Model development
MPA concentration-time profile was modeled by testing one and two-compartment models with first-order absorption and linear elimination without or with lag time. The first-order conditional estimate with extended least squares method was used in nonlinear mixed-effects model generated by Phoenix NLME 8.1. Fixed effects models were parameterized as Ka (absorption rate constants), CL and Vd (volume of distribution) for 1-compartment model as well as Ka, CL, Q (intercompartmental CL), Vc (central Vd), and Vp(peripheral Vd) for 2-compartment model. Additive, proportional and combination of additive with proportional error models were compared to evaluate residual variability. After the development of the base model, inter-individual variability was described by an exponential model as follows:
\begin{equation} \text{\ \ \ \ \ }\theta_{i}=\theta_{\text{pop}}\times exp\left(\eta_{i}\right)\nonumber \\ \end{equation}
where θi is the individual pharmacokinetic parameter, and θpop is typical value of parameter. The random variable ηi is normally distributed with mean zero and variance of ω², which is the deviation of ηifrom θpop. The covariates were identified by a stepwise forward addition and backward elimination approach. A change in objective function value (OFV) of >3.84 (P< 0.05) was necessary for forward selection, and a strict threshold ΔOFV of >7.88 (P < 0.01) was used for backward elimination.