Covariate Models Using Weight

Date: Wed, 17 Nov 1999 14:09:55 +1300 From: Nick Holford <n.holford@auckland.ac.nz> Subject: Covariate Models Using Weight I agree with your comments about the value of centering to improve the estimation of parameters in the covariance model. There is no need to be obsessional about using the median. Any convenient value that is approximately in the middle of your data is fine. Remember that the final parameter estimate you obtain will be defined in terms of this centering value. I prefer to refer to this centering value as the standard covariate value e.g. a weight of 70 kg is a widely recognized standard for human adult weight. However, I have argued (Holford 1996) on data driven and biological grounds that models for body size should be based on the allometric model: CLi = CLstd * (Wi/Wstd)**3/4 Vi = Vstd * (Wi/Wstd)**1 where CLi, Vi are CL and V in an individual with weight Wi and Wstd is a standard weight e.g. 70 kg. CLstd and Vstd are the population parameters standardized to the size of an individual with weight Wstd. The exponent value of 3/4 for CL can be justified on theoretical grounds (West et al. 1997) and is supported by allometric studies of a wide variety of body functions with an estimate of this exponent indistinguishable from 0.75 (Peters 1983). Justification for V and other body volumes having an allometric exponent of 1 has been reviewed by Anderson et al. 1997. Note these models do not have an intercept parameter. I believe it is an a priori more reasonable model to expect that CL or V will be zero when WT is zero. I prefer to put my faith in biology and mechanism when choosing a model. I resort to statistical heuristics (e.g. change in log-likelihood) when the biology or mechanism is not obvious. I suspect that empirical estimates of allometric exponents reported in the literature for PK parameters are most likely indistinguishable from the a priori value of 3/4 for CL and 1 for V. If the null hypothesis that the exponents are 3/4 and 1 is rejected then careful thought should be given to other confounding factors in the data rather than rejecting a priori well established biological principles. Anderson BJ, McKee D, Holford NHG. Size, myths and the clinical pharmacokinetics of analgesia in paediatric patients. Clinical Pharmacokinetics 1997;33:313-327 Holford NHG. A size standard for pharmacokinetics. Clin. Pharmacokin. 1996: 30:329-332 Peters RH. The ecological implications of body size. Cambridge University Press.1983 West GB. Brown JH. Enquist BJ. A general model for the origin of allometric scaling laws in biology. Science. 1997; 276:122-6 -- 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.htm