covariates

From:"Renee Ying Hong" yinghong@pharm.usyd.edu.au Subject: [NMusers] covariates Date: Wed, September 15, 2004 8:02 pm Dear All, I noticed that there used to have a lengthy argument about including covariates into the model using stepwise addition and backward elimination. Different opinions were presented to solve the stepwise problems by introducing statistical "arts". Dr Jonsson and Mats published a nice paper where stepwise procedure were briefly discussed: unicovariate model was tried in the basic model one at a time, followed by subsequent steps of trying each parameter/covariate combination in the current model. Since I am beginner of NONMEM, those "arts" are beyond my knowledge. Could someone let me know the routine steps of stepwise/backward unicovariately which suit to the practical implement. Here is the example: Subroutine: ADVAN3 TRANS4 The covariates of CL: A, B, C The covariates of V1: A, D The covariates of V2: B, D What is the steps I should follow to find the final model? Kind Regards, Renee Ying Hong Faculty of Pharmacy University of Sydney Tel: 61 2 9036 5025 Fax: 61 2 9351 4391 E-mail: yinghong@pharm.usyd.edu.au

From: "Nick Holford" n.holford@auckland.ac.nz Subject: RE: [NMusers] covariates Date: Wed, September 15, 2004 10:22 pm Renee, The first step in covariate analysis is to apply biology not statistics. Your two compartment model has 4 parameters which will vary with weight. So step 1 is to use an allometric model to describe between subject differences in CL, V1, Q, V2. No statistics required. Just do it. Then you might consider other biological covariates e.g. renal function on CL if you think the drug is renally eliminated. Finally you might have to resort to the usual Holy Grail search for effects of age, sex, race, hair colour, etc. IMHO this is mainly a waste of time for any practical application but if you do it then you should read: Ribbing J, Jonsson EN. Power, Selection Bias and Predictive Performance of the Population Pharmacokinetic Covariate Model. Journal of Pharmacokinetics and Pharmacodynamics 2004;31(2):109-134. They caution against Holy Grail searches if you have less than 50-100 subjects in your data base. Nick

From:"Renee Ying Hong" yinghong@pharm.usyd.edu.au Subject: RE: [NMusers] covariates Date: Thu, September 16, 2004 2:57 am Hello, Nick 1. My understanding of the allometric models you mentioned are as follows: CLi = CLstd * (WTi / WTstd) **0.75; Qi = Qstd * (WTi / WTstd)**0.75 V1i = V1std * (WTi / WT)**1; V2i = V2std * (WTi / WT)**1 each parameter/covariate combination will be run in NONMEM, and OFV will be compared with that of basic model. Since the subjects of my study are pediatric patients, WTstd would be 70 kg. Therefore, in my scenario, WTstd would be the media WT of the study patient cohort and (CL, Q, V)std would be the typical value of this study population. Please comment. 2. There are only 40 patients in this study. Therefore, in the second step, the stepwise/backward method will be employed to screen the other covariates? Kind Regards, Renee

