Influence of covariate distribution on the predictive performance of pharmacokinetic models in paediatric research

Abstract

Aims: The accuracy of model-based predictions often reported in paediatric research has not been thoroughly characterized. The aim of this exercise is therefore to evaluate the role of covariate distributions when a pharmacokinetic model is used for simulation purposes.

Methods: Plasma concentrations of a hypothetical drug were simulated in a paediatric population using a pharmacokinetic model in which body weight was correlated with clearance and volume of distribution. Two subgroups of children were then selected from the overall population according to a typical study design, in which pre-specified body weight ranges (10-15 kg and 30-40 kg) were used as inclusion criteria. The simulated data sets were then analyzed using non-linear mixed effects modelling. Model performance was assessed by comparing the accuracy of AUC predictions obtained for each subgroup, based on the model derived from the overall population and by extrapolation of the model parameters across subgroups.

Results: Our findings show that systemic exposure as well as pharmacokinetic parameters cannot be accurately predicted from the pharmacokinetic model obtained from a population with a different covariate range from the one explored during model building. Predictions were accurate only when a model was used for prediction in a subgroup of the initial population.

Conclusions: In contrast to current practice, the use of pharmacokinetic modelling in children should be limited to interpolations within the range of values observed during model building. Furthermore, the covariate point estimate must be kept in the model even when predictions refer to a subset different from the original population.

Keywords: covariates; model predictive power; paediatrics; simulations.

Figure 1

Diagram depicting the steps of the investigation. Simulation of the pharmacokinetic profiles and subsequent model building using the data from a population of 43 children and from the two subgroups with differing body weight ranges. The simulation scenarios are based on a model in which clearance and body weight are exponentially correlated [i.e. CL = θ₁*(WT/WTMedian)**θ₂].

Figure 2

Visual predictive check of the models obtained from the fit of the simulated plasma concentrations of the children in the full population (group C) (A) in subgroup A (B) when body weight was exponentially correlated to clearance with an exponent of 0.65

Figure 3

Predicted AUC distribution in subgroup B based on model parameter estimates obtained from data fitting of subgroup A. Upper panels show prediction distributions for an exponential correlation between clearance and body weight with an exponent of 0.65, whilst lower panels show prediction distributions for an exponent of 1.5. The line represents the true point estimate for AUC in the population. In the left panels the difference in the covariate distribution between subgroups A and B is not taken into account, with the median of the weight distribution in subgroup A being used in the simulations. In the right panels a shift is observed in the predictions when the covariate range of subgroup B is used in the simulations

Figure 4

Predicted AUC distribution in subgroup A based on model parameter estimates obtained from data fitting of the full population (group C). Upper panels show prediction distributions for an exponential correlation between clearance and body weight with an exponent of 0.65, whilst the lower panels show prediction distributions for an exponent of 1.5. The line represents the true value of AUC in the population. In the left panels the difference in the covariate distribution between group C and subgroup A is not taken into account, with the median of the weight distribution of subgroup C being used in the simulations. In the right panels a shift is observed in the predictions when the covariate range of subgroup A is used in the simulations

Figure 5

Predicted AUC distribution in subgroup B based on model parameter estimates obtained from data fitting of the full population (group C). Upper panels show prediction distributions for an exponential correlation between clearance and body weight with an exponent of 0.65, whilst the lower panels show prediction distributions for an exponent of 1.5. The line represents the true value of AUC in the population. In the left panels the difference in the covariate distribution between group C and subgroup B is not taken into account, with the median of the weight distribution of subgroup C being used in the simulations. In the right panels a shift is observed in the predictions when the covariate range of subgroup B is used in the simulations

Figure 6

Predicted AUC distribution in subgroup A based on model parameter estimates obtained from data fitting of the full population (group C) for an exponential correlation between clearance and body weight with an exponent of 0.84 and an exponential correlation between volume of distribution and body weight with an exponent of 0.807. The line represents the true value of AUC in the population. In the left panel the difference in the covariate distribution between group C and subgroup A is not taken into account, with the median of the weight distribution of subgroup C being used in the simulations. In the right panel a shift is observed in the predictions when the covariate range of subgroup A is used in the simulations

Figure 7

Predicted AUC distribution in subgroup B based on the model parameter estimates obtained from data fitting of subgroup A. The histograms show AUC predictions for a linear relation between clearance and body weight with a slope of 1.5. The line represents the true value of AUC in the population. In the left panel the difference in the covariate distribution between subgroups A and B is not taken into account, with the median of the weight distribution of subgroup A being used in the simulations. In the right panel a shift is observed in the predictions when the covariate range of subgroup B is used in the simulations