Evaluating the Use of Linear Mixed-Effect Models for Inference of the Concentration-QTc Slope Estimate as a Surrogate for a Biological QTc Model

Abstract

In concentration-QTc modeling, oscillatory functions have been used to characterize biological rhythms in QTc profiles. Fitting such functions is not always feasible because it requires sufficient electrocardiograph sampling. In this study, drug concentration and QTc data were simulated using a published biological QTc model (oscillatory functions). Then, linear mixed-effect models and the biological model were fitted and evaluated in terms of biases, precisions, and qualities of inferences. The simpler linear mixed-effect model with day and time as a factor variables provided similar accuracy of the concentration-QTc slope estimates to the complex biological model and was able to accurately predict the drug-induced QTc prolongation with less than 1 ms bias, despite its empirical nature to account for biological rhythm. The current study may guide a concentration-QTc modeling strategy that can be easily prespecified, does not suffer from poor convergence, and achieves little bias in drug-induced QTc estimates.

Figure 1

Box and whisker plots of the estimation errors for drug effect model parameters in different T_max scenarios of TQT study design. Models 1, 2, and 3 represent linear mixed effects models 1, 2, and 3, respectively, and the biological model represents a reduced model consisting of only one cosine function. Boxes denote the 25^th and 75^th percentiles and the filled circles inside the box denotes the median. Whiskers represent the 5^th and 95^th percentiles.

Figure 2

Coverage probability of slope estimates and false positive slopes. (a) Coverage probability of slope estimates containing the true slope calculated with 90% confidence intervals of slope estimates in 5 ms QTc prolongation scenario and (b) % false positive slopes of linear mixed effects models in the no QTc prolongation scenario (95% confidence interval excludes 0). Dashed line represents the 2.5% type 1 error.

Figure 3

Box and whisker plots of the estimation errors for drug effect model parameters in different T_max scenarios of phase 1 study design. Models 1, 2, and 3 represent linear mixed effects models 1, 2, and 3, respectively. Boxes denote the 25^th and 75^th percentiles and closed circle inside the box denotes the median. Whiskers represent the 5^th and 95^th percentiles.

Figure 4

Box and whisker plots of the estimation errors for ddQTc in different T_max scenarios of both TQT and phase 1 studies. Linear mixed effect model 2 was selected as the best model and difference between true ddQTc (true concentration × true slope) and model-predicted ddQTc (observed concentration x slope estimates) were calculated in ms. Boxes denote the 25^th and 75^th percentiles and closed circle inside the box denotes the median. Whiskers represent the 5^th and 95^th percentiles.