Two bootstrapping routines for obtaining imprecision estimates for nonparametric parameter distributions in nonlinear...

Area of Science:

• Pharmacometrics
• Statistical Modeling
• Computational Biology

Background:

• Estimating imprecision is crucial for parameter estimates used in predictions and decisions.
• Current methods lack imprecision estimates for nonparametric algorithms in nonlinear mixed effects models.
• Nonparametric distribution (NPD) estimation is valuable for characterizing complex population variability.

Purpose of the Study:

• To develop and validate resampling-based methods for estimating imprecision in NPD estimates.
• To assess the performance of these methods across different underlying distributional shapes (normal, bimodal, heavy-tailed).

Main Methods:

• Simulated pharmacokinetic datasets with varying random effects distributions.
• Developed two bootstrapping methods: a full method (re-estimating parametric and nonparametric steps) and a simplified method (resampling individual NPDs).
• Estimated nonparametric 95% confidence intervals (CIs) and computed mean errors (MEs) of CI width; evaluated standard errors (SEs) via stochastic simulations.

Main Results:

• Both developed methods successfully provided imprecision estimates for NPDs.
• Imprecision estimates accurately reflected reference imprecision across all tested distributional shapes and dataset sizes.
• Simplified method's SEs were consistent with those from extensive simulations; relative MEs for CI width were within acceptable ranges.

Conclusions:

• Two novel bootstrapping methods are proposed for estimating imprecision in nonparametric methods within nonlinear mixed effects modeling.
• These methods provide essential information on the precision of nonparametric parameter estimates.
• The proposed methods can serve as valuable diagnostic tools for identifying misspecified parameter distributions.