RE: covariates

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/