Getting rid of correlation issues between CL and volume parameters

-----Original Message----- From: owner-nmusers o:owner-nmusers@globomaxnm.com] On Behalf Of Mueller-Plock, Nele Sent: Monday, November 25, 2013 2:05 AM To: Leonid Gibiansky; 'nmusers' Subject: RE: [NMusers] Getting rid of correlation issues between CL and volume parameters Dear Leonid, Thanks for your answer. Maybe I was not completely clear about the reasons why I tried to account for F1. The reason is that after oral dosing, a correlation between CL and should be present, as these parameters in reality represent CL/F and V/F. One way to account for this would be to estimate the correlation via the $OMEGA BLOCK syntax. As this is sometimes hard to estimate, I looked if any alternative is available, and then found the discussion of this topic in the provided link ( http://www.wright-dose.com/tip2.php). From your answer, I would conclude that the proposed code should only account for random between-subject variability, i.e. it should only consider the ETA on F1, but not the THETA (which in my example had values of 1, 0.8 and 0.5). Is this correct? So whereas an increase in ETA on F1 without accounting for the correlation would automatically result in positive ETA values for CL and V, even without any inherent variability in true CL and V, with the code F1=1 FF1=EXP(ETA(1)) CL=THETA()*EXP(ETA())/FF1 V=THETA()*EXP(ETA())/FF1 this would already be taken care of, and the $OMEGA BLOCK could be omitted. Right? Thanks and best Nele ______________________________________________________________ Dr. Nele Mueller-Plock, CAPM Principal Scientist Modeling and Simulation Global Pharmacometrics Therapeutic Area Group Takeda Pharmaceuticals International GmbH Thurgauerstrasse 130 8152 Glattpark-Opfikon (Zürich) Switzerland Visitor address: Alpenstrasse 3 8152 Glattpark-Opfikon (Zürich) Switzerland Phone: (+41) 44 / 55 51 404 Mobile: (+41) 79 / 654 33 99 mailto: nele.mueller-plock@takeda.com http://www.takeda.com -----Original Message----- From: Leonid Gibiansky [mailto:lgibiansky@quantpharm.com] Sent: Freitag, 22. November 2013 19:44 To: Mueller-Plock, Nele; 'nmusers' Subject: Re: [NMusers] Getting rid of correlation issues between CL and volume parameters Nele, I am not sure why would you like to divide by F1. Can we just do it explicitly? F1=EXP(ETA(1)) (or F1=function(dose)*EXP(ETA(1)) CL=.. V=.. F1 can be > 1 as it is not absolute but relative (to the other subjects); I assume that this is oral dose, not IV, correct? In your code, be careful not to call it F1 as the nonmem will interpret it as bioavailability parameter, and you should not account for it twice. So it should be either F1=EXP(ETA(1)) CL=THETA()*EXP(ETA()) V=THETA()*EXP(ETA()) or F1=1 (can me implicit and omitted) FF1=EXP(ETA(1)) CL=THETA()*EXP(ETA())/FF1 V=THETA()*EXP(ETA())/FF1 but not F1=EXP(ETA(1)) CL=THETA()*EXP(ETA())/F1 V=THETA()*EXP(ETA())/F1 Leonid -------------------------------------- Leonid Gibiansky, Ph.D. President, QuantPharm LLC web: www.quantpharm.com e-mail: LGibiansky at quantpharm.com tel: (301) 767 5566 On 11/22/2013 12:14 PM, Mueller-Plock, Nele wrote: > Dear all, > > I have come across an interesting proposal to account for correlation between CL and volume parameters by dividing by bioavailability within the NONMEM control stream: > > http://www.wright-dose.com/tip2.php > > I liked the approach, however I have been wondering how exactly to interpret the resulting parameter values for CL and V. > > As an illustration, a potential problem might be that we have doses of 10, 25 and 50 mg with a fixed bioavailability of 100% for the 10 mg dose, and bioavailabilities of 80% and 50% for the doses of 25 and 50 mg, respectively. In addition, a between-subject variability on F1 of ~30% would be present. > > If I now code my CL and V as follows: > CL=THETA(1)/F1 > V=THETA(2)/F1, > to account for the correlation between CL and V, what exactly would be the meaning/interpretation of THETA(1) and THETA(2)? > As the THETAs would be the same for all doses, the CL of 50 mg would be twice as high as the one for the 10 mg dose – does that make sense, as we already estimated the reduced relative bioavailability using parameter F1? > > Any comments would be very much appreciated. > Thanks and best > Nele > > > > Dr. Nele Müller-Plock, CAPM > Principal Scientist Modeling and Simulation Pharmacometrics > Experimental Medicine > > Takeda Pharmaceuticals International GmbH > 8152 Glattpark-Opfikon (Zürich) > Switzerland > > Visitor address: > Alpenstrasse 3 > 8152 Glattpark-Opfikon (Zürich) > Switzerland > > Phone: (+41) 44 / 55 51 404 > Mobile: (+41) 79 / 654 33 99 > mailto: nele.mueller-plock > http://www.takeda.com > -------------------------------------------------------------------- > > The content of this email and of any files transmitted may contain confidential, proprietary or legally privileged information and is intended solely for the use of the person/s or entity/ies to whom it is addressed. 