STATISTICAL PROPERTIES OF FITTED ESTIMATES OF APPARENT IN VIVO METABOLIC CONSTANTS OBTAINED FROM GAS UPTAKE DATA. I. LIPOPHILIC AND SLOWLY METABOLIZED VOCs

Abstract

Gargas et al. (1986) demonstrated that the physiologically based simulation approach could be used to obtain information about rodent in vivo metabolic kinetics from gas uptake data. This statistical approach has been widely used to estimate apparent in vivo metabolic constants for use in physiologically based pharmacokinetics (PBPK) models. Despite extensive use of this methodology and the potential importance of the resulting fitted estimates of metabolic constants to the estimation of health risk, a formal evaluation of the statistical properties of this estimation procedure as applied to gas uptake data has not been performed. This article describes results from a computer simulation study to investigate three important statistical properties of this estimation procedure: bias (whether fitted estimates on average predict the true population mean), efficiency (whether fitted estimates tend to concentrate over a narrow range), and consistency (whether fitted estimates concentrate in a narrower and narrower range as sample size increases). These three statistical properties were evaluated as a function of (1) the number of experimental replicates per concentration range, (2) the choice of initial chamber concentrations, (3) the knowledge of animal-specific physiology, and (4) the conduct of experiments with a single versus multiple animals in a chamber. Carbon tetrachloride was used as a lipophilic and slowly metabolized model compound. Simulated gas uptake data were generated to reflect two major sources of variation: experimental error (2% coefficient of variation, CV) and animal-to-animal heterogeneity in physiologic and anatomic quantities (5-10% CV). Fitted estimates of metabolic constants obtained from simulated data were generally found not to exhibit significant bias. However, the physiologically based simulation approach as usually applied was found to be a relatively inefficient estimation procedure for the model compound (i.e., a large spread in fitted estimates of apparent in vivo metabolic constants about the true population mean). A single simulated data set consisting of triplicate gas uptake experiments at each of 4 different chamber concentrations was capable of giving fitted estimates of metabolic constants differing from the specified population mean by 50 to 100%. Simulation studies also indicated that the usual error model invoked for gas uptake data is incorrect, with the deleterious consequence of giving overly precise estimates of precision for fitted estimates of metabolic constants. Based on the simulation results, a tiered approach is proposed for design and conduct of gas uptake studies, with the objective of identifying a more efficient design for estimating metabolic constants.