RE: Model building algorithm

From: "Sale, Mark" <ms93267@glaxowellcome.com> Subject: RE: Model building algorithm Date: Tue, 25 Apr 2000 13:57:46 -0400 Lewis, Onward, I did have an error in my equations, TVS1 should be TVS2, as you pointed out. To make it simple, let's use only additive etas, and a linear relationship between wt and vol then TVWTS = THETA(1) ; TYPICAL VALUE OF V/WT SLOPE WTSL= TVWTS + ETA(1) ; TRUE VALUE OF V/WT SLOPE TVS2 = THETA(2) + WT*WTSL ; TYPICAL VALUE OF S2 S2 = TVS2 + ETA(2) ; TRUE VALUE OF S2 then S2 = THETA(2)+WT*(THETA(1)+ETA(1)) + ETA(2) and eta(1) and eta(2) are identifiable, at least not formally unidentifiable. I think that the equations from the previous email reduce similarly, on a log scale. I agree with your point we need not obsess (too much) about finding the best model, and I'm sure we can all agree that the objective function is not the sole criteria on which to base the model building process. However, we assume that we are looking only find the "best" model, but the "correct" model (in order to do unbiased hypothesis testing). Presumably, no model is better than the correct model, so the correct model must be the best. That, I believe is the reason for seeking the best model. Regardless, we delude ourselves that hypothesis testing is ever appropriate. Your point about the performance is well taken. I particularly like your sentence but by its faithfulness to the real world it models. I'll use that next time I discuss with Mike Hale and Keith Muir the relative merits of empiric vs biologically based models. Clinically, we are interested in making some reasonably accurate prediction - about the real world, and often extrapolating those predictions to some other data set. Mark