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A computer program is described for maximum likelihood estimation within the gamma or normal distribution which can be used to estimate pharmacokinetic parameters. Pharmacokinetic analysis using this proposed program was investigated by the Monte Carlo method. The assumed pharmacokinetic models were a one-compartment intravenous model and an oral model. The simulated drug concentrations were generated using a 10% S.D. based on the gamma or normal distribution. The gamma or normal distribution was adopted as the probability density function (p.d.f.) to estimate model parameters. The Powell method was used to maximize the logarithmic likelihood. There were no differences in the estimated parameters in terms of statistical and frequency distributions between the gamma and normal distributions using the generated data and the p.d.f. distributions. However, the number of failures to calculate the parameters using the p.d.f. with the normal distribution was more than five times that using the gamma distribution. This result suggests that it may be necessary to evaluate the validity of results computed using the maximum likelihood estimation based on a normal distribution as a data error distribution and p.d.f.

biological and pharmaceutical bulletin

A Computer Program for Pharmacokinetics Based on Maximum Likelihood Estimation Using the Gamma Distribution with a Probability Density Function: Comparison with the Normal Distribution.