Dear NONMEM users,
The PK of the compound we are working on can be described by a 2-compartment
model with non-linear protein binding in the central and in the peripheral
compartment, which from a physiological point of view makes complete sense.
The question we have is whether such model is identifiable having just total
plasma concentration (no binding information is available).
Therefore we want to simulate different kind of datasets and check if NONMEM
is able to re-estimate them properly.
* Our first question was: "Is the structure itself in principle
identifiable?"
We simulated a dataset with 100 time points per subject and
no intra- or inter-individual variability and no residual error. ('ideal'
data: plenty time points, no random error) Since under these conditions
the parameters could be re-estimated (parameter estimates were nearly
identical to the original ones, %SE is very small) we concluded that
the structure in principle is identifiable.
* Our second question was: "Are the time points of the given
study sufficient to estimate all parameters assuming 'ideal' data?"
We simulated the given dataset assuming no intra- or
inter-individual variability and no residual error. The parameter estimates
were again nearly identical to the original ones and %SE is still very
small (below 0.3 %).
* Our third question was: "Could the parameters still be
re-estimated if we assume inter- and intra-subject variability for the
simulation step?"
We simulated the given dataset assuming IIV, IOV and residual
error. Under these conditions, the parameter (fixed and random effect)
estimates are again similar, but not identical to the original ones, %SE
increased to about 9% (one exception is the SE% of the parameter for
the amount of peripheral binding sites which were estimated to be 16%).
However, when we re-estimate omitting the IIV and IOV, the estimated
parameters differ from the original ones and estimates for the peripheral
binding becomes difficult to estimate.
The questions we have are:
1. Are these experiments sufficient to conclude on the model
identifiability?
2. Does it make sense that the fixed effect parameters differ from the
original ones when IIV and IOV are omitted in the estimation step in
constrast to when they are included in the simulation step? Shouldn't the
structure of the model remain stable?
3. How often would you simulate and re-estimate the third experiment?
4. Would you vary the initial estimates to check for any potential other
set of parameters? (If yes how often?)
5. One problem is that the complete model with IIV and IOV has quite
long run times (around 24h), do you think checking the model with just IIV
would be enough?
6. Do you have any other proposal to check for the identifiability of a
model?
Your help is highly appreciated, thank you in advance,
Silke
Silke Dittberner
PhD student
Institute of Pharmacy
University Bonn
Germany
Questions about identifiability
Dear NONMEM users,
The PK of the compound we are working on can be described by a 2-compartment
model with non-linear protein binding in the central and in the peripheral
compartment, which from a physiological point of view makes complete sense.
The question we have is whether such model is identifiable having just total
plasma concentration (no binding information is available).
Therefore we want to simulate different kind of datasets and check if NONMEM
is able to re-estimate them properly.
* Our first question was: "Is the structure itself in principle
identifiable?"
We simulated a dataset with 100 time points per subject and
no intra- or inter-individual variability and no residual error. ('ideal'
data: plenty time points, no random error) Since under these conditions
the parameters could be re-estimated (parameter estimates were nearly
identical to the original ones, %SE is very small) we concluded that
the structure in principle is identifiable.
* Our second question was: "Are the time points of the given
study sufficient to estimate all parameters assuming 'ideal' data?"
We simulated the given dataset assuming no intra- or
inter-individual variability and no residual error. The parameter estimates
were again nearly identical to the original ones and %SE is still very
small (below 0.3 %).
* Our third question was: "Could the parameters still be
re-estimated if we assume inter- and intra-subject variability for the
simulation step?"
We simulated the given dataset assuming IIV, IOV and residual
error. Under these conditions, the parameter (fixed and random effect)
estimates are again similar, but not identical to the original ones, %SE
increased to about 9% (one exception is the SE% of the parameter for
the amount of peripheral binding sites which were estimated to be 16%).
However, when we re-estimate omitting the IIV and IOV, the estimated
parameters differ from the original ones and estimates for the peripheral
binding becomes difficult to estimate.
The questions we have are:
1. Are these experiments sufficient to conclude on the model
identifiability?
2. Does it make sense that the fixed effect parameters differ from the
original ones when IIV and IOV are omitted in the estimation step in
constrast to when they are included in the simulation step? Shouldn't the
structure of the model remain stable?
3. How often would you simulate and re-estimate the third experiment?
4. Would you vary the initial estimates to check for any potential other
set of parameters? (If yes how often?)
5. One problem is that the complete model with IIV and IOV has quite
long run times (around 24h), do you think checking the model with just IIV
would be enough?
6. Do you have any other proposal to check for the identifiability of a
model?
Your help is highly appreciated, thank you in advance,
Silke
Silke Dittberner
PhD student
Institute of Pharmacy
University Bonn
Germany
Dear Silke,
Before looking into the identifiability question, it is useful to know
what the differential equations and the dosing route are, please?
