QT analysis: a complex answer to a 'simple' problem.
Prolongation of the QT interval on a surface electrocardiogram is a biomarker for a potentially life-threatening arrhythmia. It is used by drug developers and regulatory agencies as a measure of drug safety. Heart rate or RR interval (the inverse of heart rate) correction of the QT interval is necessary because of the QT interval shortening that accompanies physiologic decreases in the RR interval. When a drug alters the RR interval, it is important to distinguish a QT change that is due to a drug effect versus an artefact of a heart rate change. A two-step off-drug subject-specific QT correction analysis is discussed. At the first step, a linear mixed model based only on the placebo (off-drug) RR/QT data produces a correction coefficient that can be applied to a generic formula, and QT intervals are corrected for heart rate on both placebo and treatment period data using that formula. At step two, the heart rate corrected QT interval (QTc) is then compared between placebo and treatment groups at a pre-specified heart rate (usually 60 bpm) based on another linear mixed model. This two-step QT analysis implicitly assumes the slope of log(QT) versus log(RR) is unchanged by drug. Practically, it is important to understand how much this assumption can bias the QT prolongation estimates if it is not valid. We propose a one-step off-on-drug subject-specific QT correction analysis that would pool placebo and treatment period RR/QT data and derive different subject specific coefficients for the treatment and placebo data based on a linear mixed model, which can avoid the unchanged slope assumption. It is also a known unbiased and the most efficient method. The applications of both methods are demonstrated through the QT analysis of haloperidol, a neuroleptic known to prolong QTc. Both theoretical and empirical results show that, although the two-step off-drug QT correction analysis is biased, the bias is small in the case of haloperidol (0.1-0.2 ms). The two-step off-drug QT correction analysis is shown to be almost as efficient as our one-step off- and on-drug QT analysis.