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From: owner-nmusers globomaxnm.com] On Behalf Of Bob Leary Sent: Tuesday, November 26, 2013 5:09 AM To: Nick Holford; 'nmusers' Subject: RE: [NMusers] Getting rid of correlation issues between CL and volume parameters Nick – I defer to you and the undoubtedly many other readers who know far more about pharmacokinetic theory than I do as to which particular formulation is more appropriate from a PK theoretic point of view. I was merely trying to note (and as I point out below, incorrectly) that something like the 2-eta formulation CL=THETA(1)*EXP(ETA(1)) V=THETA(2)*EXP(ETA(2)) Where ETA(1) and ETA(2) have a full 2 by 2 block correlation matrix so that correlation between ETA(1) and ETA(2) is Handled by an OMEGA(1,2) parameter Is ‘mathematically equivalent’ to a 3-eta formulation with a 3 by 3 diagonal Omega (ETA(1), ETA(2), ETA(3) independent) FF1=EXP(ETA(3)) CL=THETA(1)*EXP(ETA(1))/FF1 V=THETA(2)*EXP(ETA(2))/FF1 (The fact that FF1 formally looks like a bioavailability is irrelevant here, since I was not really intending to make any specific comments or recommendations with respect to how best to deal with bioavailabilities) Now that I look at it a bit more closely, the formulations actually are not at all mathematically equivalent (the 2 by 2 block formulation is much more General than the 3 by 3 diagonal formulation, even though they have the same number of parameters). While all 3 by 3 diagonal Omegas have Equivalent 2 by 2 block Omegas, the reverse is clearly not true. This is most easily seen in in the second 3 by 3 diagonal formulation where CL=THETA(1)*EXP(ETA(1)-ETA(3)), and V=THETA(2)*EXP(ETA(2)-ETA(3)), so cov(log CL, log V) = var(ETA(3)) >0. Thus in the second diagonal 3-eta formulation, the log CL-log V correlation must be positive (or at least non-negative), while there is no such restriction on the full block 2-eta formulation. So in fact the 2-eta block formulation is more general. I think it is even worse than this – there appear to be some regions of the block 2 eta parameter space that do not have equivalents in the diagonal 3-eta space even when the correlations are positive. (For example, if log CL and log V are highly correlated, then the variance of ETA(3) must be very large relative to the variance of ETA(2) and ETA(1) in the 3-eta formulation. But this means the variance of ETA(1) and ETA(2) in an equivalent two eta formulation must be relatively similar and roughly equal to the variance of ETA(3) in the 3-eta formulation. So without working out the details, I think there are regions of the block 2-eta space corresponding to highly correlated log CL and log V but with very different log CL and log V variances that are unattainable in the 3-eta formulations. So in fact the second 3 eta diagonal formulation is fundamentally different and less general than the first 2eta block formulation. But this just means that if CL and V are correlated only thru the F11 bioavailability like mechanism posited in the 3-eta formulation, there are restrictions as to what the corresponding 2 by 2 full block omega matrix can looks like. This leaves open the interesting point – run it both ways, and then see if the 2 by 2 and 3 by 3 methods produce compatible Omegas. If not, then this might provide some evidence that the coupling is more complicated than just that posited in the 3 by 3 diagonal model But in any event, the EM methods are not well suited to the second case, and will be inefficient relative to the first case if indeed they work at all (which may depend on the particular implementation) One problem is that the EM update of THETA(1) in the second case depends on the means for the various subjects of the posterior distributions of both ETA(1) and ETA(3) – most EM implementations usually have one or possibly several fixed effects coupled to a single random effect, and the update of that fixed effect, at least in the simple mu-modeled case, comes from a simple linear regression of the associated fixed effects on the posterior means of the single random effect. The fact that now there are multiple random effects paired with a single fixed effect is unusual and may not in fact be handled (I am not sure what NONMEM IMPEM will do with this; I am pretty sure that the analogous Phoenix NLME QRPEM will reject it). Bob From: owner-nmusers maxnm.com<mailto:owner-nmusers Sent: Monday, November 25, 2013 1:43 PM To: 'nmusers' Subject: Re: [NMusers] Getting rid of correlation issues between CL and volume parameters Bob, You use an estimation method justification for choosing between estimating the covariance of CL and V and estimating the variance of F. An alternative view is to apply a fixed effect assumption based on pharmacokinetic theory. The fixed effect assumption is that some of the variation in CL and V is due to differences in bioavailability and other factors such as linear plasma protein binding and differences in the actual amount of drug in the oral formulation. This fixed effect assumption is described in the model by the variance of F. It is quite plausible to imagine that there is still some covariance between CL and V that is not related to the differences in F. For example, if you did not know the subject's weights and therefore could not account for the correlated effects of weight on CL and V. The estimation of the variance of F would only partly account for this because of the non-linear correlation of weight with CL and V. Another non-linear correlation would occur if plasma protein binding was non-linear in the range of measured total concentrations. In such case one might propose trying to estimate the covariance of CL and V as well as including F as a fixed effect and estimating the variance of F. Do you think that SAEM or IMP would be able to come up with a reasonable estimate of the covariance of CL and V? Best wishes, Nick