RE: Model building algorithm

From: "Sale, Mark" <ms93267@glaxowellcome.com> Subject: RE: Model building algorithm Date: Tue, 25 Apr 2000 09:32:01 -0400 Bill, James, Lewis, Nick et al. This discussion has been very valuable, I am grateful for it. However, I still have a question at hand. I'm actually revising our method sheet for population pk at Glaxo right now. We, for better or worse (probably for better) live in a regulated (read SOP driven) environment. We are expected to justify every decision we make in building these models. I'm sure that "The plots looked better this way" is a perfectly good scientific justification, and my experience suggest that the FDA is very scientific in these discussions. However, we (the royal we) do need to write a method sheet with at least recommendations for a starting point. It is my view that full backwards elimination is impractical. Assume we have a 2 compartment model, with 4 key parameters, ALAG, S2, K and Ka, ignoring k23 and k32. Assume we have the bare minimum of 4 covariates to test (Age, race, weight and gender). This is 16 effects, add in the 5 or 6 typical parameters (ALAG, S2, K, KA, K23 and K32), each with and without ETA's, as well as a full covariance matrix, and I'm quite confident that this model will not converge successfully. In reality, we have many more covariates to examine (2 to 4 measures of liver function, renal function, treatment, center, concomitant medications, concurrent diseases etc, etc) Of course, a more rational approach to selection of which covariates to test on each parameter could be used either based on biology or graphics. So, I think that forward addition, with guidance from the well described graphical methods, is the only practical solution, probably followed by backward elimination with the near final model. This is our current practice. However, my question remains about whether (in forward addition) etas should be used on the parameters. Note that this does not apply only to "structural" parameters (as in my original example, K23 and K32), but can apply to the model of a covariate to a parameter, e.g. TVWTF = EXP(THETA(1)*WT)) ; TYPICAL VALUE WEIGHT EFFECT WTF = TVWTF*EXP(ETA(1)) ; TRUE VALUE WEIGHT EFFECT TVS2 = THETA(2)*WTF ; MODEL FOR VOLUME AS A FUNCTION OF WEIGHT S2 = TVS1*EXP(ETA(2)) That is, weight may effect volume differently for different people. (Arnold Schwartneggers weight effect, or cirrhosis with ascites weight effect vs the weight effect for the rest of us, adipose tissue). The extreme might be that the drug is distributed to muscle but not fat, and so Arnie has a higher volume (as well as volume/kg), the ascitic has a lower volume in spite of a higher weight, and the rest of us have no relationship of volume to weight. We clearly need an eta to pick up this effect. The classic description of forward addition is to add a single effect and test that. My question is, what is the chances of being misled by complex interactions between fixed and random effects, or more than one fixed effect. I now have one clear example that it can happen. Are there suggestions to avoid it? I think that backward elimination is probably a better algorithm, but is nearly always impractical. At the moment, I'm leaning toward testing both with and with etas before ruling out that effect, with the addition of only the theta being the "purest", but the addition of etas as well being more realistic. Mark