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

本研究的主要目的是检查最小相对熵法（MRE）的有效性，Amisaki和Eguchi于1995年提出了该方法作为药代动力学参数分析的估计方法。然而，随着研究的进展，它揭示了MRE在数学上与具有泊松方差函数的迭代重加权最小二乘（IRLS）相同。这一结果为证明IRLS方法的有效性提供了理论依据，即IRLS方法是通过最小化相对熵来工作的。IRLS以前的一个典型声明如下：该方法似乎表现良好，但适用于泊松分布的数据，即，计数数据。除了这个结果之外，本研究还从理论上和/或数值上比较了多种估计方法的性质，包括加权最小二乘、广义最小二乘、扩展最小二乘和扩展拟似然。结果表明，MRE最适合于分析个体药代动力学数据，其中每个参数的个体内变异估计无关紧要。

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.