Mixed effects modeling of concentration-QT relationships: first experiences with the new white paper
Andrea Henrich, Mike Ufer, Pierre-Eric Juif, Jasper Dingemanse, Andreas Krause
Idorsia Pharmaceuticals Ltd
Objectives: The ICH guidance documents on the analysis of drug effects on QT interval length [1, 2] were recently enhanced by a white paper with FDA scientists among its authors [3]. The technical paper defines standard analyses to evaluate QT effects at an appreciated level of detail. This work presents first experiences with this particular approach and highlights aspects that require further discussion.
Methods: A single-ascending dose study in healthy subjects provided concentration and ECG data of 6 dose groups with 8 subjects each (6 on active treatment, 2 on placebo). The compound, ACT-246475, an antiplatelet agent, was administered at doses from 1 to 32 mg [4].
Linear mixed effects (LME) modeling was employed to evaluate the effect of ACT-246475 on QT interval length change from baseline (DQTcF) [3, 5]. Estimation of intercept and slope included covariates on the intercept: treatment (active/placebo), deviation of individual baseline QTcF from average baseline QTcF (DBL), and time (categorical).
For placebo-corrected change from baseline QTcF (DDQTcF) mean and 90% confidence interval (CI), a QT effect is indicated if the upper bound of the 90% CI exceeds the regulatory threshold of 10 ms. The mean concentration-DDQTcF effect in the closed-form solution was calculated as DQTcF difference between active and placebo [3, eq. 2-5].
Robustness of results was assessed by varying concentration scale (linear vs logarithmic), analysis method (LME vs ordinary-least-squares (OLS) concentration-DDQTcF regression), derivation of CI by closed-form solution vs bootstrapping (BS). Data set programming, visualization, and modeling were performed using R and packages lme4 and ggplot2.
Results: Using concentration on a linear scale compared to logarithmic scale made a large difference. The linear scale is recommended in [3] due to undefined logarithmic values of 0 concentration (with placebo). However, on a linear scale, extreme values have a higher leverage towards the results. These few extreme observations cause the CI for the mean to be very wide. Therefore, the upper limit of the two-sided 90% CI is more likely to exceed the threshold of 10 ms, leading to a positive finding, i.e., a QT effect.
In the present case study, the linear concentration scale caused the CI to exceed the threshold of 10 ms at a substantially lower concentration (663 vs 1456 ng/mL). However, the CI of the mean included most data in the high concentration range, an implausible result since a CI can reasonably be expected to be substantially smaller than a 90% coverage interval.
Using a logarithmic scale and setting concentrations below the lower limit of quantification (LLOQ) to the LLOQ seems a reasonable choice. Setting them to smaller values can substantially influence the results, making these arbitrary to some extent.
Even though not recommended [3], rescaling of concentration was necessary to obtain model fits. Not normalizing resulted in failed convergence (lmer in R, package lme4).
OLS regression resulted in a significantly lower slope estimate (10.7 ms*mL/ng) compared to the pre-specified linear mixed-effects model (45.0 ms*mL/ng). These differences might arise from the DBL covariate in the pre-specified model.
While the CI, the key statistic in QT assessment, can be derived in closed form for the standard model, it must be derived by other means (e.g., BS) if covariates are included. This case study showed that BS CIs for concentration on the linear scale without covariates require a very large number of BS samples (10,000 or more) to be close to the closed-form solution (mean of 3.039 ms at 1305 ng/mL with closed-form solution and 3.3616 and 3.126 ms with 1000 and 10000 BS samples, respectively). This finding reflects the sensitivity of the results towards extreme values, i.e., whether or not a BS sample includes extreme values.
The exact distribution of DDQTcF follows a t-distribution. Defining the degrees of freedom is not straightforward in a mixed-effects model and [3] do not provide guidance here. We suggest that a normal distribution serves sufficiently well as approximation.
Conclusion: Even though the white paper [3] is specific in modeling details, some points of discussion remain. This case study suggests remedies and identifies a few areas for further investigation. Using a logarithmic scale for concentration data seems preferable for numerical robustness of results. For linear scales, normalization is indicated to achieve robust results.
References:
[1] ICH E14 International Council for Harmonization of technical requirements for registration of pharmaceuticals for human use. The clinical evaluation of QT/QTc interval prolongation and proarrhythmic potential for non-antiarrhythmic drugs. 2005.
[2] U.S. Department of Health and Human Services, Food and Drug Administration. E14 Clinical Evaluation of QT/QTc Interval Prolongation and Proarrhythmic Potential for Non-Antiarrhythmic Drugs — Questions and Answers (R3), Guidance for Industry. 2017.
[3] Garnett C. et al. Scientific white paper on concentration-QTc modeling. J. Pharmacokinet. Pharmacodyn. 2018.
[4] Juif P.-E. et al. Clinical safety, pharmacokinetics, and pharmacodynamics of ACT-246475: A selective reversible P2Y12 receptor antagonist. ASCPT poster PII-063, abstract #589. 2018.
[5] Fridericia L. S. The duration of systole in an electrocardiogram in normal humans and in patients with heart disease. 1920. Ann Noninvasive Electrocardiol 4;343-51. 2003.