Kind regards,
Amy
-------------------------------------------------------------------------------
S.Y.A. Cheung
Postgraduate Research Student
The Centre for Applied Pharmacokinetic Research (CAPKR)
School of Pharmacy and Pharmaceutical Sciences
University of Manchester
Stopford Building
Oxford Road
Manchester
U.K.
-----------------------------------------------------------------------------------------------------------------------
Quoted reply history
On 13/04/07, [EMAIL PROTECTED]
<[EMAIL PROTECTED]> wrote:
> Dear NONMEM users,
>
> The PK of the compound we are working on can be described by a 2-compartment
> model with non–linear protein binding in the central and in the peripheral
> compartment, which from a physiological point of view makes complete sense.
> The question we have is whether such model is identifiable having just total
> plasma concentration (no binding information is available).
>
> Therefore we want to simulate different kind of datasets and check if NONMEM
> is able to re-estimate them properly.
>
> · Our first question was: "Is the structure itself in principle
> identifiable?"
>
> We simulated a dataset with 100 time points per subject and no
> intra- or inter-individual variability and no residual error. ('ideal' data:
> plenty time points, no random error) Since under these conditions the
> parameters could be re-estimated (parameter estimates were nearly identical
> to the original ones, %SE is very small) we concluded that the structure
> in principle is identifiable.
>
> · Our second question was: "Are the time points of the given study
> sufficient to estimate all parameters assuming 'ideal' data?"
>
> We simulated the given dataset assuming no intra- or
> inter-individual variability and no residual error. The parameter estimates
> were again nearly identical to the original ones and %SE is still very
> small (below 0.3 %).
>
> · Our third question was: "Could the parameters still be re-estimated
> if we assume inter- and intra-subject variability for the simulation step?"
>
> We simulated the given dataset assuming IIV, IOV and residual error.
> Under these conditions, the parameter (fixed and random effect) estimates
> are again similar, but not identical to the original ones, %SE increased to
> about 9% (one exception is the SE% of the parameter for the amount of
> peripheral binding sites which were estimated to be 16%). However, when we
> re-estimate omitting the IIV and IOV, the estimated parameters differ from
> the original ones and estimates for the peripheral binding becomes difficult
> to estimate.
>
> The questions we have are:
> 1. Are these experiments sufficient to conclude on the model
> identifiability?
> 2. Does it make sense that the fixed effect parameters differ from the
> original ones when IIV and IOV are omitted in the estimation step in
> constrast to when they are included in the simulation step? Shouldn't the
> structure of the model remain stable?
>
> 3. How often would you simulate and re-estimate the third experiment?
> 4. Would you vary the initial estimates to check for any potential
> other set of parameters? (If yes how often?)
> 5. One problem is that the complete model with IIV and IOV has quite
> long run times (around 24h), do you think checking the model with just IIV
> would be enough?
>
> 6. Do you have any other proposal to check for the identifiability of a
> model?
>
> Your help is highly appreciated, thank you in advance,
>
> Silke
>
> Silke Dittberner
> PhD student
> Institute of Pharmacy
> University Bonn
> Germany
--
Questions about identifiabilityDear Silke,
When it comes to the structural observability/identifiability of your model I
would recommend you to use the algorithm presented by Alexandre Sedoglavic in
[1]. This algorithm tests local algebraic observability of a model structure of
linear or rational functions if given in state-space form, i.e., as a set of
ODEs with input and output signals. With this approach you can test the model
structure if no etas or epsilons are considered (I'm not sure that it can be
used in an accurate way with etas and epsilons).
Further on, the author of [1] has made an implementation of the algorithm in a
major software (I'm not sure how touchy people in this forum are when it comes
to talking about other software... ;-) so the effort of just trying it out is
low. The implementation is provided on the homepage of the author.
Good luck!
/Martin
[1] Sedoglavic, A. "A probabilistic algorithm to test local algebraic
observability in polynomial time". Journal of Symbolic Computation 33(5), pages
735-755, 2002.
----- Original Message -----
Quoted reply history
From: [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Sent: Friday, April 13, 2007 9:01 AM
Subject: [NMusers] Questions about identifiability
Dear NONMEM users,
The PK of the compound we are working on can be described by a 2-compartment
model with non-linear protein binding in the central and in the peripheral
compartment, which from a physiological point of view makes complete sense. The
question we have is whether such model is identifiable having just total plasma
concentration (no binding information is available).
Therefore we want to simulate different kind of datasets and check if NONMEM
is able to re-estimate them properly.
· Our first question was: "Is the structure itself in principle
identifiable?"
