Beyond the linear model in concentration-QT analysis

The white-paper regression model is the standard method for assessing QT liability of drugs. The quantity of interest, placebo-corrected QTc change from baseline (ΔΔQTc) with corresponding confidence interval (CI), is derived from the difference in model-estimated ΔQTc for active compound and placebo in a linear model. Model assumptions include linearity and no time delay between change in concentration and change in ΔQTc. Alternative models are commonly not considered unless there is a clear indication of inappropriateness of the assumptions. This work introduces several extensions for concentration-QT modeling in a pharmacometric context. The model is formulated as linear drug-effect model with treatment, nominal time, and centered baseline as covariates on the intercept. This approach enables straightforward use of other concentration-ΔQTc relationships, including loglinear, E_max, and indirect-effects models. In addition, the setup allows for the use of pharmacometric model assessments for ΔQTc and ΔΔQTc, including visual predictive checks and quantitative model comparison based on the Bayesian information criterion. The proposed approach is applied to several compounds from a previously published QTc study. The results suggest that a nonlinear mixed-effects model for ΔΔQTc and comparing a set of candidate models quantitatively can be a more powerful approach than fitting only the white-paper regression model. A semi-automated approach that compares nonlinear and hysteresis models to the linear model enables a reliable choice of the best model and determination of the degree of prolongation at the concentration of interest. Standard pharmacometric tools can assess the appropriateness of the models and the potential extent of hysteresis.