From: "Wixley, Dick" <Dick.Wixley@solvay.com>
Subject: metabolite modelling
Date: Thu, 9 Dec 1999 15:49:59 +0100

Dear users,

I am trying to simultaneously model parent compound and metabolite. Oral dosing - a 2-compartment model describes the parent compound well. I have used the following code. It converged but took a long time but I was not impressed with the results.

I would be interested in references on how to taCkle this problem. My next step will be to do a sequential fit. I am concerned that I may be making some basic errors in my model definition.

Dick Wixley

\$PROBLEM metabolite and parent compound
\$INPUT
SUBJ=ID DOSE=AMT TIME CPLA=DV TRT EVID MDV MDD QT PR CMT
\$DATA y:\a_pk_pd\ted_ver\data\nmnor1\NOR2sim IGNORE=C

\$MODEL
COMP = (DEPOT DEFDOSE INITIALOFF)
COMP = (CENTRAL DEFOBS)
COMP = PERIPH
COMP = (METAB )

\$PK
K12 =THETA(1)*EXP((ETA(1)))
K23 =THETA(2)*EXP((ETA(2)))
K32 =THETA(3)*EXP((ETA(3)))
K24 =THETA(4)*EXP((ETA(4)))
K40 =THETA(5)*EXP((ETA(5)))
K20 =THETA(6)*EXP((ETA(6)))
V2 =THETA(7)*EXP((ETA(7)))
V4 =THETA(8)*EXP((ETA(8)))
S2=V2 /1000
s4=V4/1000

ALAG1 = THETA(9)*EXP(ETA(9))

\$ERROR
FX=0
IF(F.EQ.0) FX=1
W=F+FX
IF (CMT.EQ.4) THEN
Y = F*EXP(ERR(2))
ELSE
Y = F*EXP(ERR(1))
ENDIF
IPRED=F
IRES=DV-IPRED
IWRES=IRES/W

\$THETA (0,3.4) (0,.24) (0,.13) (0,.27) (0,.13)
(0,21) (0,290) (0,0.9) (0,0.5)
\$OMEGA 0.25 0.25 0.25 0.25 0.25
0.25 0.25 0.25 0.25
\$SIGMA 0.25 0.25

\$ESTIMATION MAXEVAL=9999 PRINT=5 SIGDIGITS=4 POSTHOC MSFO=RUN5I.MSF
\$COVARIANCE
\$TABLE ID TIME DOSE ALAG1 K12 K23 K32 K24 K40 K20 V2 V4 CMT IPRED DV PR QT

*****

From: "Stephen Duffull" <sduffull@fs1.pa.man.ac.uk>
Subject: Re: metabolite modelling
Date: Thu, 9 Dec 1999 15:20:59 -0000

Dick Wixley wrote:

> I am trying to simultaneously model parent compound and metabolite. Oral
> dosing - a 2-compartment model describes the parent compound well.
> I have used the following code. It converged but took a long time but I was
> not impressed with the results.
...
...
> K24 =THETA(4)*EXP((ETA(4)))
> K20 =THETA(6)*EXP((ETA(6)))
> V2 =THETA(7)*EXP((ETA(7)))
> V4 =THETA(8)*EXP((ETA(8)))

All else being equal I think you have a structurally unidentifiable model. You are attempting to estimate K20 and K24. I believe that unless you have data on other fate of your drug (ie renal data or other metabolite) or you have data on administration of metabolite alone (in order to estimate V4) or you have prior data on the fraction of drug that meets the fate via K24 ... then "K24/V4" is globally identifiable but each parameter alone is not.

Without additional data you have two choices: 1) set K20=0 (ie all drug is converted to metabolite) then K24 and V4 would both then be individually globally identifiable; or 2) fix V4=V2 then you would be ok.

I hope this helps.

Regards
Steve
=====================
Stephen Duffull
School of Pharmacy
University of Manchester
Manchester, M13 9PL, UK
Ph +44 161 275 2355
Fax +44 161 275 2396

*****

Date: Thu, 9 Dec 1999 08:15:57 -0800 (PST)
From: ABoeckmann <alison@c255.ucsf.edu>
Subject: Re: metabolite modelling

Dick,

I notice one small typo in what you sent:

s4=V4/1000

The "s" is lower case. NM-TRAN does not recognize s4 as "scale for compartment 4". It only recognizes upper case S4. Hence S4 defaults to 1. It may be well be that theta(8) is not estimated (i.e., inital est = final est ; gradient always 0). This will happen if there are no observations from CMT 4. Or, if there are such observations, it will happen because V4 does not enter into the model.

