QT prolongation is recognized as a risk factor for cardiac arrhythmia and torsades de points. Adequate QT correction is essential for unbiased estimation of drug effect. However, evaluation of drug effect on QTc is challenging due to multiple source of variability and low precision of QT measures resulting in low signal to noise ratio, high between individual and between occasion variabilities, the presence of circadian rhythm and inadequacy of fixed correction methods such as Bezette’s and Fredericia’s. "Standard" QT analytical methods include 1) largest time-matched mean difference between the drug and placebo (baseline subtracted) over the collection period, 2) time-averaged QT/QTc intervals for each individual, 3) analysis for changes occurring at Cmax for each individual. However, the "standard" methods have limitations: 1) do not provide quantitative information on QT prolongation, potency & activity, 2) unable to simulate most critical situation e.g. supra-therapeutic concentration, and 3) time averaging substantially reduces the sensitivity of the test. Quantitative PK/PD analysis could reduce the risk of false-positive or false-negative signals, and could differentiate drug effect from the multiple source of variabilities. It allows for splitting the overall variability into components and estimate them with sufficient precision in order to provide more reliable assessment of the drug induced QT prolongation. In addition, quantitative PK/PD analysis allows for determining the model-based correction factor α. With adequate data per individual per study day (10-15), mixed effect modeling allows for the determination of subject-specific αi, QTc for a j-th measurement for an i-th individual: QTcij=QTij/RRijαi. If the QTc data are limited for individuals, a population corrector factor could be determined. Heart rate and QT could be subject to circadian rhythm, and can be modeled by 1 or more cosine function with different periods: QTij=QTcmi*RRαi*(1+CIRCi)*(1+εij), where QTcmi is an individual mesor value of the corrected QT interval. Circadian function CIRCi of i-th individual can be modeled for 3 oscillators (24, 12 and 6 h) as: CIRCi=A1i*cos[2π(t-Φ1i)/24]+A2i*cos[2π(t-Φ2i)/12]+A3i*cos[2π(t-Φ3i)/6], where the 1st, 2nd, and 3rd periods are 24, 12, and 6 h; A1i, A2i and A3i are the individual amplitudes; Φ1i, Φ2i, Φ3i are the acrophase parameters; T is the clock time. The optimal number of oscillators is selected based on the likelihood. Adequate capturing baseline QT/RR is essential for quantitative PK/PD analysis, at least 2 assessment days per individual. The predose QTc interval or the mean pretreatment/placebo QTc interval serves as baseline. This baseline should not be a single value, but is an individualized within-day QTci vs. time profile that would be observed if the drug is not given. To model the drug effect, a term Ei, a fractional change in QTci for an individual caused by the drug is added: QTij=QTcmi*RRαi*(1+CIRCi+Ei)*(1+εij), where Ei is a function of Ci, an individual plasma concentration predicted by a separate population PK model, and εij. is the residual error. Linear drug effect model is commonly used, but more complicated Emax (or sigmoidal) model can be used with the availability of adequate data including those at high concentration. For thorough QTc study, addition of the plasma concentration of the positive comparator together with the drug of interest will increase the validity of the study results. In conclusion, quantitative PK/PD analyses that incorporate an individual QT correction, a circadian rhythm, and a drug effect can provide better assessment of cardiovascular safety. It could be more robust with respect to outliers compared to the "standard" methods, and allow for combining two or more studies to increase the power of data analyses.
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