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.