Alison Boeckmann

*****

From: "HUTMACHER, MATTHEW" <MATTHEW.HUTMACHER@chi.monsanto.com>
Subject: RE: metabolite modeling
Date: Thu, 9 Dec 1999 10:35:22 -0600

I am not sure that the model is structurally unidentifiable. If concentration-time data exists for the parent and for the metabolite, all parameters should be unique. My reasoning is as follows: All parameters k12,k23,k32,V1,k20* (k20*=k20+k24) are identifiable in fitting the parent alone with the two compartment model. If one adds in the metabolite, then k24 can be estimated by the conversion portion of the metabolite data so that the parameters k24,V4,k40 should all be identifiable. To set k20=0 will force the conversion rate to be the same as the elimination rate of the parent which I think would induce some lack of fit unless the conversion is 100%.

Sequential fitting of the data (fitting the parent first, assessing the fit, if it fits well fixing the parameters for the metabolite fit and then fitting the metabolite) helps me cut down run time for the "getting to know the data" portion of modeling. Especially with complicated models and differing administration routes.

Matt

*****

From: "Stephen Duffull" <sduffull@fs1.pa.man.ac.uk>
Subject: Re: metabolite modeling
Date: Thu, 9 Dec 1999 17:12:32 -0000

Matthew

I'm do not agree on this point.

> parameters should be unique. My reasoning is as follows: All parameters
> k12,k23,k32,V1,k20* (k20*=k20+k24) are identifiable in fitting the parent
> alone with the two compartment model. If one adds in the metabolite, then
> k24 can be estimated by the conversion portion of the metabolite data so
> that the parameters k24,V4,k40 should all be identifiable.

As the model was described V4 is not identifiable since the amount of drug that gets converted to metabolite is not known. An analogous example would be a 1 compartment oral absorption model where V is not identifiable but V/F is -

but if F is known a priori then V is identifiable. K24 includes Fm (fraction of drug that goes to the metabolite) implicitly. If Fm is known (as you suggest when you say "conversion portion") then I agree V4 and K24 become identifiable. Setting Fm to one (ie (1-Fm)*K20 = 0) solves this problem although may not be correct, any value for Fm could be chosen - and some prior knowledge is likely to be known. To conclude if either of Fm or V4 are known then K24 and the other can be computed but without additional information the choice is to fix Fm or V4.

It should be considered that non-linear regression programs often give parameter estimates for unidentifiable models and tell the user that all was well therefore care must be taken to ensure all parameters are identifiable.

Regards
Steve
=====================
Stephen Duffull
School of Pharmacy
University of Manchester
Manchester, M13 9PL, UK
Ph +44 161 275 2355
Fax +44 161 275 2396

*****

Date: Thu, 9 Dec 1999 10:53:43 -0600
From: David_Bourne <david-bourne@ouhsc.edu>
Subject: RE: metabolite modeling

>I am not sure that the model is structurally unidentifiable. If
>concentration-time data exists for the parent and for the metabolite, all
>parameters should be unique. My reasoning is as follows: All parameters

...snip

>Without additional data you have two choices: 1) set K20=0
>(ie all drug is converted to metabolite) then K24 and V4
>would both then be individually globally identifiable; or 2)
>fix V4=V2 then you would be ok.

The additional needed data is drug and metabolite amounts excreted into urine. Total amounts are the minimum needed. See http://www.boomer.org/course/pk_bio/Ch9906b/index.htm for more information. ;-)

David

*****

From: "HUTMACHER, MATTHEW" <MATTHEW.HUTMACHER@chi.monsanto.com>
Subject: RE: metabolite modeling
Date: Thu, 9 Dec 1999 12:35:09 -0600

You are correct. For some reason I was thinking that there was a separate exponential function for the conversion and upon reflection I see that no such term exists so that the parameters are unique. Thank you for the correction.

Matt

*****

Date: Fri, 10 Dec 1999 13:10:33 +0100
From: Mats Karlsson <Mats.Karlsson@biof.uu.se>
Subject: Re: metabolite modeling

"HUTMACHER, MATTHEW" wrote:

> Sequential fitting of the data (fitting the parent first, assessing the fit,
> if it fits well fixing the parameters for the metabolite fit and then
> fitting the metabolite) helps me cut down run time for the "getting to know
> the data" portion of modeling. Especially with complicated models and

I would agree that sequential fitting is useful during model building. For drug-metabolite models, I would however, once the structural models have been selected, look into parameter correlations between drug and metabolite. These may provide information on e.g. magnitudes of metabolic pathways (even if they can be difficult to interpret sometimes). Also, metabolite data oftentimes contain information about parameters of the drug model, for example when the terminal half-life of the metabolite is the same as for drug, due to elimination rate limitation. Thus, doing sequential analysis for drug-metabolite PK data is more questionable than for PK/PD data (where PD data seldom contain much info about the PK).

