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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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  • 2
    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)
    Fulltext
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