An Approximate Method for Population Toxicokinetic Analysis With Aggregated Data

Abstract

Standard statistical models for analyzing inter-individual variability in clinical pharmacokinetics (nonlinear mixed effects; hierarchical Bayesian) require individual data. However, for environmental or occupational toxicants only aggregated data are usually available, so toxicokinetic analyses typically ignore population variability. We propose a hierarchical Bayesian approach to estimate inter-individual variability from the observed mean and variance at each time point, using a bivariate normal (or lognormal) approximation to their joint likelihood. Through analysis of both simulated data and real toxicokinetic data from 1,3-butadiene exposures, we conclude that given information on the form of the individual-level model, useful information on inter-individual variability may be obtainable from aggregated data, but that additional sensitivity and identifiability checks are recommended.