114  Models Non-Linearly Modeled in Epsilon

NONMEM 7 Technical Guide

In NONMEM, one may also model the residuals using the epsilons in a nonlinear manner, such as:

Y = F * EXP(EPS(1))

When population analysis is performed, however, NONMEM transposes this model into its linear-epsilon residual approximate form:

Y = F + F * EPS(1)

and evaluates the likelihood according to this epsilon-linearization. All analysis methods (classical as well as Monte Carlo) utilize this linearization of the likelihood in epsilon. Furthermore, the assessment of NPDE, NPD, EWRES, and ECWRES as described above utilize this linearized form with respect to the epsilon model, in keeping with the way the data was analyzed.

To most properly analyze the data in a manner that is equivalent to its epsilon exponential model form, and to also properly asses the various Monte Carlo population weighted residuals, it is best to log-transform the data, and model the residual variance to the log-transformed data follows:

Y = LOG(f) + EPS(1)

The residual variance is now linear epsilon modeled, and NONMEM will analyse the data exactly according to the true distribution of the data.