Re: Model building algorithm

From: LSheiner <lewis@c255.ucsf.edu> Subject: Re: Model building algorithm Date: Tue, 25 Apr 2000 09:24:06 -0700 Two remarks: 1. Unless I did my algebra wrong (which is usual, indeed, often inevitable), and assuming you meant S2 = TVS2*EXP(ETA(2)), your series of equations reduces to log(S2) = a + b*wt + eta1 +eta2 with a and b unknown constants. If so, then var(eta1) and var(eta2) are not identifiable (unless one or both appear somewhere else in the model not was their sum). 2. More to the point, I agree that we need at least some common practices for building models, and I also agree that saturated models for random effects get quickly out of hand. Her are some thoughts on what the "solution" should look like: 2.1. While we tend to seek the "best" among some set of models that we implicitly consider, we almost surely do not find it, unless our initial set is very small. In any event, the value of a model is not determined by whether it is best in its class, however (who is to say the class contains a model that is "good enough"?) but by its faithfulness to the real world it models, or more practically, by its performance. I think we will have more success seeking agreement on procedures for evaluating models, rather than ones for building them. My current favorites are predictive distributions of interesting marginal statistics, but much work remains to be done. 2.2 I continue to think that it does matter whether the "working" OMEGA used for model building is diagonal or not. That is why I use a full OMEGA when I use the "scale in X and Y" inter-indvidual variability model while building a regression model. We have seen some very peculiar behavior when off-diagonal OMEGA terms are excluded, including the choice of a wrong regression model. See, for example: J Pharmacokinetic Biopharm 1994 Apr;22(2):165-77 Interaction between structural, statistical, and covariate models in population pharmacokinetic analysis. Wade JR, Beal SL, Sambol NC. Department of Pharmacy, University of California, San Francisco 94143-0446. The influence of the choice of pharmacokinetic model on subsequent determination of covariate relationships in population pharmacokinetic analysis was studied using both simulated and real data sets. Simulations and data analysis were both performed with the program NONMEM. Data were simulated using a two-compartment model, but at late sample times, so that preferential selection of the two-compartment model should have been impossible. A simple categorical covariate acting on clearance was included. Initially, on the basis of a difference in the objective function values, the two-compartment model was selected over the one-compartment model. Only when the complexity of the one-compartment model was increased in terms of the covariate and statistical models was the difference in objective function values of the two structural models negligible. For two real data sets, with which the two-compartment model was not selected preferentially, more complex covariate relationships were supported with the one-compartment model than with the two-compartment model. Thus, the choice of structural model can be affected as much by the covariate model as can the choice of covariate model be affected by the structural model; the two choices are interestingly intertwined. A suggestion on how to proceed when building population pharmacokinetic models is given. LBS. _/ _/ _/_/ _/_/_/ _/_/_/ 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)