Uncertainty, Variability, and Sensitivity Analysis in Physiological Pharmacokinetic Models

Krewski, Daniel; Wang, Y; Bartlett, S.; Krishnan, Kannan

doi:10.1080/10543409508835112

Cited by 50 publications

(36 citation statements)

References 19 publications

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“…For small parameter variation, sensitivity is captured by the response coefficients R. In the probabilistic setting, we suggest two sensitivity measures, and, in both cases, the first-order approximation from Section 3.1 leads to simple formulae. Krewski et al [30] proposed a probabilistic sensitivity measure for pharmacokinetic models: Let f (x) denote a random variable that depends on the (possibly correlated) random variables x 1 , . .…”

Section: Stochastic Sensitivitymentioning

confidence: 99%

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Biochemical networks with uncertain parameters

Liebermeister

Klipp

2005

IEE Proc. Syst. Biol.

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The modelling of biochemical networks becomes delicate if kinetic parameters are varying, uncertain or unknown. Facing this situation, we quantify uncertain knowledge or beliefs about parameters by probability distributions. We show how parameter distributions can be used to infer probabilistic statements about dynamic network properties, such as steady-state fluxes and concentrations, signal characteristics or control coefficients. The parameter distributions can also serve as priors in Bayesian statistical analysis. We propose a graphical scheme, the 'dependence graph', to bring out known dependencies between parameters, for instance, due to the equilibrium constants. If a parameter distribution is narrow, the resulting distribution of the variables can be computed by expanding them around a set of mean parameter values. We compute the distributions of concentrations, fluxes and probabilities for qualitative variables such as flux directions. The probabilistic framework allows the study of metabolic correlations, and it provides simple measures of variability and stochastic sensitivity. It also shows clearly how the variability of biological systems is related to the metabolic response coefficients. IntroductionCell simulations aspired to in systems biology [1] require knowledge of enzyme kinetic parameters. However, owing to a lack of measurements, measurement errors and biological variability, most of these parameters are still unknown or uncertain, which turns out to be a major obstacle in large-scale cell modelling. In this situation, a probabilistic description of the parameters can be helpful: to assess the effects of measurement errors, to find out which model results persist for a wide range of parameters, and to derive probabilities for different model outcomes. Besides this, parameter distributions can also be employed to study the natural variability and robustness of biological systems. The effects of temporal random fluctuations in gene expression [2,3] and metabolism [4,5] have been studied. Here, we focus on models with static yet uncertain parameters: the parameters are described by a probability distribution, and the standard deviation of the resulting variable distributions (their variability) reflects how strongly the variables respond to parameter variations. (In this paper, we use the term 'variable' quite generally for quantitative model results, such as concentrations or fluxes in steady state or as functions of time, or functions of them, such as signal amplitudes or durations [6].) Of course, this influence depends on the system, on the variable of interest and on the parameter: at bifurcation points, a small parameter change can even change the qualitative dynamic behaviour. In other cases, parameters can have a weak influence on the system behaviour. In fact, various biological systems seem to have evolved robustness, that is, low sensitivity and thus low variability, against a typical amount of parameter variation (see [7] and references therein) [8 -10].If the parameter v...

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Section: Stochastic Sensitivitymentioning

confidence: 99%

“…The Monte Carlo algorithm (also in [30]) to compute this value is numerically demanding, but we can also approximate it using the linear expansion, yielding…”

Section: Stochastic Sensitivitymentioning

confidence: 99%

Biochemical networks with uncertain parameters

Liebermeister

Klipp

2005

IEE Proc. Syst. Biol.

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“…The usual procedure for incorporating measures of variability and uncertainty into pharmacokinetic modeling is Monte Carlo (MC 1 ) simulation (Farrar et al, 1989;Bois et al, 1991;Hattis et al, 1990;Gearhart et al, 1993;Krewski et al, 1995). The core of this procedure is the specification of prior model parameter probability distribution functions (pdfs).…”

Section: Methodsmentioning

confidence: 99%

“…This practice is a source of the following concerns. First, handling single values in the presence of significant variability and uncertainty is inappropriate and may be misleading (Farrar et al, 1989;Bois et al, 1991;Hattis et al, 1990;Gearhart et al, 1993;Krewski et al, 1995). Usually derived from a small sample, the mean may not be representative or even meaningful.…”

