From: "Bachman, William"Subject: [NMusers] NONMEM Tips #16 - April 2, 2003 - Modeling a "baseline" component and an additive "drug" component Date: Wed, 2 Apr 2003 09:15:33 -0500 This tip was contributed by Lewis Sheiner: I'm not sure if anyone has written this up for NMUSERS (perhaps this is simply a duplicate of stuff that's already been sent around -- the fact that I can't recall it provides no valid evidence on this point), or maybe it is so well known as not to be worth a note, but if neither of those are true, then I have found the following of occasional use, and you might want to pass it on to the group. Set-up: Usually PD, but could be PK with endogenous production. The model will have a "baseline" component and an additive "drug" component. The data consist of a baseline(pre-drug) measurement, and then serial measurements after the drug. The goal is the drug model, and the baseline is a nuisance variable. The obvious model (in NONMEM speak), illustrated for the simplest possible case (clearly the model for both IPRED and Y can be elaborated at will), (1) $ERROR IPRED = THETA(1)+ETA(1) + F Y = IPRED + ERR(1) where F(time=0) = 0, and the data includes DV at time zero (the observed baseline value), involves a model for the baseline (in this simple example, a normally distributed r.v., with mean THETA(1))), and if this model has a problem (e.g., baseline is not symmetrically distributed), then some power or precision will be lost in making inferences or estimating more interesting parameters, say the influence of a covariate on the drug response model (F). On the other hand, deleting the baseline DV, but including its value as a covariate in the data, say BSL, present in every record), and modeling (2) $ERROR IPRED = BSL + F Y = IPRED + ERR(1) avoids the problem of model (1) by conditioning on the baseline (while making no modeling assumptions about it), but has the same problem that 'subtracting the baseline' always has, namely that the baseline is measured with error and that error is also being conditioned upon. A conditional model, in the spirit of (2), but which avoids conditioning on the error, uses the same (reduced) data set as for model (2), assumes that the baseline is measured with the same noise model as all subsequent measurements, and uses (3) $ERROR IPRED = BSL + THETA(2)*ETA(1) + F Y = IPRED + THETA(2)*ERR(1) $OMEGA 1 FIX $SIGMA 1 FIX The "trick" here is that the error in BSL (that is, "true" BSL minus observed value, "persists" throughout the individual record, and hence an ETA must be used, but it must have the same variance as the epsilon error. Model (3) accomplishes this. Best, Lewis. Previous tips may be found in the NONMEM Repository@GloboMax: ftp://ftp.globomaxnm.com/Public/nonmem/tips/ See the index.txt file for a listing of previous tips. *************************************************************************** If you have a "tip" or a better way to do things, by all means, feel free to post them! One of the reasons for doing this (other than good PR for GloboMax), is to stimulate discussion. We at GloboMax can learn from your experience as well. Do you have a "tip" you would like to share, but would prefer to remain anonymous? If so, you may forward it to us and your identity will be withheld. Distribution as a "Tip of the Week" will be at the discretion of nmconsult@globomaxnm.com. *************************************************************************** nmconsult@globomaxnm.com GloboMax LLC 7250 Parkway Drive, Suite 430 Hanover, MD 21076 Voice: (410) 782-2205 FAX: (410) 712-0737 _______________________________________________________ From:Mats Karlsson Subject:Re: [NMusers] NONMEM Tips #16 - April 2, 2003 - Modeling a "baseline" componentand an additive "drug" component Date:Fri, 04 Apr 2003 20:45:11 +0200 Dear all, Just a couple of thoughts on Lewis alternatives 1 and 3 (2 seems to have no advantages over 3). Alt. 3 will differ from 1 in at least a few aspects: 1) For the FO method, Model 3 seems advatageous as the linearization would occur closer to the individuals' predictions. This could be of value whenever residual error is heteroscedastic (instead of the homoscedastic error in the simple example below). Also when BSL comes into the model in a more complex form such that it influences the predicted profiles in another way than mere scaling, this could be advantageous. 2) If there is a correlation between baseline and any other parameter, this would be incorporated into model 1 as an estimated covariance, whereas in model 3 as a covariate relationship between BSL and the parameter in question. The latter will provide a wider range of shapes for the relation than a mere correlation. This difference may well also have other implications. 3) Model 3 does not assume any distribution of BSL in the population (as Lewis points out). On the other hand simulation from the final model will rely on the empirical distribution of BSL values. Model 1 on the other hand will estimate (with imprecision estimates) the features of BSL and any covariate relations that influence BSL. If Model 3 is used, such a model could of course be developed separately but with less information speaking to BSL (all data point speak to some extent to BSL) and with additional/other assumptions about error structure. 4) Some modellers like, for indirect effect models, to estimate Kin and Kout, as true physiological parameters, rather than BSL. Model 3 would not allow such parametrisation. Best regards, Mats _______________________________________________________