Bootstrapping for pharmacokinetic models: visualization of predictive and parameter uncertainty

Area of Science:

• Pharmacokinetics and Pharmacodynamics
• Computational Biology and Bioinformatics
• Statistical Modeling

Background:

• Pharmacokinetic (PK) models are essential for understanding drug behavior in the body.
• Assessing the reliability of PK model predictions and parameter identifiability is critical for drug development and clinical application.
• Traditional methods may not fully capture the uncertainty in PK model predictions.

Purpose of the Study:

• To evaluate the utility of bootstrapping methods for quantifying the reliability of predictions derived from individual drug level data fitted to PK models.
• To enhance the understanding of parameter identifiability within complex PK models.
• To establish a method for generating confidence intervals for PK model predictions.

Main Methods:

• Simulation studies utilizing four distinct datasets (A-D) of drug concentration data after a single oral dose.
• Fitting a two-compartment PK model to each dataset.
• Employing bootstrapping techniques to analyze the variability in parameter estimates and generate empirical distributions of steady-state (SS) drug concentration predictions for confidence interval construction.

Main Results:

• Subjects A and B exhibited a narrow confidence region in parameter space, with high coefficient of variation (CV) in bootstrapped parameters (35-90%) but tightly clustered SS drug levels (CVs 2-9%).
• Subjects C and D showed significantly larger CVs for both parameters and predicted drug levels (over 5-fold increase).
• Data for C and D supported at least two PK model manifestations, unlike A and B, indicating potential overparameterization and identifying only one manifestation yielding reliable predictions.

Conclusions:

• Bootstrapping provides valuable insights into PK model parameter identifiability, aiding in model selection and decision-making.
• The method effectively quantifies predictive uncertainty, enabling the formation of confidence intervals for PK predictions when data support a single model manifestation.
• Findings for datasets C and D highlight the implications of implicit overparameterization in PK models and the importance of identifying reliable model structures.