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confidence: 99%

Incorporating Measures of Variability and Uncertainty into the Prediction of in Vivo Hepatic Clearance from in Vitro Data

Nestorov

Gueorguieva²,

Jones³

et al. 2002

Drug Metab Dispos

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ABSTRACT:The existing procedures for quantitative in vitro-in vivo clearance prediction can be significantly biased either by totally neglecting the existing variability and uncertainty by using mean parameter values or by implementing Monte Carlo simulation with statistical distribution of the parameters reconstructed from very small sets of data. The aim of the present study is to develop a methodology for the prediction of in vivo hepatic clearance in the presence of semiquantitative or qualitative data and accounting for the existing uncertainty and variability. The method consists of two steps: 1) transformation of the information available into fuzzy sets (fuzzification); and 2) computation of the in vivo clearance using arithmetic operations with fuzzy sets. To illustrate the approach, rat hepatocyte and microsomal data for eight benzodiazepine compounds are used. A comparison with a standard Monte Carlo procedure is made. The methodology proposed can be used when Monte Carlo simulation may be biased or cannot be implemented. The obtained fuzzy in vivo clearance can be used subsequently in fuzzy simulations of pharmacokinetic models.The ability to predict pharmacokinetic events in vivo, especially in humans, from in vitro data and other relevant information is of great importance both to academia in providing a quantitative framework for identification and investigation of the key processes involved and to industry in facilitating drug selection and development. Of all the pharmacokinetic parameters, most work in this endeavor has concentrated on the prediction of hepatic (metabolic) clearance. It usually comprises a series of sequential steps, starting from the estimation of intrinsic clearance in the in vitro system, through the identification of appropriate scaling coefficients, and ending with the implementation of a liver model. The ultimate goal is to achieve as accurate a quantitative prediction of the in vivo hepatic clearance as possible.The information used and generated throughout the in vitro-in vivo clearance prediction process is characterized by a large degree of uncertainty and significant variation in the experimental values Iwatsubo et al., 1997; Lavè et al., 1997;Obach et al., 1997) due to a number of highly related reasons. These include the complexity and sometimes unknown nature of the phenomena involved, the imperfect instrumentation and information processing tools, and the high inherent variability of the biological systems. The terms variability and uncertainty are used almost interchangeably in the pharmacokinetic and metabolism literature. It should be noted, however, that variability is an inherent property of the system of interest; it can be observed and recorded but not changed. In contrast, uncertainty relates to variations due to errors in assumptions, hypotheses, observations, experiments, and handling of the system studied. Accordingly, uncertainty in the information available can be decreased and theoretically eliminated by implementing "ideal" experiments and data-pro...

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“…Krewski et al, (1995) performed an uncertainty analysis on physiological models using Monte Carlo Simulation. In this study, most of the model parameters were assumed to have a nature of the doubly truncated normal distribution.…”

Section: Introductionmentioning

confidence: 99%

Model uncertainty of interfacial area and mass transfer coefficients in absorption column packings

Karunarathne¹,

Eimer²,

Øi³

2017

Linköping Electronic Conference Proceedings

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Uncertainty in model input parameters propagates through the model to make model output imprecision. Here, mathematical models used to calculate interfacial area and mass transfer coefficient for both random and structured packing in a packed bed absorption column was studied to investigate the propagation of model input parameters of viscosity, density and surface tension through the models. Monte Carlo simulation was used to examine the uncertainty propagation, and expectation E(Y) and standard deviation σ for the model output values were determined. This study reveals ±5% model output uncertainty for mass transfer coefficient and ±3.7% uncertainty for interfacial area for the Onda, Bravo and Fair models used in random packings. Further, the analysis predicts ±1.3% of uncertainty for interfacial area and ±0.8% of uncertainty for mass transfer coefficient for the Rocha's correlations used in structured packings.

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Uncertainty, Variability, and Sensitivity Analysis in Physiological Pharmacokinetic Models

Cited by 50 publications

References 19 publications

Biochemical networks with uncertain parameters

Biochemical networks with uncertain parameters

Incorporating Measures of Variability and Uncertainty into the Prediction of in Vivo Hepatic Clearance from in Vitro Data

Model uncertainty of interfacial area and mass transfer coefficients in absorption column packings

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