Using covariates with positive and negative values

From: Garry Boswell Subject:[NMusers] Using covariates with positive and negative values Date: Mon, 5 May 2003 08:51:28 -0700 NONMEM GROUP, I have data from a mouse TK study that I am attempting to analyze using NONMEM. Mice were administered IP doses of a drug and single blood samples/animal were obtained at serial time points. Both single dose and multiple dose (steady state) data were obtained. I have LN transformed DV and have been successful at fitting the data using ADVAN2 TRANS2 and the control stream below: $PROB ETA ON CL and V Sex on V $INPUT ID DATE=DROP TIME ODV DV AMT MDV EVID CMT SS II Grp Sex Wt $DATA COMBINED_LN_MOD.CSV IGNORE=c $SUBROUTINES ADVAN2 TRANS2 $PK TVCL = THETA(1) TVV=THETA(2)+Sex*THETA(4) TVKA = THETA(3) CL=TVCL +EXP(ETA(1)) V=TVV + EXP(ETA(2)) KA=TVKA K = CL/V Half= (0.693/K) S2 = V $ERROR PRD=F IPRED=0 IF(F.GT.0) IPRED=LOG(F) Y=IPRED + EPS(1) IWRE=0 IRES=DV-IPRED IF(IPRED.NE.0) IWRE=IRES/IPRED $THETA (0, 2) (0, 30) (0, 6) (1) (1) $OMEGA 0.6, 0.1 $SIGMA 0.1 $EST MAXEVALS = 3000 SIGDIGITS =4 PRINT = 10 POSTHOC METHOD=CONDITIONAL $COV CONDITIONAL $TABLE NOPRINT ID Grp Sex TIME CL V KA Half K IPRED IRES IWRE PRD ODV PRED RES WRES FILE=P129GBADVAN2TRAN2_CV17.PRN However when I try to include a covariate for weight change on either V or CL, the parameter goes negative and causes NONMEM to halt execution. This occurs with weight change added as either an additive or portortional covariate. I did not LN transform the weight data since both positive and negative changes were allowed. Would someone with experience with this type of problem offer a suggestion? Garry Boswell, Ph.D. Senior Director, Pharmaceutical Development Pharmacyclics, Inc. 995 Arques Avenue Sunnyvale, CA 95085 (408) 328-3635 E-mail: gboswell@pcyc.com

From: "Bhattaram, Atul" Subject: RE: [NMusers] Using covariates with positive and negative values Date:Mon, 5 May 2003 12:08:48 -0400 Hello Garry Did you try a power model or an exponential model? This should take care of the positive and negative changes. Venkatesh Atul Bhattaram CDER, FDA.

From:"Bachman, William" Subject:RE: [NMusers] Using covariates with positive and negative values Date: Mon, 5 May 2003 12:34:07 -0400 couple of observations: 1. do you really want to add an exponential term or multiply by the exponential term: CL=TVCL *EXP(ETA(1)) V=TVV* EXP(ETA(2)) 2. in the absence of a meaningful estimate of the covariate effect, I suggest using a small value to only minimally perturb the system from the base model, e.g your theta(4) and theta(5) are large and causing the parameters to go negative. Try something like 0.001 instead of 1 for their estimates and use the final estimates from your base model for the other parameter estimates. That way you start off no worse than the base model. 3. Once you get your model to at least begin to iterate, you can use NOABORT on the $EST record to let the minimization proceed in the presence of negative parameters. nmconsult@globomaxnm.com GloboMax LLC 7250 Parkway Drive, Suite 430 Hanover, MD 21076 Voice: (410) 782-2205 FAX: (410) 712-0737

From: Leonid Gibiansky Subject: Re: [NMusers] Using covariates with positive and negative values Date:Mon, 05 May 2003 12:35:25 -0400 Garry, The model that you used is incorrect, you should not use CL=TVCL +EXP(ETA(1)). Use CL=TVCL*EXP(ETA(1)) (or CL=TVCL+ETA(1) ). To account for weight covariate, use something like CL=TVCL*EXP( THETA(?)*(WT/WT0-1)+ETA(1)) where WT0 is the mean or median weight, and similarly for V. Also, with just one point per animal, you may have problems with you model since you will have three parameter per animal (two eta's and one sigma) to fit just one data point. If your sampling points are at fixed time relative to the dose, I would rather try simple concentration versus covariate model C(fixed time, the same for all animals) = A+B*sex + C*(WT/WT0-1). If not, you may try to remove random effect from either volume or clearance and see how this will affect the result (covariate can be added to the parameter even if there are no random effect on this parameter). Leonid

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/ _______________________________________________________