BAYESIAN DESIGN CRITERIA - COMPUTATION, COMPARISON, AND APPLICATION TO A PHARMACOKINETIC AND A PHARMACODYNAMIC MODEL

In this paper 3 criteria to design experiments for Bayesian estimation of the parameters of nonlinear models with respect to their parameter s, when a prior distribution is available, are presented: the determin ant of the Bayesian information matrix, the determinant of the pre-pos terior 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 compa red with the criterion obtained from a linearization of the model abou t the mean of the prior distribution for tire parameters. This procedu re is applied to two models commonly encountered in the area of pharma cokinetics and pharmacodynamics: the one-compartment open model with b olus intravenous single-dose injection and the E(max) model. They both involve two parameters. Additive as well as multiplicative gaussian m easurement errors are considered with normal prior distributions. Vari ous 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 situ ation often occurs in practice when Bayesian estimation is performed. The optimal Bayesian designs that result vary with the variances of th e parameter distribution and with the measurement error. The two-point optimal designs sometimes differ from tire D-optimal designs for tire mean of the prior distribution and may consist of replicating measure ments. For the studied cases, the determinant of the Bayesian informat ion matrix and its linearized form lead to the same optimal designs. I n some cases, the pre-posterior covariance matrix can be far from its lower bound namely, the inverse of the Bayesian information matrix, es pecially for the E(max) model and a multiplicative measurement error. The expected information provided by, the experiment and the determina nt of the pre-posterior covariance matrix generally lead to the same d esigns except for the E(max) model and the multiplicative measurement error. Results shore that these criteria can be easily computed and th at they could be incorporated in modules for designing experiments.