During this past grant year we have implemented and investigated a Markov Chain Monte Carlo method, for use in individual Bayesian estimation of pharmacokinetic/pharmacodynamic models. The Independence Metropolis-Hastings (IMH) algorithm has been implemented for the general class a pk/pd models. In this implementation the prior density can be specified as a mixture of multivariate Normal or Lognormal densities. This has allowed us to investigate the case when the prior density is multimodal, which may occur, for example, when a minor subpopulation of subjects has pk/pd parameters distinct from the major population density. Our implementation of the IMH method is currently being used for individual Bayesian estimation as part of a clinical protocol of the drug Busulfan at the Saint Jude Research Hospital. We have also begun to investigate, using ideas from renewal processes, a regenerative MCMC method. The motivation is to provide an error analysis as part of a sample-based estimation scheme. Our first effort produces a regenerative Markov Chain by imbedding a IMH sampling within a non-Markov rejection sampling method. The combined method is referred to as a reject IMH sampler (RIMH). While this represents the simplest of nonlinear Bayesian estimation examples, it does illustrate the methods feasibility and will provide a useful initial example to further explore the performance of the RIMH algorithm.
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