Re: centering variables

From: "Nick Holford" <n.holford@auckland.ac.nz> Subject: Re: centering variables Date: Thu, 4 Mar 1999 21:02:39 +1300 >> 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 datae. All linear >models will ultimately break down for parameters that >reflect real (positive) biological quantities One way to avoid negative clearance yet using a simple extension to the linear model without worrying about a priori constraints on THETA(age) is to use: CLtv = CLpop * EXP(THETA(age)*(AGE-AGEstd)) For small values of THETA(age)*(AGE-AGEstd) this is essentially the same as: CLtv = CLpop * (1+THETA(age)*(AGE-AGEstd)) If THETA(age)*(AGE-AGEstd)) becomes large and would cause a negative Cl in the linear model then the exponential model will gently decrease the clearance asymptotically towards zero. On the other hand, for small differences between Clpop and CLtv, THETA(age) has the same interpretation as with the linear model. -- Nick Holford, Dept Pharmacology & Clinical Pharmacology University of Auckland, Private Bag 92019, Auckland, New Zealand email:n.holford@auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556 http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.html