Model-Based Correction to the QT Interval for Heart Rate for Assessing Mean QT Interval Change Due to Drug Effect

Abstract

Drugs that alter ventricular repolarization have been associated with malignant ventricular arrhythmia, which has been shown to increase with increasing QT interval—the time required for ventricular depolarization and repolarization. To determine whether a new drug, especially a nonanti-arrhythmia drug, can cause an increase in the QT interval is a necessary step in safety evaluation. Since the QT interval is inversely related to the heart rate, this relationship needs to be accounted for in the assessment of drug effect. In current practice, the most commonly-used approach for assessing mean change in the QT interval is to correct the QT interval by one of many competing correction methods to QT_C, then to conduct statistical analysis on QT_C, a disjoint two-step approach. The shortcomings of such an approach are: 1. The correction formulas often fail to correct the QT interval for the change in heart rate and this can lead to biased estimation of the drug effect; and 2. The analysis based on QT_C only provides estimation of the drug effect at a fixed heart rate (60 bpm), which ignores potential interaction between the drug effect on the QT interval and the heart rate. The analysis based on QT_C also ignores the variability in data-driven correction formulas, which can lead to incorrect inferences.

In this article a new approach is proposed based on statistical modeling of the functional relationship between the QT interval and the heart rate. Such modeling captures the nature of the relationship between the QT interval and the heart rate based on measurements from placebo subjects or at baseline, then uses this relationship to provide adjustments to the estimation of the drug effect on the QT interval for the heart rate change at a given heart rate. The key idea behind this new approach is that the potential drug effect on the QT interval at a given heart rate can be perceived as the change in the QT interval after dosing -the change in QT interval due to the heart rate after dosing. This new approach unifies the two-step procedure into a one-step analysis so that the estimated drug effect is always adjusted for the heart rate change and the variability of the estimated QT interval and heart rate relationship is taken into account in the inferential statistics for the drug effect automatically. Finally, this new approach is demonstrated in an example.