Assessing nonlinearity in compartment models via the relative curvature measure

In pharmacokinetics, compartment models often play an important role in the description of the concentration of the drug in the blood over time after its administration to an individual. Statistical inference in these models can be conducted based on a linear approximation with respect to the parameter related to pharmacokinetic indices, in the same way that the usual nonlinear regression models are dealt with. Therefore, it is necessary to assess the degree of nonlinearity in a compartment model and to evaluate its effect on the linear approximation. The relative curvature measure that enables us to assess the intrinsic and parameter-effects (PE) nonlinearity can be used, but in practice it has not been applied to compartment models in pharmacokinetics. One reason may be that the relative curvature measure cannot be directly applied to blood drug concentration data that exhibit heteroscedasticity. Therefore, the relative curvature measure including the heteroscedastic variance function was utilized to assess the nonlinearity in the compartment models, and in particular, the influences of some of the reparameterizations that are empirically used in fitting the compartment models were examined. Several examples showed that the reparameterized compartment model had less PE nonlinearity than the original compartment model, but that several reparameterizations could increase the PE nonlinearity. In addition, by means of a simulation experiment with heteroscedastic blood drug concentration data, the accuracy, and precision of the relative curvature measure with the heteroscedastic variance function were evaluated and compared with those of the original relative curvature measure. The results showed that the relative curvature measure with the variance function was not affected by heteroscedastic blood drug concentration data and could be utilized for the assessment of the nonlinearity in compartment models.