From: "Nick Holford" n.holford@auckland.ac.nz Subject: RE: [NMusers] covariates Date: Thu, September 16, 2004 3:34 am Renee, > > Hello, Nick > > 1. My understanding of the allometric models you mentioned are as follows: > > CLi = CLstd * (WTi / WTstd) **0.75; Qi = Qstd * (WTi / WTstd)**0.75 > V1i = V1std * (WTi / WT)**1; V2i = V2std * (WTi / WT)**1 > > each parameter/covariate combination will be run in NONMEM, and OFV will be > compared with that of basic model. Since the subjects of my study are > pediatric patients, WTstd would be 70 kg. Therefore, in my scenario, WTstd > would be the media WT of the study patient cohort and (CL, Q, V)std would > be the typical value of this study population. Please comment. The allometric model you have written is correct. However, I think it is pointless to look at the OFV change compared to a model without weight. The allometric model is a priori correct as far as I am concerned. Just use the allometric model on all the parameters and get on with your life :-) You can use Wtstd=70 or some other number e.g. the median of your patients, when estimating the parameters. In theory it is better to centre the parameter estimates somewhere in the middle of the actual covariate values but I don't think it makes any big difference. However, for reporting the results I prefer to standardize all parameter values to 70 kg so that they can be readily compared to other results. > 2. There are only 40 patients in this study. Therefore, in the second > step, the stepwise/backward method will be employed to screen the other > covariates? If you only have 40 patients then the Ribbing and Jonsson paper suggest it is a waste of time to do blind searches for covariates using forward/backward step methods. If your patient population is under 1 year old then you might want to try models based on post-conceptional age to describe the maturation of development e.g. Bouwmeester NJ, Anderson BJ, Tibboel D, Holford NH. Developmental pharmacokinetics of morphine and its metabolites in neonates, infants and young children. Br J Anaesth 2004;92(2):208-17. Anderson BJ, van Lingen RA, Hansen TG, Lin YC, Holford NHG. Acetaminophen developmental pharmacokinetics in premature neonates and infants: a pooled population analysis. Anesthesiology 2002;96(6):1336-45 There is at least some biological expectation and empirical evidence that clearance and volume change in the first year of life. 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/

From: drfreedman@drfreedmaninc.com Subject: RE: [NMusers] covariates Date: Thu, September 16, 2004 8:33 am Nick and Renee Please note there can additional causes of weight dependence. If, for example, a concomitant medication dosed by BSA impacts Emax by killing receptors, I would expect Emax to depend somewhat on WT. If this additional medication also modulates CL, then CL may, in principle, show WT dependence additional to allometric scaling. If significant weight loss occurs throughout the study and admission weight is the WT covariable, I would also expect some residual dependence of OFV on WT. Regards Immanuel Freedman, PhD, MIEEE (619) 884-1347

From: "Leonid Gibiansky" leonidg@metrumrg.com Subject: RE: [NMusers] covariates Date: Thu, September 16, 2004 8:46 am Nick, Renee, Allometric model may be a valid guess, but I would be cautious to take those laws for granted. You may test them, but at least the results should be checked: plots of random effects (computed by the allometric-scale model) against WT should be reviewed. If the plots reveal any WT-trends, then allometric scaling is not accounting for the entire WT-dependence. You may argue that the remaining dependences should be treated via gender-dependence (gender is highly correlated with WT) or age-dependence (for pediatric patients age and WT are very strongly correlated) but in any case, this should be considered. On the other hand, if the model without WT describes data better than the one with WT (you can check it via OF or just looking on the fit) then it make no sense to use allometric scaling in the model. I think it is better to report the results for pediatric patients (say, 0-5 year old) using base WT that is close to the mean/median WT in the target population rather than using base WT=70. At least, the parameter values for a typical patient in the target population should be provided. Screening of covariates can be done formally, via likelihood test (OF) or informally, just looking on the plots of random effects (computed from the base model) versus covariates. You should be able to catch all strong dependencies just by eye. Leonid ========================== Metrum Research Group LLC 15 Ensign Drive Avon, CT 06001 www.metrumrg.com

From: "Nick Holford" Subject: RE: [NMusers] covariates Date: Thu, September 16, 2004 11:10 pm Immanuel, I agree there may be other ways that WT may influence PK parameters. But I think it's important to get the allometric component sorted out before searching for empirical relationships. It's not so clear if within subject variability in WT would vary allometrically especially if WT changes are due to disease progression. 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/