Mats

*****

From: "HUTMACHER, MATTHEW" <MATTHEW.HUTMACHER@chi.monsanto.com>
Subject: RE: metabolite modeling
Date: Fri, 10 Dec 1999 10:06:11 -0600

Mats

I am not saying that once you get your structural models nailed down that you shouldn't simultaneously fit them. I think you should simultaneously model them for as you say, key correlations could be lost. I think that sequential fitting helps to come to a good structural model in terms of cutting down run time during the "getting to know the data" phase of model building.

Matt

*****

Date: Fri, 10 Dec 1999 12:34:05 -0500
From: Sandra R B Allerheiligen <ALLERHEILIGEN_SANDRA_R_B@Lilly.com>
Subject: RE: metabolite modeling

Hi Matt

We have simulatanous analyzed a number of parent and metabolite profiles. I am not clear how you could get meaningful parameter estimates for the metabolite without simultaneously fitting the parent concentrations in addition to having some way on knowing the fraction of parent molecule clearance that reflects the formation rate.

Regards
Sandy A

*****

From: "Leon Aarons" <laarons@fs1.pa.man.ac.uk>
Date: Mon, 13 Dec 1999 12:23:37 GMT
Subject: RE: metabolite modeling

I agree with Mats that the metabolite data can support the drug data, if for no other reason that effectively the number of degrees of freedom are increased. However I would inject a note of caution.

A number of years ago we did some nonlinear regression modelling on lignocaine (or lidocaine depending on which side of the Atlantic you come from) (P.N.Bennet, L.J. Aarons, M.R. Bending, J.A. Steiner, M. Rowland, 'Pharmacokinetics of lidocaine and its de-ethylated metabolite: dose and time dependency studies in man', J.Pharmacok.Biopharm. 10, 265-281 (1982)). The fit to the drug data (iv) was good. When the iv and oral data were fitted simultaneously they both looked lousy. By deconvolution the problem was found to be the link between the iv and oral data. In this case a simply time delay sufficed to correct the problem and, to be fair, the simultaneous fit did add something.

The same thing can happen with simultaneous drug & metabolite modelling. If the link between drug and metabolite is not correctly specified, then the fit to the drug will suffer, for the reasons mentioned by Mats.

So although there are advantages to simultaneous fitting, the link between drug and metabolite needs to be carefully investigated. Sequential fitting would seem a sensible first alternative and deconvolution, if possible is also useful.

__________________________________________________
Leon Aarons
School of Pharmacy and Pharmaceutical Sciences
University of Manchester
Manchester, M13 9PL, U.K.
tel +44-161-275-2357
fax +44-161-275-2396
email l.aarons@man.ac.uk

*****

Date: Mon, 13 Dec 1999 07:48:24 -0500
From: Nick Holford <n.holford@auckland.ac.nz>
Subject: Re: metabolite modeling

Leon,

You make a good point that the fit may not be good when for parent and metabolite models. But this should be a cause for celebration not dismay. Anybody can fit the data separately and get what seem to be good fits but the good fits are not really any good if the parent and metabolite simultaneous fits are lousy. If the model does not fit the data then this is an opportunity to think more carefully about why the model is wrong (as you describe below) and learn more by searching for a better model. A simultaneous fit is an excellent method for evaluating the overlall parent and metabolite model. Because the a priori mechanistic link between parent and metabolite is so strong we should not be satisfied until a combined model is available or failing that a critical experiment is proposed to provide more data to understand the system better.
--
Nick Holford, Center for Drug Development Science
Georgetown University, 3900 Reservoir Rd NW, DC 20007-2197
email:n.holford@auckland.ac.nz tel:(202)687-1618 fax:687-0193
http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.htm

Subject: RE: metabolite modeling
Date: Wed, 15 Dec 1999 14:00:36 +0100

The problem of precursor-product model identifiability has a long history. BTW, Professor Cobelli who invites us to Chicago 2000 contributed a lot to it in the 70th. The model that has just been discussed is a simplest one: the metabolite of interest is formed only systemically (i.e., no "first-pass" metabolism). Consider the situation when only plasma concentrations are available (no urine data that help identifying the model, as David Bourne mentioned). The identifiability problem can be solved (at least in case of a single individual) pretty well by assuming V(metabolite)=V(parent). However, if the metabolite is formed during absorption AND systemically (and this is rather a rule than an exception), the model remains unidentifiable unless we administer the metabolite to the same individual (if I recall it well this issue has been addressed in the paper by Venot et al. JPB 15:179-89, 1987). However, if we look at the problem from the population perspective it becomes almost inresolvable.

