Physiological Pharmacokinetic Analysis Using Population Modeling and Informative Prior Distributions

Gelman, Andrew; Bois, Frédéric; Jiang, Jiming

doi:10.1080/01621459.1996.10476708

Cited by 273 publications

(210 citation statements)

References 45 publications

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“…Finally, most of the time, prior physiological information is simply about population averages and is not directly applicable to any particular individual for which data were obtained. Fortunately, all these problems can be solved in a unified way though a Bayesian population toxicokinetic approach, which is worth implementing even in the case of small numbers of study subjects (7)(8)(9)(10). Bayesian statistics provides a natural way of merging a priori knowledge gained by implementing a physiological model, with the in vivo experimental data.…”

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confidence: 99%

Statistical analysis of Clewell et al. PBPK model of trichloroethylene kinetics.

Bois

2000

Environ Health Perspect

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A physiologically based pharmacokinetic model for trichloroethylene (TCE) in rodents and humans was calibrated with published toxicokinetic data sets. A Bayesian statistical framework was used to combine previous information about the model parameters with the data likelihood, to yield posterior parameter distributions. The use of the hierarchical statistical model yielded estimates of both variability between experimental groups and uncertainty in TCE toxicokinetics. After adjustment of the model by Markov chain Monte Carlo sampling, estimates of variability for the animal or human metabolic parameters ranged from a factor of 1.5-2 (geometric standard deviation [GSDI). Uncertainty was of the same order as variability for animals and higher than variability for humans. The model was used to make posterior predictions for several measures of cancer risk. These predictions were affected by both uncertainties and variability and exhibited GSDs ranging from 2 to 6 in mice and rats and from 2 to 10 for humans. The recent development of a comprehensive physiologically based pharmacokinetic (PBPK) model of trichloroethylene (TCE) disposition and metabolism in mice, rats, and humans (1) offers us the opportunity to examine issues of variability and uncertainty for that solvent. In particular, uncertainties in prediction of various cancer dose metrics deserve to be computed, since they could be directly used as input for improved risk assessments.PBPK modeling provides a strong mechanistic basis for prediction of disposition and metabolism of toxicants. Yet much uneasiness remains with the use of these models in toxicology (2). Similarly, as discussed in a recent review and an accompanying commentary, PBPK modeling has not seen the development it promised for therapeutic compounds (3,4). The reason for this essentially lies in the lack of statistical methods for calibrating these models. Because of individual variability and uncertainty, many parameters are difficult to measure accurately even for inbred animal strains. Using input parameters or presenting results in the form of a single value can therefore be very misleading (5). In the absence of rigorous statistical treatment, inference presented by PBPK modeling is largely empirical, hypotheses are left unvalidated, and predictions lack realistic measures of uncertainty. This state of affairs is unfortunate, when considering the consequences (for public health and national welfare) of the decisions made using these models.Obviously, correct statistical treatment of PBPK models is difficult, since these are large nonlinear models with relatively small data sets and a high degree of uncertainty and biological variability (6). It is also essential to respect the fundamental specificity of PBPK models, i.e., their high prior information content, which they provide through the opportunity to use physiological information on parameter values. Yet, although several parameters have physiological meaning and a narrow range of possible values, others-often specific of the com...

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confidence: 99%

Statistical analysis of Clewell et al. PBPK model of trichloroethylene kinetics.

Bois

2000

Environ Health Perspect

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“…Monte Carlo methods are based on a Bayesian statistical approach that involves the use of experimental data to update estimates of a hypothesized "prior" probability distribution for one or more model parameters. Examples of Monte Carlo methods applied to PBPK models can be found in [22][23][24][25][26][27][28][29][30][31].…”

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confidence: 99%

Probabilistic methods for addressing uncertainty and variability in biological models: application to a toxicokinetic model

Banks

Potter

2004

Mathematical Biosciences

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Population variability and uncertainty are important features of biological systems that must be considered when developing mathematical models for these systems. In this paper we present probability-based parameter estimation methods that account for such variability and uncertainty. Theoretical results that establish well-posedness and stability for these methods are discussed. A probabilistic parameter estimation technique is then applied to a toxicokinetic model for trichloroethylene using several types of simulated data. Comparison with results obtained using a standard, deterministic parameter estimation method suggests that the probabilistic methods are better able to capture population variability and uncertainty in model parameters.

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“…We used reference values derived mainly from the Caucasian population. We used Markov Chain Monte Carlo (MCMC) approach to draw samples of these parameters from the posterior distribution (Gelman et al 1996). Each parameter (such as the 133 PC ab 's) came from a population distribution with given mean, and variance.…”

Section: Mcmc For Estimation Of the Posterior Distributionsmentioning

confidence: 99%

“…In this paper, we demonstrated an advantageous approach using Bayesian analysis (Gelman et al 1996) for the estimation of the posterior distribution of human parameters in a physiologically-based pharmacokinetic (PBPK) model that was extrapolated to steady state conditions, which allowed ease of interpretation. The Bayesian approach also made use of available prior information for the estimation of the posterior distribution of the model parameters.…”

Section: Introductionmentioning

confidence: 99%

“…The use of known prior information on the model parameters was not taken into account in these models. The traditional frequentist approach of using a mixture of exponential functions, or simple one or two-compartmental models results in a host of potential problems including statistical issues of identifiability, convergence, as well as the possibility of unrealistic physiologic models (Gelman et al 1996).…”

Section: Introductionmentioning

confidence: 99%

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Estimating metabolic rate for butadiene at steady state using a Bayesian physiologically-based pharmacokinetic model

et al. 2009

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In a study of 133 volunteer subjects, demographic, physiologic and pharmacokinetic data through exposure to 1,3-Butadiene (BD) were collected in order to estimate the percentage of BD concentration metabolized at steady state, and to determine whether this percentage varies across gender, racial, and age groups. During the 20 min of continuous exposure to 2 parts per million (ppm) of BD, five measurements of exhaled concentration were made on each subject. In the following 40 min washout period, another five measurements were collected. A Bayesian hierarchical compartmental physiologically-based pharmacokinetic model (PKPB) was used. Using prior information on the model parameters, Markov Chain Monte Carlo (MCMC) simulation was conducted to obtain posterior distributions. The overall estimate of the mean percent of BD metabolized at steady state was 12.7% (95% credible interval: 7.7-17.8%). There was no significant difference in gender with males having a mean of 13.5%, and females 12.3%. Among the racial groups, Hispanic (13.9%), White (13.0%), Asian (12.1%), and Black (10.9%), the significant difference came from the difference between Black and Hispanic with a 95% credible interval from −5.63 to −0.30%. Those older than 30 years had a mean of 12.2% versus 12.9% for the Stat (2011) 18:131-146 younger group; although this was not a statistically significant difference. Given a constant inhalation input of 2 ppm, at steady state, the overall mean exhaled concentration was estimated to be 1.75 ppm (95% credible interval: 1.64-1.84). An equivalent parameter, first-order metabolic rate constant, was also estimated and found to be consistent with the percent of BD metabolized at steady state across gender, race, and age strata.123 132 Environ Ecol

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Physiological Pharmacokinetic Analysis Using Population Modeling and Informative Prior Distributions

Cited by 273 publications

References 45 publications

Statistical analysis of Clewell et al. PBPK model of trichloroethylene kinetics.

Statistical analysis of Clewell et al. PBPK model of trichloroethylene kinetics.

Probabilistic methods for addressing uncertainty and variability in biological models: application to a toxicokinetic model

Estimating metabolic rate for butadiene at steady state using a Bayesian physiologically-based pharmacokinetic model

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