.
(2) Trial-wise power 1 − β = 0.90.
(3) Assume a simple compound symmetry structure for the variance-covariance matrix, ρ TP = 0.1.
O** Sample size based on formula (7) with β′ = 1 − (1 − β*)1/K .
(1) Trial-wise α = 0.05.
(2) Trial-wise 1 − β = 0.90.
(3) Assume a simple compound symmetry structure for the variance-covariance matrix.
Original sample size based on formula (4) and β′ = 1 − (1 − β*)1/4.
(1) Trial-wise α = 0.05.
(2) Trial-wise 1 − β = 0.90.
(3) Assume a simple compound symmetry structure for the variance-covariance matrix.
Original sample size based on formula (7) with β′ = 1 − (1 − β*)1/4.
(1) Trial-wise α = 0.05.
(2) Trial-wise 1 − β = 0.90.
(3) Assume a simple compound symmetry structure for the variance-covariance matrix.
Original sample size based on formula (7) with β′ = 1 − (1 − β*)1/4.
(1) Trial-wise α = 0.05.
(2) Trial-wise 1 − β = 0.90.
(3) Assume a simple compound symmetry structure for the variance-covariance matrix.
Origial sample size based on formula (10). α* is calculated based on formula (12).
(1) Trial-wise α = 0.05.
(2) Trial-wise 1 - β = 0.90.
(3) Assume a simple compound symmetry structure for the variance-covariance matrix.
Original sample size based on formula (11). α* is calculated based on formula (12).
*(1) Trial-wise α = 0.05.
(2) Trial-wise 1 − β = 0.90.
(3) Assume a simple compound symmetry structure for the variance-covariance matrix.
Original sample size based on formula (11). α* is calculated based on formula (12).
This article represents the point of views of the author. It does not necessarily represent the official position of U.S. FDA.