From: "Nick Holford" n.holford@auckland.ac.nz Subject: RE: [NMusers] covariates Date: Thu, September 16, 2004 11:28 pm Leonid, Allometry is beyond guesswork. It is one of the best understood and experimentally tested pieces of quantitative biology known. Please take a look at these papers: West GB, Brown JH, Enquist BJ. The fourth dimension of life: fractal geometry and allometric scaling of organisms. Science 1999;284(5420):1677-9. West GB, Brown JH, Enquist BJ. A general model for the origin of allometric scaling laws in biology. Science 1997;276:122-26. Gillooly JF, Brown JH, West GB, Savage VM, Charnov EL. Effects of Size and Temperature on Metabolic Rate. Science 2001;293:2248-2251. I agree that one should probably centre on the median WT in the popln but in our experience this has not made any difference to the estimates. We prefer to report results per 70 kg for comparison with much more widely available adult values. I think one should rely on the allometric weight model first then try to explain the remaining variability with more empirical possibilities e.g. age. This provides a rational basis for disentangling the strong correlation between weight and age. See these papers for examples: Bouwmeester NJ, Anderson BJ, Tibboel D, Holford NH. Developmental pharmacokinetics of morphine and its metabolites in neonates, infants and young children. Br J Anaesth 2004;92(2):208-17. van der Marel CD, Anderson BJ, van Lingen RA, Holford NH, Pluim MA, Jansman FG, et al. Paracetamol and metabolite pharmacokinetics in infants. Eur J Clin Pharmacol 2003;59(3):243-51. Anderson BJ, van Lingen RA, Hansen TG, Lin YC, Holford NHG. Acetaminophen developmental pharmacokinetics in premature neonates and infants: a pooled population analysis. Anesthesiology 2002;96(6):1336-45. I disagree with this assertion "if the model without WT describes data better than the one with WT (you can check it via OF or just looking on the fit) then it make no sense to use allometric scaling in the model". It is not unexpected that the OFV might get worse by adding WT. But this does not invalidate the underlying biology. If you don't put WT in the model then it becomes problematic for extrapolation from adults to children. At least by standardizing parameter values to adult values it then becomes obvious how to extrapolate outside the observed weight range. IMHO it makes no sense to conclude on the basis of inadequate design (e.g. limited weight range) that WT has no influence on parameter values when the prior biological knowledge is overwhelming. I suggest you look at Ribbing & Jonsson before advocating the use of OFV based tests for empirical covariate searches. Ribbing J, Jonsson EN. Power, Selection Bias and Predictive Performance of the Population Pharmacokinetic Covariate Model. Journal of Pharmacokinetics and Pharmacodynamics 2004;31(2):109-134 Nick

From: "Leonid Gibiansky" leonidg@metrumrg.com Subject: RE: [NMusers] covariates Date: Fri, September 17, 2004 7:29 am Nick I do not question allometric scaling law described in the papers that you cited. I question an assertion that this law implies CL, Q_i~WT^(3/4), V_i~WT dependences for each and every drug. This is a good guess that should be checked and corrected if needed. Any compartmental model is just a crude approximation of the very complicated biological processes, and it is hard to expect that coefficients of that approximation behave exactly as CL~WT^(3/4), V~WT for every drug. If data contradict these dependencies, one should follow the data rather than impose artificial restriction on the model. In particular, if the model without WT describes the data better than the one with WT (better in terms of model diagnostic: e.g., observed vs. predicted plots stratified by WT) I do not see why should one ignore it. For covariate search, I advocate common sense rather that OF search: you should look on diagnostic (random effect versus covariate plots) in addition to OF. There are also statistical approaches to multiple testing (roughly, if you conduct a lot of tests, you should be more stringent in terms of OF drop in order to claim significance). But OF drop is a good measure for a quick screening of multiple covariates. Leonid

From: "Nick Holford" n.holford@auckland.ac.nz Subject: RE: [NMusers] covariates Date: Fri, September 17, 2004 7:51 pm Leonid, Thanks for making it clear that we agree that allometric scaling is a plausible model. It seems we disagree on whether or not one can assume that CL, V1, Q, V2 parameters of the two compartment disposition model are correlated with physiological/anatomical properties. I accept that it is an assumption that I make when I use allometric models to scale these parameters. Given my understanding of the physiological/anatomical processes that I expect to govern pharmacokinetic disposition I do not see any need to seriously question this assumption. I agree that common sense should be used to guide a covariate search - in particular biological/mechanistically guided common sense. I accept that one might use OFV changes as a screening procedure but of course not for formal hypothesis testing given the well known failure of the chi-square assumption for the null OFV change distribution using NONMEM. I do not consider covariate effects are of practical importance unless one can also show that the random effect variance (e.g. as estimated by OMEGA) for a parameter of interest (e.g. clearance) is reduced by some relevant amount. It is not uncommon to see drops in OFV suggesting covariate effects but with a negligible change in OMEGA e.g. See Matthews et al. for an example where the contribution of several covariates in explaining the variability in clearance was estimated and the predictive performance of each covariate model was tested. There are examples where the OFV fell but there was no improvement in clearance variance nor improvemement in predictive performance. Matthews I, Kirkpatrick C, Holford NHG. Quantitative justification for target concentration intervention - Parameter variability and predictive performance using population pharmacokinetic models for aminoglycosides. British Journal of Clinical Pharmacology 2004;58(1):8-19 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/