And I ask myself: why do we need a full model? If the goal is to obtain a good approximation for the parent drug and the metabolite plasma concentration profiles that can be used for predictions (say for further PK-PD modelling) why not to fit independent models to the parent drug curve and the metabolite curve? In the latter case the "absorption" part can be modelled by a first- or zero-order process or by some combination. Of course this will make our model very empirical, however, as the matter of fact, all standard PK models are purely empirical, aren't they?

----------------------------------------------------------------------
Janssen Research Foundation
Clinical Pharmacokinetics (ext. 5463)
B-2340 Beerse
Belgium
Email: vpiotrov@janbe.jnj.com

*****

From: "Stephen Duffull" <sduffull@fs1.pa.man.ac.uk>
Subject: Re: metabolite modeling
Date: Thu, 16 Dec 1999 09:13:18 -0000

> The model that has just been discussed is a simplest one:
> the metabolite of interest is formed only systemically (i.e., no
> "first-pass" metabolism).

I agree that the case was simplier than one that includesconsideration of first-pass metabolism. Having said that it remains possible to retain a globally identifiable model even under these circumstances, although it does require some parameters to be fixed (at prior or arbitrary values). If this is done the model may not retain biological exactness with respect to the fate of the drug (eg you may have to assume that the drug is only absorbed intact or converted to one metabolite on first-pass) - but nevertheless will reflect the observed data accurately.

> And I ask myself: why do we need a full model? If the goal is to obtain a
> good approximation for the parent drug and the metabolite plasma
> concentration profiles that can be used for predictions (say for further
> PK-PD modelling) why not to fit independent models to the parent drug curve
> and the metabolite curve?

If you fit independent models not only do you have almost all of the assumptions of fitting a full model but you eliminate the influence of metabolite on the parent (which as has been discussed by Mats and Leon is important), and also importantly the influence of changes in input variables or parent PK on metabolite PK.

Where possible the full model, even under various assumptions, would seem preferable.

Regards
Steve
=====================
Stephen Duffull
School of Pharmacy
University of Manchester
Manchester, M13 9PL, UK
Ph +44 161 275 2355
Fax +44 161 275 2396

*****

Subject: RE: metabolite modeling
Date: Fri, 17 Dec 1999 08:39:00 +0100

Steve,

Your last argument seems convincing. However, I am still not sure the LINEAR composite model developed on the basis of single-dose data will produce wrong predictions for multiple dosing. The situation has to be tested by simulations/fittings.

As to the NONLINEAR case (the effect of metabolite on the parent is an example), it is totally different from the LINEAR one. In general, nonlinear systems have less identifiability problems as compared to linear systems. For instance, if metabolite inhibits its own formation, you can estimate its ke even having no metabolite concentration measured at all. I showed the relevant example during the last NONMEM workshop in Uppsala. Also, the "first-pass" case becomes much simpler if the kinetics of metabolism is saturable.

Best regards,
----------------------------------------------------------------------
Janssen Research Foundation
Clinical Pharmacokinetics (ext. 5463)
B-2340 Beerse
Belgium
Email: vpiotrov@janbe.jnj.com

*****

Date: Fri, 17 Dec 1999 09:01:56 +0100
From: "Jean-Xavier.Mazoit@kb.u-psud.fr" <Jean-Xavier.Mazoit@kb.u-psud.fr>
Subject: metabolite modeling

Dear all,
I followed with interest the debate about metabolite and identifiability of parameters (I am currently fitting morphine and glucuronide data using a similar model). Indeed, it is evident that the model presented by Dick is not fully identifiable. However, I am slightly astonished by all the discussions and arguments presented: In fact, the problem relates only to the difference between intensive and extensive variables. Rates are rates and concentrations are amounts divided by volumes. The linearity of the system and the principle of superposition tell us that concentration is proportional to the dose and inversely proportional to the volume. It is impossible to calculate volumes from concentrations without knowing the dose (for metabolites, the faction of the dose metabolised by the system). In other words, in a simple one compartment model, it is impossible to estimate the volume if the dose is unknown. On another hand, it is always possible to estimate half-life (or rate constant, or time constant) which is a basic parameter, contrary to Nick Holford's opinion. Also, it seems that there is a frequent confusion between identifiability which as an intrinsic property of the system and sensitivity. With that respect, I think that most considerations presented in David Bourne's course on identifiability deal with sensitivity rather than with identifiability.

