RE: covariate selection question

From: mark.e.sale@gsk.com Subject: RE: [NMusers] covariate selection question Date: Tue, 17 Jan 2006 10:15:58 -0500 Joern, Thanks for the opportunity for me to once again rant on my favourite subjects, the limitations of step wise model building. This behaviour is well documented (see Wade JR. Beal SL. Sambol NC. Interaction between structural, statistical, and covariate models in population pharmacokinetic analysis. Journal of Pharmacokinetics & Biopharmaceutics. 22(2):165-77, 1994 Apr.). First, as you imply, one should clearly not base the final model decision on -2LL alone. Does the covariate addition have any ther good or bad effects (better plots, better PPC, smaller inter individual variances)? Is it biologically plausible or even almost certainly the case? But, on to your question. Imagine, if you will, that you are trying to explain the area of a rectangle. One covariate is a (very) imprecise measure of the length, another is a somewhat less imprecise measure of the width. You put in the length covariate and find a small improvement in ability to explain area - it is a very imprecise measure - or perhaps your structural model is wrong (rather than Area = theta(1)*cov_l x theta(2), you have Area = theta(1)*exp(cov_l) x theta(2), where cov_l is the covariate proportional to length). Next you try cov_w on theta(2) (Area= theta(1) x theta(2)*cov_w) - and this is better. Now, you go back and try cov_l as a predictor of theta(1) - and you find it is helpful, now you have the correct structural and covariate model (with cov_l a predictor of length and cov_w a predictor of width). It can be shown that this can easily occur (the Wade and Beal paper demonstrates it for structural, covariate and variance effects). Hence, my view that step wise searches will only give you the correct answer if all effects are independent - which they never are in complex biological systems. Therefore, step wise searches will never give you the correct answer. so, the answer is, put the covariate in. Mark Sale M.D. Global Director, Research Modeling and Simulation GlaxoSmithKline 919-483-1808 Mobile 919-522-6668