Decrease in OFV with a fixed effect

From: "Bonate, Peter" pbonate@ilexonc.com Subject: [NMusers] Decrease in OFV with a fixed effect Date: Mon, August 23, 2004 9:06 am Hi, everyone. I am having trouble understanding how something could happen. Perhaps I am having a brain hiccup. I don't know. I fit a 2-compartment model to data from 97 subjects (2 to 9 observations per subject) using FOCE-I. Abbreviated NONMEM code: TVCL = THETA(1)*(CRCL/7.2)**THETA(5)*EXP(ETA(1)) V1 = THETA(2) Q = THETA(3) V2 = THETA(4) The variance associated with V1, Q2, and V2 was small, <1E-4, and so I removed these from the model. The remaining variance component on CL was ~30% with 15% IOV. Residual error was an exponential error model (15%). The OFV was -134. With this class of drugs, weight has been shown to be a consistent predictor of V1. Now in my model, V1 is a fixed effect. Just to see what would happen I modeled V1 using the following TVCL = THETA(1)*(CRCL/7.2)**THETA(5)*EXP(ETA(1)) V1 = THETA(2)*(WGT/60)**THETA(6) Q = THETA(3) V2 = THETA(4) Theta(6) was 1.19 +/- 0.551. The OFV for this model was -155, a decrease of 21 points. Imagine my surprise. At first I thought maybe I was at a local minima with the reduced model. I perturbed the estimates of the reduced model a few times but consistently obtained -134 as the OFV. I don't think local minima explains this. I am having a hard time understanding this. How can a covariate explain a fixed effect when the effect is a constant? Any thoughts on this would be appreciated. As an aside, how many people reduce their base model, removing small variance components, prior to moving on towards covariate model development? I can see arguments for and against both practices. I'd be interested in hearing arguments for and against both sides. Thanks alot. Pete Bonate Peter L. Bonate, PhD, FCP Director, Pharmacokinetics ILEX Oncology 4545 Horizon Hill Blvd San Antonio, TX 78229 phone: 210-949-8662 fax: 210-949-8219 email: pbonate@ilexonc.com

From: "Leonid Gibiansky" lgibiansky@emmes.com Subject: RE: [NMusers] Decrease in OFV with a fixed effect Date: Mon, August 23, 2004 9:30 am Hi Peter, Although I do not have any good statistical explanation for this effect I've seen it several times: covariate on fixed effect may decrease OF and improve fit even if random effect is absent (small or does not improve the OF). Leonid

From: "Xiao, Alan" alan_xiao@merck.com Subject: RE: [NMusers] Decrease in OFV with a fixed effect Date: Mon, August 23, 2004 10:03 am I saw this before too. Sometime, you could estimate the random effect again. Alan

From: "Mats Karlsson" mats.karlsson@farmbio.uu.se Subject: RE: [NMusers] Decrease in OFV with a fixed effect Date: Mon, August 23, 2004 10:12 am Hi Pete, The fact that you get an estimate of 10-4 for V1 variance, may be because variance is truly small (in which case adding covariate should not improve OFV), or because it is downwards biased due to model misspecification (e.g. through a diagonal omega structure). In the latter case, you can well expect an improvement in OFV if you add a true covariate (and maybe if you add a false one too it is difficult to know what can happen in misspecified models). Mats -- Mats Karlsson, PhD Professor of Pharmacometrics Div. of Pharmacokinetics and Drug Therapy Dept. of Pharmaceutical Biosciences Faculty of Pharmacy Uppsala University Box 591 SE-751 24 Uppsala Sweden phone +46 18 471 4105 fax +46 18 471 4003 mats.karlsson@farmbio.uu.se

