Re: residual error model, endogeneous drug

From: LSheiner <lewis@c255.ucsf.edu> Subject: Re: residual error model, endogeneous drug Date: Thu, 03 May 2001 14:04:40 -0700 See below. Paul.Tanswell@bc.boehringer-ingelheim.com wrote: > THE PROBLEM: > 1. Although the model ran well and the plots of PRED vs DV and IPRED vs DV > were satisfactory, the individual values of CBAS, which are a small cluster > of values at the lower end of the DV range, were systematically > underestimated by about 30%. A plot of IPRED (y) vs DV (x) just for the CBAS > yielded an approximately linear relationship but with slope 0.68. This is puzzling, as the IPRED should certainly be centered about the actual observations. It may have to do with the fact that the model you use for the obserfations involves "interaction" between eta(4) and eps(1), for example, which is famous for giving problems if it is not accounted for (although I do not recall this particular bias). To see if this is what is going on, try an additive error model, or try using 'FOCE with interaction' with the model you have, or see below. > 2. The code does not seem quite right to me. Considering CBAS, which is a > single pre-dose endogenous measurement per subject, it seems logical to give > it an ETA, but it does not seem reasonable to allow an EPS additionally. > However, in the code as written, the estimate for the sum of the endogenous > and exogenous drug (FTOT) allows both levels of random variability. When > FTOT decreases to near CBAS or equals CBAS, then CBAS will effectively have > both an ETA and an EPS assigned to it. > > My questions to the group: > - is there a method of coding such that F but not CBAS is allowed to have > an EPS assigned to it It could be done, ... but it would not be right (in the famous words of Richard Nixon, who claimed the last clause was said, but not recorded on tape, when he was asked by Haldeman/Erlichman whether they should pay off the Watergate burglars to be quiet ..). The baseline measurement is a measurement like any other: Under your model the observed baseline value has a mean (theta(5)), interindividual variability (eta(4)), and measurement error (eps(1)). Seems just right to me. However, if you did not care about this nicety, you could certainly let all the variability of the baseline be "absorbed" by the eta. This would also remove the interaction, and would not increase the number of parameters. You might do this with code such as $ERROR > W=F**THETA(6) > FTOT=F+CBAS > Y=FTOT+W*(EPS(1)) > IPRED=FTOT > IRES=CP-IPRED > IWRES=IRES/W Two final points: 1. This model does not allow for feedback inhibition of endogenous substance production. 2. There is another way to deal with this problem that I actually prefer. It involves conditioning on the baseline observation, but recognizing that it has error of the same magnitude as any other. Unfortunately, the code is tricky enough (one must constrain the variance of an eta to be the same as that of eps, and must recognize (NEWIND) and fix initial conditions), especially for a 2-compartment model (because both compartments must be initialized) that I don't trust myself to write it off the top of my head... -- _/ _/ _/_/ _/_/_/ _/_/_/ Lewis B Sheiner, MD (lewis@c255.ucsf.edu) _/ _/ _/ _/_ _/_/ Professor: Lab. Med., Bioph. Sci., Med. _/ _/ _/ _/ _/ Box 0626, UCSF, SF, CA, 94143-0626 _/_/ _/_/ _/_/_/ _/ 415-476-1965 (v), 415-476-2796 (fax)