Jean Xavier Mazoit MD, PhD
Laboratoire d'Anesthésie
Université Paris-Sud
Faculté de Médecine du Kremlin-Bicêtre
F-94276 Bicêtre France
Tel. (33) (0)1 49 59 67 35-37
(33) (0)1 45 21 34 41 (Hopital)
Fax (33) (0)1 45 21 28 75
e-mail Jean-Xavier.Mazoit@kb.u-psud.fr

*****

Date: Fri, 17 Dec 1999 21:30:21 +1300
From: Nick Holford <n.holford@auckland.ac.nz>
Subject: Re: metabolite modeling

"Jean-Xavier.Mazoit@kb.u-psud.fr" wrote:

> the dose is unknown. On another hand, it is always possible to estimate
> half-life (or rate constant, or time constant) which is a basic parameter,
> contrary to Nick Holford's opinion.

Its all a matter of perspective. If you think only in terms of amount then half-life does seem to be the basic parameter but its a rather weak conceptual framework because to connect half-life to a real drug elimination process e.g. metabolism or renal excretion then I find it hard to imagine a process that is driven by amount rather than by concentration. From the perspective of concentration I find it is much easier to imagine concentration driven physical processes. Given the concentration viewpoint then volume and clearance become the natural basic parameters and half-life is clearly a derived parameter. I can readily propose physical mechanisms that can independently change either clearance of volume but there are no physical mechanisms which control half-life independently of either clearance or volume.

Being able to estimate a parameter is not a sufficient criterion for considering it a primary or basic parameter. We can readily compute AUC but that does not make it a basic parameter. AUC and dose can be used to estimate CL which is the basic parameter.

> of the system and sensitivity. With that respect, I think that most
> considerations presented in David Bourne's course on identifiability deal
> with sensitivity rather than with identifiability.

I agree with you here. I think it is not a good idea to mix up identifiability with sensitivity sometimes called a posteriori identifiability. Sensitivity is a continuous reflection of the experimental design points whereas identifiability is a binary property of a parameter given a specific design.

--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, Private Bag 92019, Auckland, New Zealand
email:n.holford@auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556
http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.html

*****

Date: Fri, 17 Dec 1999 09:41:37 -0800
From: Lewis B Sheiner <lewis@c255.ucsf.edu>
Subject: Re: metabolite modeling

Just so!
Thanks for such a clear and succinct statement.
LBS.

"Jean-Xavier.Mazoit@kb.u-psud.fr" wrote:
>
> Dear all,
> I followed with interest the debate about metabolite and identifiability of
> parameters (I am currently fitting morphine and glucuronide data using a
> similar model). Indeed, it is evident that the model presented by Dick is
> not fully identifiable. However, I am slightly astonished by all the
> discussions and arguments presented:
> In fact, the problem relates only to the difference between intensive and
> extensive variables. Rates are rates and concentrations are amounts
> divided by volumes. The linearity of the system and the principle of
> superposition tell us that concentration is proportional to the dose and
> inversely proportional to the volume. It is impossible to calculate
> volumes from concentrations without knowing the dose (for metabolites, the
> faction of the dose metabolised by the system). In other words, in a
> simple one compartment model, it is impossible to estimate the volume if
> the dose is unknown. On another hand, it is always possible to estimate
> half-life (or rate constant, or time constant) which is a basic parameter,
> contrary to Nick Holford's opinion. Also, it seems that there is a
> frequent confusion between identifiability which as an intrinsic property
> of the system and sensitivity. With that respect, I think that most
> considerations presented in David Bourne's course on identifiability deal
> with sensitivity rather than with identifiability.
>
> Jean Xavier Mazoit MD, PhD
> Laboratoire d'Anesthésie
> Université Paris-Sud
> Faculté de Médecine du Kremlin-Bicêtre
> F-94276 Bicêtre France
> Tel. (33) (0)1 49 59 67 35-37
> (33) (0)1 45 21 34 41 (Hopital)
> Fax (33) (0)1 45 21 28 75
> e-mail Jean-Xavier.Mazoit@kb.u-psud.fr

--
Lewis B Sheiner Professor, Lab. Med., Biopharmaceut. Sci, Med.
Box 0626 - UCSF 415-476-1965 (voice)
San Francisco, CA 415-476-2796 (fax)
94143 lewis@c255.ucsf.edu