RE:constant CV

From: "Sale, Mark" <ms93267@GlaxoWellcome.com> Subject: RE:constant CV Date: Thu, 26 Apr 2001 08:14:12 -0400 Clement, In my view there is a continuum of criteria for selection of any models for empiric pk/pd modeling. The ends of the spectrum are the purely statistical (what best fits the data/can be statistically defended) and the physiologic (what makes sense based on our understanding of they physiology/pharmacology). Most of us are somewhere in between, insisting on some (in my view limited) statistical rigor, but based in our understanding of the physiology. Among nonmem users, I tend to lean toward the statistical end, among statisticians, I'm far toward the physiologic end. So, the issues to address are: What do the data tell us the model should be: What makes sense physiologically. The first is easy to address, just run all of them and see which has the lowest objective function (corrected for degrees of freedom, also will successfully complete a covariance and have an estimation correlation matrix with all off-diagonal element with absolute value < 0.95). Of course, trying 4 different model for each parameter/covariate model and each interindividual error, and all the possible combinations leads to literally millions of models. The second is harder. First, I think that the second and third models are overparameterized. THETA(1) and THETA(2) are indistinguishable. I usually use something like. TVCL = THETA(1)*EXP(THETA(2)*(WT-60)/11) Where the standard deviation of WT is 11, and the mean is 60. (Don't know if I mean geometric of arithmetic mean, probably geometric) First, note that WT is centered and scaled. This improves the numerical stability, and give THETA(1) the nice property of being the value for a typical individual. Note however, that in this model, there will be a positive value for someone with a WT of 0. Personally, this doesn't bother me, since I've never seen someone with a WT of zero. But it does bother some people. However, the model TVCL = THETA(1)*WT Is a different model, you are making a different statement about physiology, that TVCL is proportion not to EXP(WT), but to WT. Generally, in adults we don't have sufficient range in WT to distinguish these models, so they can often be used interchangeable. However, if there is a wide range of WT (e.g., peds and adults), you may find that one is "better" (lower objective function) than the other. In this case, I'd run both and choose the one with the lower objective function. The same approach applies to the selection of the interindividual error, a balance between statistical and physiologic criteria. We often find that population parameters are log normally distributed. In this case the model CL = TVCL*EXP(ETA(1)) is appropriate. This model also has the nice property of never having a negative value for CL (if TVCL is positive). This is useful if you are using METHOD = 1, or POSTHOC. This model is usually my default. The other two (+ETA and *(1+ETA)) can be tried if you have reason to believe that the parameter is normally distributed. We recently used this error for a model of Hemoglobin A1c, where we knew that baseline value was normally distributed. However, in general, we use the log normal distribution for pretty much everything, since we always run POSTHOC and often use METHOD = 1. Mark