Re: centering variables

From: LSheiner <lewis@c255.ucsf.edu> Date: Wed, 03 Mar 1999 15:18:16 -0800 Subject: Re: centering variables --In response to Dr. Charles' message---- In the renal clearance case, indeed, the intercept is the component of clearance in the absence of renal function. What does it mean to speak about the component of clearance in the absence of age? How can there be an age-independent component if age is a surrogate (as it is in model (A))) for size as well? The notion of the covariate-independent part of clearance is only meaningful (at least to me) for the covariates that can be "absent" or zero and be meaningful (as, for example, the deviation of age from mean age can, indeed, be zero meaningfully) Absent renal function is an observable and meaningful state. Absent age is not (unless you define age=0 as time of birth, and then the intercept has the meaning of clearance at time of birth ... making it obvious why you would never want to use such a model if all your data were from people aged 18 and over - it is absurd to imagine that one could extrapolate such data down to time of birth!). > > Furthermore, when using Model (B) in a mostly elderly population > (age distribution skewed to the right) isn't there the risk of getting > negative CL values for the younger subjects? > This is the problem of using linear models to extraoplate beyond the limits of one's data. All linear models will ultimately break down for parameters that reflect real (positive) biological quantities. But, technically, for any data set, you will get the identical model whether you use (A) or (B), so if you have the problem with one parameterization, you have the same problem with the other: recall, the only differences are (i) ease of finding solution, and (ii) interpretability of the untransformed parameters, and hence direct estiamtes of SE's of interpretable parameters. The model will predict the exact same values of CL as a function of age with either parameterization. LBS. -- Lewis B Sheiner, MD Professor: Lab. Med., Biopharm. Sci., Med. Box 0626 UCSF, SF, CA 94143-0626 voice: 415 476 1965 fax: 415 476 2796 email: lewis@c255.ucsf.edu