From: "Ying Hong" yinghong@pharm.usyd.edu.au Subject: RE: [NMusers] covariates Date: Fri, September 17, 2004 10:50 pm Hello, Nick, Leonid I did try the allometric scaling law for each PK parameter (CL, V1, Q, V2) one by one in the basic model. Unfortunately, the results are either Minimization terminated or insignificant change of OFV. It seems that allometric scaling model doesn't fit to my study data. Perhaps, the formulation of this study drug, liposome, may modify the disposition of encapsulated drug which can not be explained by allometric scaling model. I also tried the covariate equation like that: TVP = THETA(1) * (1 + THETA(2) * (COV - median(COV)) ; P is the PK parameter ;COV is the covariate However, error message shows that P is negative (don't know why?). So, I am back to the allometric modelling again, and this time I replace 0.75 or 1 with THETA(5) like that: TVP = THETA(1) * (WT / 21) ** THETA(5) ; 21 is the median of WT in the study patient cohort ; the minimum and maximum limit of THETA(5) was given in the THETA block The results seems to be OK since OFV decreased significantly and CV% of CL and V1 also decreased. Is it proper to do in this way by letting NONMEM to find the THETA(5) estimate? If yes, Can I fix this THETA(5) to the final estimate when running the next level by incorporating more covariates? Kind Regards, Renee

From:"Leonid Gibiansky" leonidg@metrumrg.com Subject: RE: [NMusers] covariates Date: Fri, September 17, 2004 10:50 pm Nick, I think the range of disagreement even more narrow: the only point that I'd like to add to your allometric-scale CL and V representations is that we need to check whether random effects of the resulting model are independent of WT. If they are, this is great, it would be another confirmation of the general law. If, for some particular drug, random effects depend on WT even after the allometric scaling, it needs to be corrected either by changing the power x of the dependencies (CL~ WT^x,V~WT^x) or by addition of some other covariates that correlate with WT and can remove observed dependence of random effects on WT. Thanks for the references, Leonid

