Diagnostics for Fitting of Compartment Models Based on Curvature.

Daimon Takashi, Goto Masashi

doi:10.5023/jappstat.31.189

Pharmacokinetics aims to clarify the kinetics of a drug administered in a human body, by the time course of drug disposition, composed of absorption, distribution, metabolization, and excretion. As a tool for this clarification, a compartment model is often used in practice. In this paper, we considered the diagnostics about the validity of statistical inference of the compartment models. We utilized the relative curvature measure as this diagnostic tool and investigated its appropriateness by some pharmacokinetic literatures and a simulation study. In investigation of the pharmacokinetic literatures, we applied this relative curvature measure and assessed the degree of nonlinearity underlying in the compartment models. Then, we focused on the heteroscedasticity of the blood drug concentration data as the deviation of them from the assumption on the ordinary statistical model, and examined the effects of the heteroscedasticity on this measure. Intending to improve the deviation from this assumption and to evaluate it quantitatively, we utilized the power-transformation approach and presented the relative curvature measure depending on this approach. As a result, in the power-transformation approach, the heteroscedasticity of the blood drug concentration data and the skewness of the distribution of them were improved and the nonlinearity depending on the parameters in the model was decreased. Furthermore, we utilized some diagnostic measures that are concomitant with the relative curvature depending on the power-transformation approach and could understand the properties of the compartment models, without being affected by the heteroscedasticity of the blood drug concentration data. In the simulation study, we assumed the situation where the blood drug concentration data were heteroscedastic, and evaluated the effects of the sample size of the blood drug concentration data, the variability, and the sampling type, on the relative curvature measure. Consequently, it was shown that the parameter-effects curvature for the powertransformation approach was not affected by the heteroscedasticity of the blood drug concentration data. It was suggested that the relative curvature measure could provide productive knowledge for the diagnostics for the statistical inference of compartment models in pharmacokinetics.

Diagnostics for Fitting of Compartment Models Based on Curvature.

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