RE: VD as a fraction of another VD
Dear Elke, Orlando and Nick,
I have to give Nick my full hearted support in this question. Parent
drug/metabolite models are common practice in population PK and there should
be a kind of best practice for how to parameterize these instead of
inventing one new way after another. I do not doubt that the Knibbe model
gives an excellent fit to that data and is predictive with respect to
external data. That is not the point, the point is that an identical fit to
the data could have been obtained by another parameterization that makes for
a much more straight forward interpretation.
The volume of distribution for the metabolite (e.g. M3G) is unidentifiable
in the exact same way that the volume of distribution is unidentifiable for
any drug where only data following oral administration is available. The
estimate of both Volume and CL for the metabolites will be estimates over
Fmet (i.e. the fraction of the parent compound that forms the metabolite).
To estimate V2 as a fraction of V1 is a pointless parameterization that
serves no purpose. It is reasonable to believe that there will be a high
correlation between the volumes of distribution (e.g. V1 and V2) and this
can be assessed by applying an OMEGA BLOCK to estimate the covariance (e.g.
OMEGA1 and OMEGA2, see below).
V1 = THETA(1)*EXP(ETA(1)) ; central volume for morphine
V2 = THETA(2)*EXP(ETA(2)) ; central volume for M3G/Fm3g
$OMEGA BLOCK(2) 0.1 ; VAR_V1
0.08 ; COVAR_V1_V2
0.1 ; VAR_V2
The outcome of this could be that the estimated covariance corresponds to
approximately 100% correlation. In this case it is still not clearly
justified to reduce the model to assume the same OMEGA variance for both
parameters since the magnitude of variability could still differ between the
two parameters. To assume 100% correlation but different variances can be
done with this parameterization:
V1 = THETA(1)*EXP(ETA(1)) ; central volume for morphine
V2 = THETA(2)*EXP(ETA(1)*THETA(3)) ; central volume for M3G/Fm3g
Where THETA(4) relates the standard deviation of V2 to the standard
deviation of V1 random effect. This model is hierarchically related to a
parameterization that is mathematically equivalent to the parameterization
in the Kibbe model:
V1 = THETA(1)*EXP(ETA(1)) ; central volume for morphine
V2 = THETA(2)*EXP(ETA(1)) ; central volume for M3G/Fm3g
This parameterization could very well turn out to be a sufficient
characterization of the system but it is not true that it cannot be tested
if a more complex model is better (see above steps).
When it comes to the fraction of morphine that is metabolized into M3G and
M6G it can as pointed out not be estimated without access to data following
iv. administration of the metabolites or making very strong assumption such
as fixing distribution volumes etc. Instead it is better to in the model
have all morphine that is eliminated forms both M3G and M6G. This way the
estimated clearance parameters for the metabolites will be (CLm3g/Fm3g and
CLm6g/Fm6g). By the same logic that it isnt identifiable to quantify the
relative formation of M3G and M6G it is also impossible to characterize any
additional rout of elimination.
Reducing the model by setting similar volumes of distribution to the one and
same parameter is nothing that I would practice and I think that it is more
transparent to show the certainty estimates for each parameter in the model.
Let me again stress that I do not question the predictive performance of the
Knibbe model or that it has been useful for its purposes. I have no insight
to this . However I dont think that it has applied a type of
parameterization that should be put forward as a good example since it has
no advantages compared to the standard parameterization that I suggest that
does facilitate a straight forward interpretation and easy comparison to
results from other studies (with or without data following iv administration
of M3G/M6G).
Regards,
Martin Bergstrand, PhD
Pharmacometrics Research Group
Dept of Pharmaceutical Biosciences
Uppsala University
Sweden
<mailto:[email protected]> [email protected]
Visiting scientist:
Mahidol-Oxford Tropical Medicine Research Unit,
Bangkok, Thailand
Phone: +66 8 9796 7611
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of e.krekels
Sent: den 23 maj 2012 16:46
To: 'Carlos Orlando Jacobo Cabral'; 'nonmem users'
Subject: RE: [NMusers] VD as a fraction of another VD
Dear Orlando,
There are multiple models available for morphine in children younger than
three years. The model by Knibbe is based on a data-driven analysis, which
causes this model to be empirical, but supported by the data. In addition to
that and very importantly the Knibbe model is the only model that was proven
to have accurate model performance in extensive internal and external
validation procedures. (Clin Pharmacokinet. 2011 Jan;50(1):51-63 & Pharm
Res. 2011 Apr;28(4):797-811)
Based on the available data, it was not possible to determine the
distribution volume of the metabolites in the model. This would require data
on the metabolites after direct intravenous infusion of the metabolites, but
this is unethical and therefore not possible in children. We were therefore
bound to include assumptions in our model. We have chosen to estimate the
distribution volumes of the metabolites as a proportion of the central
morphine compartment using the following code:
V1 = THETA(1)*EXP(ETA1) ; central volume for morphine
V2 = THETA(2)*V1 ; volume for M3G
By using only 1 eta, we made the implicit assumption that the
inter-individual variability in the volume of the metabolites is
proportional to the variability in the central volume of morphine. This
assumption cannot be proven or disproven with the available data, but to us
it does not seem to be too unrealistic to envision that if one of the
volumes increases or decreases the others will proportionally increase or
decrease as well.
Additionally, we found that when estimating the fraction for M3G and M6G
independently, their 95% confidence interval overlapped significantly and
the same was true for the distribution volume of the peripheral and central
compartment of morphine. According to the rule of parsimony these parameters
were therefore set to be equal.
V3 = V2 ; volume for M6G equal to volume M3G
V4 = V1 ; peripheral volume morphine equal to central volume
For both adults and children morphine elimination through routes other than
glucuronidation has been reported. In our model, with our assumptions, we
found that when estimating a clearance parameter for elimination through
other routes, 0 was included in 95% confidence interval of this parameter.
According to the rule of parsimony we therefore did not include this
parameter in the model. I would suggest that for your data you test
inclusion of this parameter and decide based on statistical criteria and
validation of your model whether you retain it or not.
Regards,
Elke
_____
From: [email protected] [mailto:[email protected]] On
Behalf Of Carlos Orlando Jacobo Cabral
Sent: Tuesday, May 22, 2012 6:42 AM
To: nonmem users
Subject: RE: [NMusers] VD as a fraction of another VD
Dear Nick,
I want to try a previously reported PK model (Knibbe et al. Clin
Pharmacokinet 2009; 48 (6): 371-385) to fit data similar to mine of morphine
and its metabolites in which the volumes of distribution of metabolites were
estimated as a fraction of volume of parent drug what seems to show good
estimates. But also probably I´ll try to estimate the volumes of metabolites
as separate parameters THETA with its corresponding variabilities, do you
have any other suggestions?, thank you.
And thanks also to Bill and Rob.
Kind regards,
Orlando.
PhD student Carlos Orlando Jacobo Cabral
Departamento de Farmacología, Lab.34
Centro de Investigación y de Estudios Avanzados del I. P. N.
Email: [email protected]; [email protected]
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