The effects of active metabolites on parameter estimation in linear mixed effect models of concentration–QT analyses

Abstract

Monte Carlo simulation was used to assess the performance of linear mixed effect models (LMEMs) to characterize the concentration-effect relationship when both parent and metabolite concentrations were available. Parent and metabolite concentrations were simulated under an experimental design that mimicked a thorough QT study. Simulations were done where both parent and metabolite concentration prolonged double-delta time-matched placebo controlled QTc (ddQTc) intervals. LMEMs were then estimated where parent and metabolite concentrations, parent concentrations alone, or metabolite concentrations alone were used as the independent variables. The relative error in the estimation of the parent and metabolite slope compared to known theoretical values was calculated. Additional simulations were done comparing the estimate of the one-sided upper 95% confidence interval at 1 time unit post-dose in an under- and overfit model compared to the true data generating model. When both parent and metabolite were included in the LMEM and both parent and metabolite prolonged ddQTc intervals, despite some high correlations between parent and metabolite concentrations, under all conditions the parent slope parameter θ(p) was estimated with good accuracy, having a mean relative error within ±20% of the true value, whereas estimation of the metabolite slope θ(m) was overpredicted with bias increasing as the ratio of the metabolite elimination rate constant (K(elm)) to metabolite formation rate constant (K(f)) increased. Variability in θ(m) relative error increased as the metabolite potency decreased. Metabolite ratio had no effect on the ability to estimate the parent or metabolite slope. When only parent or metabolite concentration was used as the independent variable in a LMEM and both parent and metabolite concentrations prolonged ddQTc intervals, severe omitted variable bias resulted. When estimating the one-sided upper 95% confidence interval, underfitted models tended to have higher predicted values which would suggest that an underfitted model would be more likely to declare a "QT effect", whereas an overfitted model resulted in little difference compared to the true model. When time-matched parent and metabolite concentrations are available, both parent and metabolite concentrations should be included in the model simultaneously recognizing that the estimation of the metabolite slope may be biased under certain conditions. It is better to have an overfitted model than an underfitted model, although model simplification through removal of nonsignificant model terms in an overfitted model should not be neglected. Including both parent and metabolite concentrations in a model, even when the metabolite does not affect ddQTc intervals, does not tend to result in biased parameter estimates and in most cases will not result in inflated confidence intervals for predicted values, e.g., around maximal concentrations at the therapeutic dose. It is recommended that when time-matched parent and metabolite concentrations are available, parent and metabolite concentrations not be analyzed separately because either one or the other will result in biased parameter estimates and inflated point estimates and confidence intervals for predicted values.