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  • 1
    Electronic Resource
    Electronic Resource
    Bayesian design criteria: Computation, comparison, and application to a pharmacokinetic and a pharmacodynamic model (1995)
    Springer
    Journal of pharmacokinetics and pharmacodynamics 23 (1995), S. 101-125 
    Details
    ISSN: 1573-8744
    Keywords: Bayesian designs ; Bayesian estimation ; prior distribution ; pharmacokinetics ; pharmacodynamics ; E max model ; nonlinear models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract In this paper 3 criteria to design experiments for Bayesian estimation of the parameters of nonlinear models with respect to their parameters, when a prior distribution is available, are presented: the determinant of the Bayesian information matrix, the determinant of the preposterior covariance matrix, and the expected information provided by an experiment. A procedure to simplify the computation of these criteria is proposed in the case of continuous prior distributions and is compared with the criterion obtained from a linearization of the model about the mean of the prior distribution for the parameters. This procedure is applied to two models commonly encountered in the area of pharmacokinetics and pharmacodynamics: the one-compartment open model with bolus intravenous single-dose injection and theE max model. They both involve two parameters. Additive as well as multiplicative gaussian measurement errors are considered with normal prior distributions. Various combinations of the variances of the prior distribution and of the measurement error are studied. Our attention is restricted to designs with limited numbers of measurements (1 or 2 measurements). This situation often occurs in practice when Bayesian estimation is performed. The optimal Bayesian designs that result vary with the variances of the parameter distribution and with the measurement error. The two-point optimal designs sometimes differ from the D-optimal designs for the mean of the prior distribution and may consist of replicating measurements. For the studied cases, the determinant of the Bayesian information matrix and its linearized form lead to the same optimal designs. In some cases, the pre-posterior covariance matrix can be far from its lower bound, namely, the inverse of the Bayesian information matrix, especially for theE max model and a multiplicative measurement error. The expected information provided by the experiment and the determinant of the pre-posterior covariance matrix generally lead to the same designs except for theE max model and the multiplicative measurement error. Results show that these criteria can be easily computed and that they could be incorporated in modules for designing experiments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02353788
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Drug–Drug Pharmacodynamic Interaction Detection by a Nonparametric Population Approach. Influence of Design and of Interindividual Variability (1999)
    Springer
    Journal of pharmacokinetics and pharmacodynamics 27 (1999), S. 531-554 
    Details
    ISSN: 1573-8744
    Keywords: drug–drug interactions ; NPML ; experimental design ; pharmacodynamic variability ; pharmacokinetics ; entropy ; covariate ; second stage model ; controlled trial
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Population approaches are appealing methods for detecting then assessing drug–drug interactions mainly because they can cope with sparse data and quantify the interindividual pharmacokinetic (PK) and pharmacodynamic (PD) variability. Unfortunately these methods sometime fail to detect interactions expected on biochemical and/or pharmacological basis and the reasons of these false negatives are somewhat unclear. The aim of this paper is firstly to propose a strategy to detect and assess PD drug–drug interactions when performing the analysis with a nonparametric population approach, then to evaluate the influence of some design variates (i.e., number of subjects, individual measurements) and of the PD interindividual variability level on the performances of the suggested strategy. Two interacting drugs A and B are considered, the drug B being supposed to exhibit by itself a pharmacological action of no interest in this work but increasing the A effect. Concentrations of A and B after concomitant administration are simulated as well as the effect under various combinations of design variates and PD variability levels in the context of a controlled trial. Replications of simulated data are then analyzed by the NPML method, the concentration of the drug B being included as a covariate. In a first step, no model relating the latter to each PD parameter is specified and the NPML results are then proceeded graphically, and also by examining the expected reductions of variance and entropy of the estimated PD parameter distribution provided by the covariate. In a further step, a simple second stage model suggested by the graphic approach is introduced, the fixed effect and its associated variance are estimated and a statistical test is then performed to compare this fixed effect to a given value. The performances of our strategy are also compared to those of a non-population-based approach method commonly used for detecting interactions. Our results illustrate the relevance of our strategy in a case where the concentration of one of the two drugs can be included as a covariate and show that an existing interaction can be detected more often than with a usual approach. The prominent role of the interindividual PD variability level and of the two controlled factors is also shown.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1023290530853
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  • 3
    Electronic Resource
    Electronic Resource
    Optimal Sampling Times for Bayesian Estimation of the Pharmacokinetic Parameters of Nortriptyline During Therapeutic Drug Monitoring (1999)
    Springer
    Journal of pharmacokinetics and pharmacodynamics 27 (1999), S. 85-101 
    Details
    ISSN: 1573-8744
    Keywords: nortriptyline ; Bayesian design ; Bayesian estimation ; information criterion ; optimal sampling times ; therapeutic drug monitoring
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Sampling times for Bayesian estimation of the pharmacokinetic parameters of an antidepressant drug, nortriptyline, during its therapeutic drug monitoring were optimized. Our attention was focused on designs including a limited number of measurements: one, two, and three sample designs in which sampling times had to be chosen between 0 and 24 hr after the last intake of a test-dose study. The optimization was conducted in four groups of patients defined by their gender and the administration or not of concomitant drugs inhibiting the metabolism of nortriptyline. The Bayesian design criterion was defined as the expected information provided by an experiment. A stochastic approximation algorithm, the Kiefer–Wolfowitz algorithm, was used for the criterion maximization under experimental constraints. Results showed that optimal Bayesian sampling times differ between patients in monotherapy and polytherapy. For one-sample designs the measurements have to be performed either at the lower (0 hr) or at the upper (24 hr) bound of the admissible interval. Replications were often found for 2- and 3-point designs. Other sampling designs can lead to criterion close to the optimum and can therefore be performed without great loss of information. In contrast, we found that several designs lead to low values of the information criterion, which justifies the approach.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1020634813296
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Robust Optimal Design for the Estimation of Hyperparameters in Population Pharmacokinetics (1998)
    Springer
    Journal of pharmacokinetics and pharmacodynamics 26 (1998), S. 689-716 
    Details
    ISSN: 1573-8744
    Keywords: experimental design ; population pharmacokinetics ; D-optimality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The expectation of the determinant of the inverse of the population Fisher information matrix is proposed as a criterion to evaluate and optimize designs for the estimation of population pharmacokinetic (PK) parameters. Given a PK model, a measurement error model, a parametric distribution of the parameters and a prior distribution representing the belief about the hyperparameters to be estimated, the EID criterion is minimized in order to find the optimal population design. In this approach, a group is defined as a number of subjects to whom the same sampling schedule (i.e., the number of samples and their timing) is applied. The constraints, which are defined a priori, are the number of groups, the size of each group and the number of samples per subject in each group. The goal of the optimization is to determine the optimal sampling times in each group. This criterion is applied to a one-compartment open model with first-order absorption. The error model is either homoscedastic or heteroscedastic with constant coefficient of variation. Individual parameters are assumed to arise from a lognormal distribution with mean vector M and covariance matrix C. Uncertainties about the M and C are accounted for by a prior distribution which is normal for M and Wishart for C. Sampling times are optimized by using a stochastic gradient algorithm. Influence of the number of different sampling schemes, the number of subjects per sampling schedule, the number of samples per subject in each sampling scheme, the uncertainties on M and C and the assumption about the error model and the dose have been investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1020703007613
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    Paper (German National Licenses)
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