Optimal sampling times for pharmacokinetic experiments

D’Argenio, David Z.

doi:10.1007/bf01070904

Cited by 294 publications

(96 citation statements)

References 17 publications

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“…However, this choice for b is not optimal in a strict sense. The author did not explore a truly optimal strategy, because it is generally impossible to predict the actual value of E. Formally, the error of the Gauss-Laguerre quadrature can be written as (9) where h lies somewhere in (0, ∞), and g(t)¤e t f(t/b) in this work. Using the Stirling formula, the error term for the mono-exponential function (e Ϫlt ), for example, can be approximated by…”

Section: Discussionmentioning

confidence: 99%

Gaussian Quadrature as a Numerical Integration Method for Estimating Area Under the Curve.

Amisaki

2001

Biological & Pharmaceutical Bulletin

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The area under the concentration-time curve (AUC) is a simple but very important measure in pharmacokinetics. The estimate of AUC may be obtained as an immediate result of nonlinear regression analysis, in which a set of observed concentrations are fitted to a certain pharmacokinetic function by estimating its parameters. However, the role of AUC is more significant in cases where the estimate is obtained by direct integration of data with the spirit of noncompartmental pharmacokinetic analysis.1) Despite the importance of AUC in such a situation, there has only been a single class of methods for estimating AUC: piecewise interpolatory methods. This class of methods includes trapezoidal/log-trapezoidal rules, spline fitting, and the so-called Lagrange method, as well as hybrids of each of them. There have already been several reports regarding comparative performances of these methods.2-6) Among the class of methods, Purves reported that "parabolas-through-the-origin then logtrapezoidal rule" (PTTO) performed best, 4) whereas Jawień pointed out the possible drawback of Purves' method in theoretical situations.6) It remains controversial as to which method is optimal in actual settings.In the piecewise interpolatory methods, an interpolating polynomial is constructed for each sub-interval specified by two adjacent data points. Then, the approximate value of AUC is given as a sum of the partial areas bounded by the polynomials. Accuracy of approximation depends on the locations of the sampling points, and several criteria were proposed as part of an optimal sampling strategy. 7,8) In general, as is the case with parameter estimation, 9-12) these criteria were driven so as to minimize the variance of AUC estimates. However, these optimizing strategies seem to be useful in restricted settings, because these strategies require prior knowledge concerning both pharmacokinetic and variance models.Another difficulty involved in the piecewise interpolatory methods is the accuracy of the extrapolated portions of the AUC from the final sampling time to time infinity. To accurately compute the extrapolated portions as completely as possible, the portions are usually calculated from several terminal data points by means of log-/non-linear regressions. However, this operation assumes a regression model and departs to some extent from the framework of noncompartmental analysis. Furthermore, the two operations (quadrature up to the final point and extrapolation) appear to lack theoretical consistency between them. For example, optimizing the locations of sampling times may increase errors in estimated parameters for the extrapolated region, thus increasing the error of the total AUC. In this article, the author proposes a different numerical integration scheme for estimating the AUC over the infinite time interval [0, ∞). The method is based on the Gaussian quadrature.13) Unlike the piecewise interpolatory quadratures, the Gaussian quadrature gains its accuracy by specifying abscissas (sampling times), which in turn can be viewe...

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Section: Discussionmentioning

confidence: 99%

Gaussian Quadrature as a Numerical Integration Method for Estimating Area Under the Curve.

Amisaki

2001

Biological & Pharmaceutical Bulletin

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“…Further information on this subject might be found elsewhere. 11 Pilot studies are also recommended as a means of estimating the appropriate number of subjects to be used, i.e., the sample size for pivotal BE study. Furthermore, this number depends on several factors including variance of the response, differences in the two formulations and level of the rejection of the hypothesis.…”

Section: Basic Principlesmentioning

confidence: 99%

Os estudos de bioequivalência: Relevância para a medicina veterinária

Palermo-Neto

Righi

2008

Braz. J. Vet. Res. Anim. Sci.

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Bioequivalence (BE) studies are scientific methods that allow comparison of different medicinal products containing the same active substance, or different batches of the same medicinal products or, in a broad sense, different routes of administration of the same product. Actually, legislation on generic drugs and bioequivalence only exist in Brazil for drugs intended for human purposes. In the field of Veterinary Medicine, BE is being used in many countries as part of the necessary requirements for registration of animal health products, i.e., to provide efficacy and safety animal data and to allow consumers safety; indeed, they also assure the quality of the food derived from treated animals. The present manuscript was designed to review and discuss BE; for that, it was divided into three major parts: 1-understanding bioequivalence: importance of BE studies for animal and human health; 2-type of BE studies included; 3-general consideration on experimental design involved o BE studies.

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“…Of course it is possible to conduct a set of experiments which, one by one, improve the parameter estimates. Such an approach is called sequential design (Chernoff, 1972;D'Argenio, 1981;DiStefano, 1981). Another (more realistic) approach is to assume some distributions for nominal parameters, not constant values.…”

Section: Introductionmentioning

confidence: 99%

“…Then one tries to choose such time moments for which the sensitivities are "less correlated". This is done by determining the so-called Fisher information matrix (FIM) (D'Argenio, 1981;DiStefano, 1981). A similar approach is also used for identifiability checking (Jacquez and Greif, 1985;Jacquez, 1998).…”

Section: Introductionmentioning

confidence: 99%

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Planning identification experiments for cell signaling pathways: An NFκB case study

Fujarewicz¹

2010

International Journal of Applied Mathematics and Computer Science

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Mathematical modeling of cell signaling pathways has become a very important and challenging problem in recent years. The importance comes from possible applications of obtained models. It may help us to understand phenomena appearing in single cells and cell populations on a molecular level. Furthermore, it may help us with the discovery of new drug therapies. Mathematical models of cell signaling pathways take different forms. The most popular way of mathematical modeling is to use a set of nonlinear ordinary differential equations (ODEs). It is very difficult to obtain a proper model. There are many hypotheses about the structure of the model (sets of variables and phenomena) that should be verified. The next step, fitting the parameters of the model, is also very complicated because of the nature of measurements. The blotting technique usually gives only semi-quantitative observations, which are very noisy and collected only at a limited number of time moments. The accuracy of parameter estimation may be significantly improved by a proper experiment design. Recently, we have proposed a gradient-based algorithm for the optimization of a sampling schedule. In this paper we use the algorithm in order to optimize a sampling schedule for the identification of the mathematical model of the NFκB regulatory module, known from the literature. We propose a two-stage optimization approach: a gradient-based procedure to find all stationary points and then pair-wise replacement for finding optimal numbers of replicates of measurements. Convergence properties of the presented algorithm are examined.

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Optimal sampling times for pharmacokinetic experiments

Cited by 294 publications

References 17 publications

Gaussian Quadrature as a Numerical Integration Method for Estimating Area Under the Curve.

Gaussian Quadrature as a Numerical Integration Method for Estimating Area Under the Curve.

Os estudos de bioequivalência: Relevância para a medicina veterinária

Planning identification experiments for cell signaling pathways: An NFκB case study

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