Centering (was Re: Missing covariates)

From: Nick Holford <n.holford@auckland.ac.nz> Subject: Centering (was Re: Missing covariates) Date: Tue, 03 Jul 2001 08:21:39 +1200 Joga, Let me pick up on your remarks about centering. Imagine this simple model using AGE to explain variability in CL: CL=POPCL*(1+THETA(age0)*(AGE-0)) ; centered on 0 CL=POPCL*(1+THETA(age40)*(AGE-40)) ; centered on 40 Algebraically these are identical given appropriate values for THETA(age0) and THETA(age40) but I believe that the robustness of the estimation procedure can be affected by whether or not centering is used. I am afraid I cannot give any reference for this (apart from saying that I think I heard Lewis Sheiner make a similar remark on some occasion). I wonder if Lewis or somebody else would like to offer some support for centering as a means of obtaining "better" estimates. If centering is "better" does this mean improved precision of the estimate of THETA(age40) or less bias or what? If the parameter estimates for THETA(age0) and THETA(age40) have any difference in precision or bias then won't this alter statistical inferences based on these parameters? The second issue relates to the convenience of using a suitable centered value. I am an enthusiastic advocate of doing this. When parameter estimates are reported then if a covariate such as age is in the model then the parameter value is centered on the centering value. In the first case POPCL estimated using THETA(age0) will be for someone of age 0 and using THETA(age40) will for someone of age 40. I would say it is much more convenient to be able to talk of the clearance for someone of age 40 if the original data was obtained in adults. I would go one step further and say that if one can choose a centering value that can be considered a standard eg. 40 years for age, 70 kg for weight, 6 L/h for creatinine clearance, then it becomes possible to easily compare population clearances across different studies and different drugs. No matter what centering value is used for the estimation the parameter estimates one should consider reporting them using a standard value. The convenience comes from using a centering value that is the same as the standard value. Holford NHG. A size standard for pharmacokinetics. Clin. Pharmacokin. 1996: 30:329-332 Jogarao Gobburu 301-594-5354 FAX 301-480-3212 wrote: > > Centering is done for convenience, it does not alter statistical > inference. > > Regards, > Joga Gobburu > Pharmacometrics, > CDER, FDA. bvatul@ufl.edu wrote: > >Hello All > >Could somebody please clarify this: > > > >I am analysing a data set in which I have covariates (wge, ht, wt, > crcl) > >for 70% of the patients. Is it a good idea to substitute the median > >values of these covariates for the missing covariates ie., in patients > >in whom I dont have the covariates?In case we are substituting the > >median values and analysing the covariates is it still necessary to > >center the covariates? Are there any reported papers where the addition > >of missing covariates has led to misinterpretation of data? When should > >we substitute the missing covariates with the median values and when > >should we not? > >Thanks > >Atul > > -- Nick Holford, Divn Pharmacology & Clinical Pharmacology University of Auckland, 85 Park Rd, 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