Verification on the effectiveness of minimum relative entropy method for pharmacokinetic analysis

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Primary aim of this research had been to examine the effectiveness of the minimum relative entropy method (MRE), which, in 1995, Amisaki and Eguchi proposed as the estimation method for phamacokinetic parameter analysis. However, as the research progressed, it revealed that MRE is mathematically identical to the iteratively reweighted least squares (IRLS) with a Poisson variance function. This result provides the theoretical basis for justifying the IRLS,that is, the method works by minimizing the relative entropy. A previous typical claim for the IRLS has been as follows : the method seems to perform well, but would be appropriate for data from a Poisson distribution, i.e., counted data. In addition to this result, this research theoretically and/or numerically compared the properties of many kinds of estimation methods, including weighted least squares, generalized least squares, extended least squares, and extended quasi-likelihood. As a result, it is shown that MRE is best suited for analyzing individual pharmacokinetic data where estimation of intra-individual variation of each parameter is of no concern.