An Exact Application of Maximum Likelihood Method to Pharmacokinetic Analysis.

Abstract

It is well known that there exist inter-individual variations of pharmacokinetic parameters. We can analyze pharmacokinetic data by Bayesian models expressing these variations by a prior distribution. Some programs, such as MULTI(ELS), are developed on this method and population distribution of pharmacokinetic parameters are estimated by maximizing log likelihood. In this program, however, the linear approximation by Taylor expansion is used in calculation of log likelihood and this linear approximation brings significant error in calculation of maximum log likelihood. We need to calculate maximum log likelihood unbiassedly for model selection by AIC.In this paper, we employ Monte Carlo method to calculate the likelihood of Bayesian models. We find that the estimate of maximum log likelihood by MULTI(ELS) has bias caused by the linear approximation in calculation of log likelihood. We propose the use of Monte Carlo method for unbiassed calculation of the log likelihood of Bayesian models.