Re: FO VS FOCE VS FOCE WITH INTERACTION

From: John Lukas <johnl@u.washington.edu> Subject: Re: FO VS FOCE VS FOCE WITH INTERACTION Date: Mon, 26 Feb 2001 12:31:22 -0800 Hi Venkatesh, NONMEM assumes a multivariate normal "mean-variance" model with a mean for the error "epsilon" as E[epsilon_ij] = 0. When you have a heteroscedastic error distribution in your data and use a constant coefficient of variatyion structure as your error model, the variance of the error model is Var[epsilon_ij] = F(eta_ij,b)**2 x sigma**2 where eta_ij are your random effects and sigma is a constant. That variance is the variance-covariance matrix "omega". As yoiu see epsilon in this case is a function of eta, so INTERACTION if you wish is "naturally" included in the problem! From my experience it does make a big difference if you specify INTERACTION in your control file with FOCE especially when your on the limit of your ability to distribute information on variability to the sigma or the omega matrix such as the case of an infusion regimen in a small population where you reach the 1st half life troughs only with a single measurement at that trough. The method works best (as all in NONMEM) if you explore the full covariance structure in the etas not limiting to the diagonal. If your data appear to have a constant error distribution and this is the same across subjects then you may have a homoscedastic (constrant variance) structure in which case you don't need INTERACTION. The FO linearizes both your PK/PD structural and residual models around eta_ij = 0, the assumed population mean of the random effects, so Var[epsilon_ij] = F(0,b)**2 x sigma**2. INTERACTION is not applicable here. This approximation however can cause problems as your residual model may be strongly nonlinear in the eta_s and removing this with the linearization may cause a bias in your fit. Davidian and Giltinan in their "Nonlinear Models for Repeated Measurement Data" book explain quite well this method in a couple of pages once you get accustomed to the symbols they use for the effects. A lot on this, and quite well presented, is in the NONMEM user's guide- Part VII. Cheers, John + + John C Lukas, MS, PhD Resource Facility for Population Kinetics Department of Bioengineering Mail Stop 352255 University of Washington Seattle, WA 98102 +(206) 543 4120 +(206) 543 3081 (fax) johnl@u.washington.edu http://tanami.saam.washington.edu/lukas.html + +