title: Identifiability of PBPK models with applications to dimethylarsinic acid exposure.
abstract: Any statistical model should be identifiable in order for estimates and tests using it to be meaningful. We consider statistical analysis of physiologically-based pharmacokinetic (PBPK) models in which parameters cannot be estimated precisely from available data, and discuss different types of identifiability that occur in PBPK models and give reasons why they occur. We particularly focus on how the mathematical structure of a PBPK model and lack of appropriate data can lead to statistical models in which it is impossible to estimate at least some parameters precisely. Methods are reviewed which can determine whether a purely linear PBPK model is globally identifiable. We propose a theorem which determines when identifiability at a set of finite and specific values of the mathematical PBPK model (global discete identifiability) implies identifiability of the statistical model. However, we are unable to establish conditions that imply global discrete identifiability, and conclude that the only safe approach to analysis of PBPK models involves Bayesian analysis with truncated priors. Finally, computational issues regarding posterior simulations of PBPK models are discussed. The methodology is very general and can be applied to numerous PBPK models which can be expressed as linear time-invariant systems. A real data set of a PBPK model for exposure to dimethyl arsinic acid (DMA(V)) is presented to illustrate the proposed methodology.
authors.affiliation: Department of Biostatistics, University of North Carolina, Chapel Hill, NC, 27599, USA.
authors.forename: Ramon I
authors.initials: RI
authors.lastname: Garcia
authors.affiliation: Department of Biostatistics, University of North Carolina, Chapel Hill, NC, 27599, USA.
authors.forename: Joseph G
authors.initials: JG
authors.lastname: Ibrahim
authors.affiliation: United States Environmental Protection Agency, National Center for Computational Toxicology, Research Triangle Park, NC, 27711, USA.
authors.forename: John F
authors.initials: JF
authors.lastname: Wambaugh
authors.affiliation: United States Environmental Protection Agency, National Health and Environmental Effects Laboratory, Research Triangle Park, NC, 27711, USA.
authors.forename: Elaina M
authors.initials: EM
authors.lastname: Kenyon
authors.affiliation: United States Environmental Protection Agency, National Center for Computational Toxicology, Research Triangle Park, NC, 27711, USA. setzer.woodrow@epa.gov.
authors.forename: R Woodrow
authors.initials: RW
authors.lastname: Setzer
mesh_terms: D000818:Animals; D001499:Bayes Theorem; D001711:Biotransformation; D002101:Cacodylic Acid / Q000009:adverse effects / Q000493:pharmacokinetics* / Q000652:urine; D003198:Computer Simulation; D004781:Environmental Exposure / Q000009:adverse effects; D004785:Environmental Pollutants / Q000009:adverse effects / Q000493:pharmacokinetics* / Q000652:urine; D006801:Humans; D016014:Linear Models; D008744:Methylamines / Q000493:pharmacokinetics; D051379:Mice; D008954:Models, Biological; D015233:Models, Statistical; D018570:Risk Assessment
chemical_list: D004785:Environmental Pollutants; D008744:Methylamines; D002101:Cacodylic Acid; C005855:trimethyloxamine
keywords: Dimethyl arsinic acid; Gibbs sampling; Identifiability; Metropolis–Hasting algorithm; PBPK Models