Statistical issues of QT prolongation assessment based on linear concentration modeling

The ICH (2005) defined drug-induced prolongation of QT interval, i.e., the duration of depolarization and repolarization of ventricles, as evidenced by an upper bound of the 95% confidence interval around the mean effect on QTc (QT corrected for heart rate) of 10ms. Furthermore, it defined that 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 10ms. This objective leads to the application of intersection-union tests by testing the mean difference between test treatment and placebo of QTc change from baseline at each of the matched time points at which the observations are collected. The nature of the higher false positive rate due to more observational time points leads to the concern of study efficiency. Based on the concept of clinical pharmacology, a concentration-response modeling approach is often adopted to assess the prolongation size of QTc interval induced by a drug without carefully examining the validity of the assumptions involved. In most of the applications, the model is assumed either to be linear, log-linear, or logistic. The supporter of the modeling often emphasizes the advantage of power improvement and reduction in estimation error. However, it has been often pointed out by statisticians and pharmacologists that modeling under an invalid uniformity assumption across study population often leads to severe bias in testing and estimation. In this article, we examine data sets of New Drug Applications to illustrate the bias and lack of validity of the linearity assumptions.