RE: covariates

From: "Leonid Gibiansky" leonidg@metrumrg.com Subject: RE: [NMusers] covariates Date: Fri, September 17, 2004 11:52 pm Renee, Well, I am afraid you will get conflicting advices from me and Nick. I would do the following: add WT as a power model to all the parameters AT THE SAME TIME with different powers (TVP ~ THETA(1)*(WT/21)**THETA(5), TCL ~ THETA(2)*(WT/21)**THETA(6), etc.) and see whether this results in any improvement of the model (OF drop + plots of random effect versus WT). You may observe that some of the power parameters (like THETA(5) ) are relatively large and well-defined (small relative standard error = SE/(parameter value) ) while the others are either small or not-well-defined. I would exclude the latter and refit the model to make sure that this would not damage the fit; and continue until you end up with the simplest model that is as good as the full model (where the full model is the one with WT to all parameters). This is similar to the backward elimination procedure, but for one covariate. Let's refer to this simplest model as model 1. To be more in line with Nick suggestions, you may fit the model where all the parameters depend on WT according to the allometric scaling (i.e., CL, Q ~ WT^0.75, V ~ WT, Kij=Q/V ~ WT^(-0.25). Let's call it allometric model. You may compare allometric model with the model 1 and check which one is better. To compare, look on OF, variances of the parameters, PRED vs DV fit, ETAs vs WT plots. Also, it make sense to plot PRED of the model 1 versus PRED of the allometric model to see whether there is any difference. The third way, a combination of the first two, would be to fit the allometric model and then look on the dependencies of the random effects on WT. If you see any, you may take them into account by introducing covariates that are highly correlated with WT. For the pediatric study it can be age. For the adult study it can be gender or BMI (or some other measure of obesity). On the more technical side: Dependence TVP = THETA(1) * (1 + THETA(2) * (COV - median(COV)) is not too good. The part (COV - median(COV)) is negative for half of the patients. If THETA(2) is sufficiently large, TVP can be negative. You may try TVP = THETA(1) * EXP( THETA(2) * (COV - median(COV))/median(COV) ) instead. You should not fix THETA(5) while looking for the other covariates. Good luck and let us know the results. Leonid.