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Re: Simultaneous vs sequential for modeling parent AND metabolites in pop PK

From: Nick Holford <n.holford>
Date: Thu, 11 Dec 2008 09:11:30 +1300

James, Mahesh,

The "F=1 fallacy" has caused me no end of stress over the years, and
next time I may have to contend with the (almost irrefutable) argument
"but Nick Holford said it was true".

As I never said this was a fallacy I dont think you need be stressed by
it. Everytime you use a model to describe oral PK data alone you must
make an assumption about the dose that is absorbed. By default NONMEM
will make the assumption that Foral=1 but of course when you interpret
the parameters you should remember the assumption.

Similarly you may assume Fm=1 and estimate metabolite parameters of
CLm/Fm and Vm/Fm where Fm is the fraction of parent converted to
metabolite. For simply descriptive purposes the Fm=1 assumption is fine
but more might be learned by making a different assumption (as Mahesh
points out). Fm might be guessable from in vitro descriptions of
metabolism or one may assume a Vm (metabolite volume) perhaps the same
as the parent. The latter can aid in proposing plausible values for Fm
but the descriptive value of the model is unchanged whichever assumption
is used.

I dont understand why Mahesh adds to each of the assumptions "[and
preferably do simultaneous parent/metabolite modeling]". Perhaps he
could give some reasons for this because I dont see it has anything to
do with the choice of which assumption to make.

IMHO the important thing is to recognize that an assumption must be
made. I have seen people use NONMEM to estimate Fm and CLm and Vm as if
they could identify these 3 parameters independently. NONMEM will do
what it is told and make estimates of the parameters even though one of
them cannot be identified. This is the important lesson to learn for
those who have not had experience of parent metabolite modelling with

I want to stick to my original assertion that PKPD and parent-metabolite
models are similar when applying a modelling strategy of either
sequential or simultaneous fitting of data.

We should remember the Box aphorism "All models are wrong but some
models are useful". Part of the process is modelling is to evaluate the
model to see how wrong it is. The sequential then simultaneous approach
can be helpful for model evaluation as described by Liping Zhang in her
second paper on PKPD models.

I see no reason why this should not apply to parent-metabolite models.
However, usually parent-metabolite models are simpler because commonly
one has first-order kinetics and essentially immediate conversion of
parent to metabolite. The implicit assumptions of complete, rapid and
first-order conversion may be fine but it still sensible to look at the
data to check that these assumptions are compatible with the results
from a sequential model.


James G Wright wrote:
>> Nick Holford wrote:
>> Non-proportionality (aka non-linearity) of metabolite formation from
>> parent is not really an issue. With the right design (i.e. suitable
>> doses of parent) then this can be discovered from just giving the
>> parent.
> The key assumptions of metabolite models are about how the metabolite is
> formed - linearly or nonlinearly, from plasma or during first-pass,
> immediately or not. Making sure your assumptions are true is really the
> issue for me with any analysis.
>> But to really know how much of the parent is eventually
>> transformed to the metabolite needs additional information i.e. direct
>> administration of the metabolite.
> Of course, if fraction formed is the parameter that you need to
> estimate.
> Fitting a metabolite PK model is not dependent on assuming 100%
> metabolite formation from parent, as you originally stated, unless you
> mislabel the parameters as actual CL, instead of CL/F. Not knowing F
> doesn't affect the application and predictive utility of the model any
> more than not knowing F for the parent after oral administration.
> The widespread presentation of "F=1" as an "unverifiable assumption"
> causes model end-users to suspect that the assumption could in some
> sense be wrong ("Aah, but how do you know F=1?"), leading to the
> perception that the metabolite model is misleading and unreliable.
> I think it would be helpful if you could explicitly retract your
> assertion regarding the assumption "that all drug goes to metabolite".
> The "F=1 fallacy" has caused me no end of stress over the years, and
> next time I may have to contend with the (almost irrefutable) argument
> "but Nick Holford said it was true".
> Best regards, James
Mahesh wrote:

> Dear NMusers,
> I think in trying to generalize the case between sequential PK/PD vs.
> sequential parent/metabolite we maybe forgetting some PK concepts.
> 1) In the case of parent/metabolite modeling the metabolite data often
> carries important information about the parent drug.
> Eg.a. If there is formation limited kinetics going on then the
> terminal slopes of the parent and metabolite will both be reflective
> of the parent's kel
> Eg.b. If there is severe flip-flop kinetics going on then the
> terminal slopes of the parent and metabolite will both be reflective
> of the parent drug's ka
> 2) There are common parameters (e.g.. k-metabolite) between the parent
> and metabolite that may be estimated in a more meaningful manner using
> simultaneous modeling.
> Given these considerations, my guess is that simultaneous modeling of
> the parent and metabolite maybe more scientifically useful (use all
> the information to get the best parameter estimates).
> On a related note; it is generally well known that if you administer
> only the parent and measure parent & metabolite then the volume of
> metabolite is not identifiable. In this case there are 3 options:
> a) Fix the metabolite volume to that of the parent [and preferably do
> simultaneous parent/metabolite modeling]
> b) Use prior knowledge to assign a fixed fraction of the parent to
> get converted to metabolite [and preferably do simultaneous
> parent/metabolite modeling]
> c) If you have no idea about the Vm or fm then use a sequential
> empirical (transit/delay) compartmental modeling recently described by
> Don Mager in a DMD paper [2004 Aug;32(8):786-93]
> Is there any consensus on which of these 3 approaches to use.
> Best regards,
> Mahesh

Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
Received on Wed Dec 10 2008 - 15:11:30 EST

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