From: "Nick Holford" n.holford@auckland.ac.nz Subject: RE: [NMusers] covariates Date: Fri, September 17, 2004 11:37 pm Renee, > > Hello, Nick, Leonid > > I did try the allometric scaling law for each PK parameter (CL, V1, Q, V2) > one by one in the basic model. I don't recommend applying the allometric model to each parameter separately. The biology predicts that allometry applies to all 4 parameters at the same time. If you apply the allometric model on all 4 parameters then you will have some justification for extrapolation of your results beyond the observed range of WT. If you take an empirical approach then you would need to be much more cautious about extrapolation. > Unfortunately, the results are either > Minimization terminated or insignificant change of OFV. It seems that > allometric scaling model doesn't fit to my study data. I don't put any trust in whether or not NONMEM terminates with rounding errors as a diagnostic of the appropriateness of the model. A negligible decrease when you compare an allometrically scaled model with a model without weight does not invalidate the allometric model. If you don't have much range of WT in your subjects you won't see much effect on OFV. > Perhaps, the > formulation of this study drug, liposome, may modify the disposition of > encapsulated drug which can not be explained by allometric scaling model. The allometric scaling relationship does not depend on whether or not you are using liposomes. The allometric theory scales clearance like functions to the power 3/4 and volume like structures to the power 1. You may of course have some model misspecification due to the liposomes e.g. saturable uptake/removal instead of a first-order clearance. > I also tried the covariate equation like that: > > TVP = THETA(1) * (1 + THETA(2) * (COV - median(COV)) > ; P is the PK parameter > ;COV is the covariate > > However, error message shows that P is negative (don't know why?). This occurs quite commonly if THETA(2) is negative. It is possible for THETA(2) * (COV - median(COV)) to become < 1 which will make TVP negative. If you want to use this kind of empirical covariate function then a similar and more robust function is: TVP = THETA(1) * EXP(THETA(2) * (COV - median(COV)) Note that for small x that EXP(x) is approx 1+x which means that these two empirical functions give similar predictions for small covariate effects. The EXP() function will always be positive for any reasonable values of THETA and COV and protect you from negative values of TVP. > So, I am back to the allometric modelling again, and this time I replace > 0.75 or 1 with THETA(5) like that: > > TVP = THETA(1) * (WT / 21) ** THETA(5) > ; 21 is the median of WT in the study patient cohort > ; the minimum and maximum limit of THETA(5) was given in the THETA block > > The results seems to be OK since OFV decreased significantly and CV% of CL > and V1 also decreased. > > Is it proper to do in this way by letting NONMEM to find the THETA(5) estimate? Many people do this but I think it is silly. Whey estimate THETA(5) when there is a perfectly good theory that says the value of this parameter is 3/4? If you want to play this kind of game then it would make more sense to do this with your basic PK model: C=Dose/V*THETA(1)**(-CL/V*TIME) i.e. estimate the value of 'e' rather than assume the value (2.718...) associated with first-order elimination! It is less probable that your drug has first order kinetics than the allometric scaling law is inappropriate. This is because allometry has been tested over 18 orders of magnitude. I do not know of any drug that has has first order kinetics confirmed over a range of 18 orders of magnitude. As Leonid points out in another contribution to this thread -- if you find that the allometric model still leaves some systematic relationship with WT unexplained then you should be looking for other ways in which WT affects your parameter in addition to the allometric relationship not instead of it. E.g. if you use total body weight for WT and some of your subjects are obese then you should try to find a way to convert total body weight to WT associated with a 'normal' body composition. 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/

From: "Leonid Gibiansky" leonidg@metrumrg.com Subject: RE: [NMusers] covariates Date: Fri, September 17, 2004 11:52 pm Renee, Well, I am afraid you will get conflicting advices from me and Nick. I would do the following: add WT as a power model to all the parameters AT THE SAME TIME with different powers (TVP ~ THETA(1)*(WT/21)**THETA(5), TCL ~ THETA(2)*(WT/21)**THETA(6), etc.) and see whether this results in any improvement of the model (OF drop + plots of random effect versus WT). You may observe that some of the power parameters (like THETA(5) ) are relatively large and well-defined (small relative standard error = SE/(parameter value) ) while the others are either small or not-well-defined. I would exclude the latter and refit the model to make sure that this would not damage the fit; and continue until you end up with the simplest model that is as good as the full model (where the full model is the one with WT to all parameters). This is similar to the backward elimination procedure, but for one covariate. Let's refer to this simplest model as model 1. To be more in line with Nick suggestions, you may fit the model where all the parameters depend on WT according to the allometric scaling (i.e., CL, Q ~ WT^0.75, V ~ WT, Kij=Q/V ~ WT^(-0.25). Let's call it allometric model. You may compare allometric model with the model 1 and check which one is better. To compare, look on OF, variances of the parameters, PRED vs DV fit, ETAs vs WT plots. Also, it make sense to plot PRED of the model 1 versus PRED of the allometric model to see whether there is any difference. The third way, a combination of the first two, would be to fit the allometric model and then look on the dependencies of the random effects on WT. If you see any, you may take them into account by introducing covariates that are highly correlated with WT. For the pediatric study it can be age. For the adult study it can be gender or BMI (or some other measure of obesity). On the more technical side: Dependence TVP = THETA(1) * (1 + THETA(2) * (COV - median(COV)) is not too good. The part (COV - median(COV)) is negative for half of the patients. If THETA(2) is sufficiently large, TVP can be negative. You may try TVP = THETA(1) * EXP( THETA(2) * (COV - median(COV))/median(COV) ) instead. You should not fix THETA(5) while looking for the other covariates. Good luck and let us know the results. Leonid.

