Comparing models for perfluorooctanoic acid pharmacokinetics using Bayesian analysis

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Abstract

Selecting the appropriate pharmacokinetic (PK) model given the available data is investigated for perfluorooctanoic acid (PFOA), which has been widely analyzed with an empirical, one-compartment model. This research examined the results of experiments [Kemper R. A., DuPont Haskell Laboratories, USEPA Administrative Record AR-226.1499 (2003)] that administered single oral or iv doses of PFOA to adult male and female rats. PFOA concentration was observed over time; in plasma for some animals and in fecal and urinary excretion for others. There were four rats per dose group, for a total of 36 males and 36 females. Assuming that the PK parameters for each individual within a gender were drawn from the same, biologically varying population, plasma and excretion data were jointly analyzed using a hierarchical framework to separate uncertainty due to measurement error from actual biological variability. Bayesian analysis using Markov Chain Monte Carlo (MCMC) provides tools to perform such an analysis as well as quantitative diagnostics to evaluate and discriminate between models. Starting from a one-compartment PK model with separate clearances to urine and feces, the model was incrementally expanded using Bayesian measures to assess if the expansion was supported by the data. PFOA excretion is sexually dimorphic in rats; male rats have bi-phasic elimination that is roughly 40 times slower than that of the females, which appear to have a single elimination phase. The male and female data were analyzed separately, keeping only the parameters describing the measurement process in common. For male rats, including excretion data initially decreased certainty in the one-compartment parameter estimates compared to an analysis using plasma data only. Allowing a third, unspecified clearance improved agreement and increased certainty when all the data was used, however a significant amount of eliminated PFOA was estimated to be missing from the excretion data. Adding an additional PK compartment reduced the unaccounted-for elimination to amounts comparable to the cage wash. For both sexes, an MCMC estimate of the appropriateness of a model for a given data type, the Deviance Information Criterion, indicated that this two-compartment model was better suited to describing PFOA PK. The median estimate was 142.1 ± 37.6 ml/kg for the volume of the primary compartment and 1.24 ± 1.1 ml/kg/h for the clearances of male rats and 166.4 ± 46.8 ml/kg and 30.3 ± 13.2 ml/kg/h, respectively for female rats. The estimates for the second compartment differed greatly with gender—volume 311.8 ± 453.9 ml/kg with clearance 3.2 ± 6.2 for males and 1400 ± 2507.5 ml/kg and 4.3 ± 2.2 ml/kg/h for females. The median estimated clearance was 12 ± 6% to feces and 85 ± 7% to urine for male rats and 8 ± 6% and 77 ± 9% for female rats. We conclude that the available data may support more models for PFOA PK beyond two-compartments and that the methods employed here will be generally useful for more complicated, including PBPK, models.

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