From: "Kowalski, Ken" Ken.Kowalski@pfizer.com Subject: RE: [NMusers] Decrease in OFV with a fixed effect Date: Mon, August 23, 2004 11:46 am Hi Pete, To expand on Mats' comments you should be careful not to over-interpret a variance component that is estimated near zero to mean that there is no interindividual variability. It may be that there is insufficient information in the design to accurately estimate this variance component (I note that you indicate that for some subjects you only had 2 observations). Also, if there is model misspecification in omega by using a diagonal omega structure when there is a true non-zero correlation between parameters (say CL and V) it may be that NONMEM will partition the interindividual variability into only one of these components. I have observed that variance components estimated near zero (say for V) for a diagonal omega will no longer be estimated near zero when fitting a block omega that allows for the covariance to be estimated (say between CL and V). Based on these observations I have a couple of suggestions/questions: 1) If you fit a block omega structure does NONMEM still want to estimate the variance components for V1, Q2, and V2 near zero? 2) For the model fit you describe below with a 21 point drop in OFV did you ee a reduction in the omega for CL relative to the estimate when you did not include the WT effect on V1? It may be that some of the interindividual variability is getting partitioned into the random effect for CL due to misspecification of omega. If so, then I would expect that the fixed effect for WT on V1 would to some extent reduce the omega estimate for CL. Ken

From: "Serge Guzy" GUZY@xoma.com Subject: RE: [NMusers] Decrease in OFV with a fixed effect Date: Mon, August 23, 2004 1:26 pm May be I did not understand but if you model V1 the way you did, V1 across individuals will be different because of their difference in weight. Your first model will give you the same V1 for everybody. If I am right, the two models are different. If there is a real correlation between V1 and weight, the latter could be bigger than the remaining random effect which then can be ignored. Serge Guzy

From:"Piotrovskij, Vladimir [PRDBE]" VPIOTROV@PRDBE.jnj.com Subject: RE: [NMusers] Decrease in OFV with a fixed effect Date: Tue, August 24, 2004 6:16 am Pete, I would recommend to keep all BIV-related random effects in the model until the full covariate model is finalized. Usually, due to practical reasons the base model (w/o covariate effects) implements a diagonal random effect matrix. It is not uncommon the data do not support estimation of BIV in all parameters, however, before you build the covariate model you cannot say, which component of the matrix is not estimable. If you drop one or more ETAs based on the fact that the corresponding OMEGAs are negligible in the base model you are at risk of selecting a wrong matrix for the final model. Best regards, Vladimir ----------------------------------------------------------------- Vladimir Piotrovsky, Ph.D. Research Fellow, Advanced PK-PD Modeling & Simulation Global Clinical Pharmacokinetics and Clinical Pharmacology (ext. 5463/151) Johnson & Johnson Pharmaceutical Research & Development Turnhoutseweg 30 B-2340 Beerse Belgium

From:"Vanapalli_Sreenivasa" Vanapalli_Sreenivasa@allergan.com Subject: RE: [NMusers] Decrease in OFV with a fixed effect Date: Tue, August 24, 2004 11:05 am Peter, Looks like you've fixed THETA(2), which was V1 in the first model and your assumption of fixing V1 was right. However, you have incorporated other variables in the equation in the second model which is 'body weight' and also THETA(6). Now you are computing V1 based on all these parameters not just with 'fixed THETA(2)'. I don't see V1 fixed anymore with all these new variables into equation. With changing body weights the fit looks much better (not fixed) resulting in decreased OBJ value. I may be wrong with my explanation. Regards, Sreenivasa Rao Vanapalli, Ph.D. Scientist, Clinical Pharmacokinetics Allergan Inc. 2525 Dupont Drive, RD2-2B Irvine, CA 92623-9534 E-mail: vanapalli_sreenivasa@allergan.com Phone: (714) 246-4325 Fax: (714) 246-5538

From: "Serge Guzy" GUZY@xoma.com Subject: RE: [NMusers] Decrease in OFV with a fixed effect Date: Tue, August 24, 2004 12:18 pm You are right about V1 not being fixed and therefore you speak about two different models. The issue was that without covariate, V1 does not have random effect associated with it (eta is very very small). This seems to suggest that V1 is the same across all individual and therefore we should not expect a correlation between weight and V1. However, confounding factors that flip flop random effects with covariate effect is not uncommon. When there are no covariate, most of the interindividual variability can be found in some of the parameters and not in V1(may be by chance only). When assuming a correlation (without random effect), a flip flop between 2 different effects occur. I am pretty sure that at least one random effect from all other parameters (except V1) is different in the covariate model and the one without covariate. Serge Guzy _______________________________________________________