From: "Nick Holford" n.holford@auckland.ac.nz Subject: RE: [NMusers] covariates Date: Sat, September 18, 2004 1:41 am Leonid, I agree it would be worth looking for other ways that WT might be correlated with parameter variability e.g. via differences in body composition or disease state associated with WT. But I don't see any point in abandoning the allometric model in favour of outright empiricism by estimating the power x. 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/

From: Renee Ying Hong [mailto:yinghong@pharm.usyd.edu.au] Subject: RE: [NMusers] covariates Sent: Monday, September 20, 2004 2:31 AM Hello, Nick and Leonid, I ran NONMEM following your instructions. It is the other way around this time Firstly, I ran the power model by adding WT to all the parameters simultaneously, which was suggested by Leonid. OFV increased double compared to the basic model. Therefore, I didn't keep on going. Then I ran the allometric model at the same time as suggested by Nick. OFV decreased 20.4. The THETA and relative standard error is OK, However, ETA of CL decreased dramatically, from 0.0612 (CV%24.7%) to 0.000291(1.7%). The standard error of ETA (CL) is 0.0626, which suggested the estimate of ETA(CL) is not correct. I attached the diagnostic plots. In addition, I have a few questions: 1. can I report the CV% of CL is 1.7%? 2. Covariance is aborted sometimes when I ran NONMEM even the minimization is successful. How can it be avoided? 3. Leonid suggested me to plot ETAs vs WT. Is ETA calculated from EXP (CLi / TVCL)? Please comment! Screening covariates is a painstaking process. And I found myself very lucky having your two NONMEM artists to help me do it properly. I benefit a lot from your friendly arguments! Kind Regards, Renee

From: "Leonid Gibiansky" leonidg@metrumrg.com Subject: RE: [NMusers] covariates Date: Mon, September 20, 2004 5:28 am Renee, Something in not correct with the implementation of the first approach. You can try to re-run it with the initial values of the power parameters equal to the ones from the allometric scaling (0.75, -0.25 or 1). Then you should have the same results as for the allometric model to better (in terms of OF). If you start from the small values (around zero) then you should have results as good as for the base model or better. Meanwhile, I rerun my latest project following Nick suggestion (with allometric scaling on all parameters). It gave slightly higher OF (15 points for FOCE) and similar CVs as my model with LBW on 3 parameters. The fit was good, and I think by adding BMI or something similar I should be able to improve it further. So I benefited from this discussion as well, thanks, Nick Leonid

From: "Nick Holford" Subject: RE: [NMusers] covariates Date: Mon, September 20, 2004 2:57 pm Renee, There is something wrong with the results you have obtained. The OFV must be at least as good as the model with the power parameters fixed to their allometric theoretical values. The power parameters are very non-linear and therefore harder to estimate reliably. I suspect you are in a local minimum with Leonid's model. Try starting the model using the final parameter estimates you got from the allometric model but then let the allometric power parameters be estimated. This will ensure the fit cannot be worse than the allometric model. Question 1 -- the very small estimate of OMEGA for CL (0.000291) is suspicious (I am assuming you are using an exp(ETACL) model) and it's high uncertainty (SE 0.0626) supports this. Very small values like this suggest that the between subject variability in CL is not well defined in your data. This is very surprising as CL is usually a very robust parameter. I think there is something strange about your model/data. Question 2 -- do not worry that thed $COV step failed to run. This means nothing. Question 3 -- I don't think there is any 'right way' calculate ETA on CL. You can simply output ETA(x) or calculate TVCL*(EXP(ETA(x()-1) to do the plots against WT to look for any remaining WT effect. However, don't expect to see much unless you can fix your problem with the very low OMEGA for clearance. Note that the 'diagnostic plots' you sent are worthless in diagnosing these kinds of problem. The standard 'diagnostic plots' are not much help in deciding if you have an appropriate model. Nick 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/ _______________________________________________________