Methods

Theophylline concentrations from 12 subjects were described by a one-compartment model with first-order absorption (Figure 1), estimated with SAEM in nlmixr2.

Structure of the final model.

Figure 1: Structure of the final model.

The model is defined by the following equations:

\[ \begin{aligned} {ka} & = \exp\left({tka}+{eta.ka}\right) \\ {cl} & = \exp\left({tcl}+{eta.cl}\right) \\ {v} & = \exp\left({tv}+{eta.v}\right) \\ \frac{d \: depot}{dt} & = -{ka} {\times} {depot} \\ \frac{d \: central}{dt} & = {ka} {\times} {depot}-\frac{{cl}}{{v}} {\times} {central} \\ {cp} & = \frac{{central}}{{v}} \\ {cp} & \sim add({add.sd}) \end{aligned} \]

Results

The objective function value was 123.05. Table 1 lists the final parameter estimates.

Table 1: Final parameter estimates.
Back-transformed CI Lower CI Upper %RSE BSV(CV%)
tka 1.586 1.089 2.308 41.554 71.516
tcl 2.750 2.356 3.210 7.803 26.159
tv 31.604 28.920 34.538 1.311 14.351
add.sd 0.697 0.604 0.789 6.772