A Confidence Interval for the Maximal Mean QT Interval Change Caused by Drug Effect

A statistical problem of primary interest in a thorough QT/QTc study is that of deciding if a drug is noninferior to placebo in terms of QT/QTc prolongation. A standard way of approaching this problem is to construct a 90% two-sided (or a 95% one-sided) confidence interval, using the t distribution, at each time point in the study for the difference in mean QTc between drug and placebo and to conclude that the drug is noninferior to placebo if the upper end points of all of these confidence intervals is less than a prespecified constant, such as 10 ms. Under standard normality assumptions, this procedure corresponds to both an intersection-union test and the likelihood ratio test of size .05. It is not without its drawbacks, however. It is conservative in that the probability of a type I error may be smaller than the intended level .05. It is also biased, which means that the power function, for some values of parameters in the alternative space, takes values less than .05. The May 12, 2005, draft of the International Conference on Harmonisation E14 guidance states: “a negative ‘thorough QT/QTc study’ is one in which the upper bound of the 95% one-sided confidence interval for the largest time-matched mean effect of the drug on the QTc interval excludes 10 ms.” In this article, we show how an approximate confidence interval can be constructed for the largest difference in population mean QT/QTc between drug and placebo. The interval is approximate in the sense that, as sample sizes increase, the asymptotic probability of coverage is at least as large as intended. The results of simulations on a proposed one-sided 95% confidence interval are provided and discussed. Situations in which this interval works well, and does not work well, are delineated.