Re: Using covariates with positive and negative values

From: Nick Holford Subject:Re: [NMusers] Using covariates with positive and negative values Date:Tue, 06 May 2003 08:17:57 +1200 Garry, The example you show of SEX as a covariate (and the verbal description of using WT) indicate that you are using an additive covariate model e.g. IF (SEX.EQ.1) THEN CLSEX=THETA(male) ELSE CLSEX=0 ENDIF CLWT=THETA(wt)*WT CLREST=THET(rest) ; the rest of the clearance not predicted by SEX or WT TVCL = CLREST + CLSEX + CLWT As you have noticed it is quite possible to get problems with negative values for CL with this model. Even if you avoid this during estimation it can be possible to apply your final model with WT outside the original range and predict negagive CL. Sometimes these models even get published! Note you could easily get a negative estimate for CLREST which emphasizes its non-biological meaning. I prefer to use multiplicative models for covariate effects. This makes it easy to describe the relative importance of each covariate, can be readily written to prevent negative values and allows a convenient way to combine several covariate effects e.g. ; FSEX, FWT and FAGE are the fractional changes in CL due to each covariate ; e.g. if FSEX is 1.2 if would mean that CL was 20% higher in men compared with women IF (SEX.EQ.1) THEN FSEX=THETA(male) ELSE FSEX=1 ENDIF FWT=(WT/70)**0.75 ; allometric model centered on 70 kg FAGE=EXP(THETA(age)*(AGE-40)) ; empirical age effect centered on 40 y TVCL = CLSTD*FSEX*FWT*FAGE The empirical EXP() model I show for modelling the effect of AGE can be used with any continuous covariate. It has the property of preventing non-positive typical values for parameters like CL. When the covariate effects are small (and they typically are) then the EXP() model approximates a linear model: FAGE=1+THETA(age)*(AGE-40) ; approx EXP(x) when x is small The parameter THETA(age) is easily interpreted as the fractional change in CL per unit change in AGE. Note that I refer to the population estimate of CL as CLSTD. This is a reminder that it will be the CL in a standard individual. In this case a 70 kg, 40 year old female. The only time I would deliberately use an additive rather than a multiplicative model for a covariate effect is when the biology clearly pointed this way. An example is the additive nature of renal and non-renal clearance. I know that these components of CL are additive so I would write: TVCL = CLnr + RF*CLr where RF is renal function. I compute RF=CLcr/CLcrstd where CLcr is an estimate of creatinine clearance (e.g. obtained from Cockcroft&Gault using serum creatinine) and CLcrstd is CLcr in my standard individual e.g. 6 L/h/70kg. I would include other covariates multiplicatively e.g. TVCL = (CLnr*FSEX*FAGE + RF*CLr)*FWT This says I suspect a sex and age effect on non-renal CL (but not on renal CL) and I expect WT to affect both non-renal and renal clearance. Leonid has already pointed out the EXP() model although I would not use it for WT because I know the allometric model has much stronger biological support. He has also suggested that it would be more usual to express the random effects with an EXP() model: CL=TVCL*EXP(ETA(cl)) The model you were using would have forced all the random effects to be positive and so your TVCL value would necessarily become less than the lowest actual individual CL. Nick -- Nick Holford, Dept Pharmacology & Clinical Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556 http://www.health.auckland.ac.nz/pharmacology/staff/nholford/ _______________________________________________________