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Re: Identifiablity of parent / metabolite PK with interconversion

From: Leonid Gibiansky <LGibiansky>
Date: Tue, 03 Feb 2009 23:34:16 -0500

I would move the discussion from Nonmem properties to equation
properties and availability of the data. Nonmem is the implementation of
the numerical algorithms that should (and in most cases will) give a
correct answer when it is asked a correct question. If the results are
questionable, this is likely to be the problem of the model rather than
of the numerical algorithm implementation, especially in this case of
the simple linear equations. The question is not whether Nonmem gives
correct results but whether the solution of the system is unique (or
identifiable based on the data).

If K32=0 and dose is IV rather than oral, solution of the system for
parent drug should be mono exponential while with K32 comparable to K20
and K23, the second exponent should be visible. Oral dose and KA may
cloud the picture. Without seeing the data it is hard if not impossible
to say whether you have enough information to identify all the
parameters. Correlation matrix and bootstrap should be able to visualize
correlations if they exist. Alternatively, you may try to fix K32 = 0.
If you see the same fit, then the data are not sufficient to estimate
all the parameters.


Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
e-mail: LGibiansky at
tel: (301) 767 5566

Dong-Seok Yim wrote:
> Leonid,
> Thank you for your comprehensive comment.
> Once I raised this, I wish to ask the question in a different way.
> Suppose we measured concentrations of CMT2 (parent) and CMT3 (metabolite).
> In a situation where K20 comparable to K30 > K23 >> K32 near to 0, can
> NONMEM give reliable estimates of K20 and K23 ?
> As long as the sum of rate constants going out of CMT2 (K23 + K20) remain
> unchanged, any pair of estimates of K23 and K20 may be given by NONMEM, I am
> concerned. Then, K20 may be underestimated near to 0 with K23 and K30
> overestimated accordingly; some flip-flop like situation.
> Is fixing V3 identical to that of V2 good enough to prevent this kind of
> erroneous NONMEM results ?
> Dong
> -----Original Message-----
> From: Leonid Gibiansky [mailto:LGibiansky
> Sent: Monday, February 02, 2009 11:46 PM
> To: yimds
> Cc: nmusers
> Subject: Re: [NMusers] Identifiablity of parent / metabolite PK with
> interconversion
> Hi Dong-Seok Yim,
> If equilibration rates (K23, K32) are much larger than the elimination
> rates, then parent and metabolite will be at equilibrium (K23 A2 = K23
> A3), and you will not be able to estimate K23, K32 separately, only K23
> to K32 ratio. If this is true, you can see it on the plot of parent vs.
> metabolite concentrations (by subject): the plot should show strong
> correlation.
> If you have enough data in the range where the parent and drug
> concentrations are not proportional, you should be able to estimate all
> the parameters.
> One visual test that may help is to plot scatter-plot matrix of random
> effects (ETAs vs. ETAs) and look for strong correlations. Also, you may
> check correlation of parameter estimates.
> should give you the eigenvalues of the correlation matrix. If the ratio
> of the largest to the smallest is above 1000, parameters may not be
> trusted. Correlation matrix itself may help to identify correlated
> parameters, so look on the correlation between K23 and K32, in particular.
> A helpful way to visualize parameter correlations is to do a bootstrap,
> and then look at the scatter plot matrix of the parameters vs.
> parameters plots. For example, you may be interested in K32 vs K23 (for
> all bootstrap samples) plot. If the run time is short, use 1000 samples.
> If it is long, 100 should give you a general idea of what is going on.
> Also, the code that you show us should not compile since VS and VA are
> not defined. I guess, it is just a typo, but you are missing VS=V2,
> VA=V3 somewhere.
> Thanks
> Leonid
> --------------------------------------
> Leonid Gibiansky, Ph.D.
> President, QuantPharm LLC
> web:
> e-mail: LGibiansky at
> tel: (301) 767 5566
> Dong-Seok Yim wrote:
>> Hi, colleagues,
>> I am currently trying to model plasma concentrations of parent and
>> metabolite with interconversion. (nmtran code is in the bottom).
>> The data came from a densely sampled PK study in healthy subjects. I put
>> the metabolite Vd identical to the parent Vd as recommended. Then, I
>> managed to obtain some estimates that make the individual plots look nice.
>> However, I doubt whether we can get reliable estimates for K23 or K32
>> and (hence, even K20 and K30 ) without urine concentration data and
>> without any priori knowledge on the metabolic ratios etc.
>> I suspect that the estimates of K23, K32, K20, K30 and V2 are all
>> interconnected as the Ka and Ke are in the flip-flop phenomenon - Am I
>> wrong ?
>> Searching for some references for the metabolite PK modeling using
>> NONMEM, I found an article reporting detailed pop PK parameters of
>> CPT-11 and its metaolites in patients (Rujia Xie, Ron H.J. Mathijssen,
>> Alex Sparreboom, Jaap Verweij, and Mats O. Karlsson. Journal of
>> Clinical Oncology, Vol 20, No 15 (August 1), 2002: pp 3293-3301)
>> In the paper, interconversion rate constants of interconverted
>> forms (CPT-11 lactone and CPT-11 carboxylate / SN-38 lactone and SN-38
>> carboxylate ) were tabulated without using any urine data. -
>> If any of the authors comment on the method to obtain reliable values
>> using plasma concenentrations only, I would appreciate.
>> Any comments from nmusers other than above authors are also much welcomed
> !
>> Thanks !
>> Dong-Seok Yim
>> ----------------------------------------
>> $PK
>> KA = THETA(1)*EXP(ETA(1))
>> K20 = THETA(2)*EXP(ETA(2))
>> V2 = THETA(3)*EXP(ETA(3)) ; V2 = parent Vd
>> K30 = THETA(4)*EXP(ETA(4))
>> V3 = V2 ; V3 = metabolite Vd
>> K23 = THETA(5)*EXP(ETA(5))
>> K32 = THETA(6)*EXP(ETA(6))
>> CL20 = K20*VS
>> CL30 = K30*VA
>> S2=VS
>> S3=VA
>> $DES
>> DADT(1)=-KA*A(1)
>> DADT(2)=KA*A(1)-K23*A(2)+K32*A(3)-K20*A(2)
>> DADT(3)=K23*A(2)-K32*A(3)-K30*A(3)
>> Dong-Seok Yim M.D., Ph.D.
>> Associate Professor
>> Department of Pharmacology
>> College of Medicine
>> The Catholic University of Korea
>> 505 Banpo-Dong, Seocho-Gu, Seoul 137-701, Korea
>> Tel +82-2-590-1201
>> Fax +82-2-536-2485
>> yimds
Received on Tue Feb 03 2009 - 23:34:16 EST

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