The clinical utility of pharmacometric models

Pharmacometric models are powerful tools that can be used for a variety of purposes in clinical pharmacology, drug development and dose individualization. Lewis Sheiner famously described the process of learning versus confirming in the setting of drug development 1 and as applied to pharmacometrics. An example of learning is the quantitative description of the human coagulation network 2 which was then paired with prospective clinical data 3 to confirm the predictive performance of this model. Additionally, models can be used to help design clinical trials via simulation 4 and even provide information for the labelling of drug products 5. The clinically relevant goal is to determine if and how doses can be individualized.

There are limitations to the use of pharmacometric approaches, and this is the most relevant for models that are built for the purpose of learning. Sometimes, these models are limited by the data driving model development (e.g. population size and variability; i.e. healthy volunteer studies). In this case, the ability to extrapolate the model needs to be verified in a well‐designed clinical trial in the appropriate population or via external model validation. Even validated ^, (confirming) models have limitations. An example of these limitations includes whether all the necessary information to execute the model (i.e. covariates) are available. If they are not, the model cannot be used clinically.

The motivation for this editorial was a recently published paper in this journal that described an external model validation 7 for a previously published model 8. This model was used to investigate the influence of organ failure, as well as inflammation (using C‐reactive protein as a biomarker) on midazolam clearance in critically ill children 8. The work reported in the paper sought to evaluate the predictability of the original model in children and extrapolate the predictability in two new populations, namely, adults and preterm neonates 7. However, the original model did not accurately predict the clearance or concentrations of midazolam in preterm neonates (median prediction error; MPE > 60%, Table 1), and the authors correctly concluded that this model was not applicable to this population.

Table 1.

Median prediction error (MPE) for predicted concentrations vs. observed concentrations, and individual‐predicted clearance vs. population‐predicted clearance

		MPE% a
Datasets	Patient population	Plasma concentrations	Clearance
Model building	Critically ill children	−13.7	5.27
New data for external validation	Critically ill children	−14.1	25.4
	Infants after cardiac bypass surgery	3.1	22.0
New data for extrapolation	Preterm neonates	−63.5	1746
	Preterm neonates	−68.3	186
	Healthy male adults	−35.6	1.48
	Critically ill adults	−40.6	−1.67

Table modified from 6.

^aThe MPE is the median of the prediction error, which reflects for plasma concentrations the percentage difference in observed and predicted concentrations. For clearance, the difference in individual predicted and population‐predicted clearance was calculated.

At face value, the MPEs (based on population level predictions) for clearance values were <30% in all groups aged from term neonates through to adults (Table 1). It would have been useful to include variability parameters around the estimates of the MPEs (e.g. confidence interval or an estimate of precision). The model underpredicted concentrations of midazolam in adults by around 60% (Table 1). A dose prediction based on this model would result in a higher, potentially toxic, dose. The authors correctly suggested that the underprediction occurred due to the original model not accurately estimating the volume of distribution in adults.

The limitation of the paper is that the analysis is done using population‐level predictions. Ideally, the model could be used with individual data (drug concentrations and covariates) and adaptive Bayesian dose prediction 9. The advantage of this method is that it balances the influence of the population model as well as the individual patient data, and this may improve the predictive performance of the model in paediatric patients. It may also be possible to improve the concentration predictions in adults despite the weakness in the model highlighted above. This method fully maximizes the potential for pharmacometric models to individualize therapy. In populations such as preterm neonates where sampling is difficult, adaptive dosing may not be feasible, so the population‐level predictions must suffice for guiding dosing.

After reviewing this paper, we think that in general, authors publishing pharmacometric models must provide sufficient detail in the Methods section so that those familiar with the methodology can learn from and apply these methods in their work. This may be achieved with supplementary materials, an example of this is the paper by Duong et al. where supplementary methods were provided to describe the modelling in more detail than was provided in the main text 10. Furthermore, for reader wanting to learn more about pharmacometric models, a good introduction to interpreting pharmacometric models can be found in the paper by Wright et al. 11 and the review by Standing 12. A good way to identify pharmacometric models with clinical utility is whether they have dose simulations based on patient characteristics such as body weight 13 or renal function 14 or if they explore the appropriateness of current clinical guidelines for dosing 15, 16.

Different types of pharmacometric models serve different purposes and their clinical utility is dependent on this context. The motivating example in this editorial was a model validation paper. The paper did verify the predictive performance of the published model in a similar patient population on which it was built, but could not be extrapolated to new populations. This paper demonstrates that the previously published model can be used to predict midazolam doses in children but not in preterm neonates or adults.

Kumar, S. S. , Biltaji, E. , Bies, R. , and Sherwin, C. M. (2018) The clinical utility of pharmacometric models. Br J Clin Pharmacol, 84: 1413–1414. doi: 10.1111/bcp.13603.