We simulated a dataset with 100 time points per subject and no
intra- or inter-individual variability and no residual error. ('ideal' data:
plenty time points, no random error) Since under these conditions the
parameters could be re-estimated (parameter estimates were nearly identical
to the original ones, %SE is very small) we concluded that the structure in
principle is identifiable.
· Our second question was: "Are the time points of the given study
sufficient to estimate all parameters assuming 'ideal' data?"
We simulated the given dataset assuming no intra- or
inter-individual variability and no residual error. The parameter estimates
were again nearly identical to the original ones and %SE is still very
small (below 0.3 %).
· Our third question was: "Could the parameters still be re-estimated
if we assume inter- and intra-subject variability for the simulation step?"
We simulated the given dataset assuming IIV, IOV and residual
error. Under these conditions, the parameter (fixed and random effect)
estimates are again similar, but not identical to the original ones, %SE
increased to about 9% (one exception is the SE% of the parameter for the
amount of peripheral binding sites which were estimated to be 16%). However,
when we re-estimate omitting the IIV and IOV, the estimated parameters differ
from the original ones and estimates for the peripheral binding becomes
difficult to estimate.
The questions we have are:
1. Are these experiments sufficient to conclude on the model
identifiability?
2. Does it make sense that the fixed effect parameters differ from the
original ones when IIV and IOV are omitted in the estimation step in constrast
to when they are included in the simulation step? Shouldn't the structure of
the model remain stable?
3. How often would you simulate and re-estimate the third experiment?
4. Would you vary the initial estimates to check for any potential other
set of parameters? (If yes how often?)
5. One problem is that the complete model with IIV and IOV has quite
long run times (around 24h), do you think checking the model with just IIV
would be enough?
6. Do you have any other proposal to check for the identifiability of a
model?
Your help is highly appreciated, thank you in advance,
Silke
Silke Dittberner
PhD student
Institute of Pharmacy
University Bonn
Germany
Amy,
Just one comment about identifiability. A very simple and efficient way to see
whether your model has identifiability problem is to randomly change your
initial guesses to see whether your parameter estimates are stable. In
addition, that your simulation proves no identifiability problem does not
necessarily mean your model will not have identifiability problem to your real
data.
Alan
Quoted reply history
-----Original Message-----
From: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED] Behalf Of Amy Cheung
Sent: Friday, April 13, 2007 4:45 AM
To: [EMAIL PROTECTED]
Cc: [EMAIL PROTECTED]
Subject: Re: [NMusers] Questions about identifiability
Dear Silke,
Before looking into the identifiability question, it is useful to know
what the differential equations and the dosing route are, please?
Kind regards,
Amy
-------------------------------------------------------------------------------
S.Y.A. Cheung
Postgraduate Research Student
The Centre for Applied Pharmacokinetic Research (CAPKR)
School of Pharmacy and Pharmaceutical Sciences
University of Manchester
Stopford Building
Oxford Road
Manchester
U.K.
-----------------------------------------------------------------------------------------------------------------------
On 13/04/07, [EMAIL PROTECTED]
<[EMAIL PROTECTED]> wrote:
>
>
> Dear NONMEM users,
>
> The PK of the compound we are working on can be described by a 2-compartment
> model with non–linear protein binding in the central and in the peripheral
> compartment, which from a physiological point of view makes complete sense.
> The question we have is whether such model is identifiable having just total
> plasma concentration (no binding information is available).
>
> Therefore we want to simulate different kind of datasets and check if NONMEM
> is able to re-estimate them properly.
>
>
> · Our first question was: "Is the structure itself in principle
> identifiable?"
>
> We simulated a dataset with 100 time points per subject and no
> intra- or inter-individual variability and no residual error. ('ideal' data:
> plenty time points, no random error) Since under these conditions the
> parameters could be re-estimated (parameter estimates were nearly identical
> to the original ones, %SE is very small) we concluded that the structure
> in principle is identifiable.
>
>
>
> · Our second question was: "Are the time points of the given study
> sufficient to estimate all parameters assuming 'ideal' data?"
>
> We simulated the given dataset assuming no intra- or
> inter-individual variability and no residual error. The parameter estimates
> were again nearly identical to the original ones and %SE is still very
> small (below 0.3 %).
>
> · Our third question was: "Could the parameters still be re-estimated
> if we assume inter- and intra-subject variability for the simulation step?"
>
> We simulated the given dataset assuming IIV, IOV and residual error.
> Under these conditions, the parameter (fixed and random effect) estimates
> are again similar, but not identical to the original ones, %SE increased to
> about 9% (one exception is the SE% of the parameter for the amount of
> peripheral binding sites which were estimated to be 16%). However, when we
> re-estimate omitting the IIV and IOV, the estimated parameters differ from
> the original ones and estimates for the peripheral binding becomes difficult
> to estimate.
>
> The questions we have are:
> 1. Are these experiments sufficient to conclude on the model
> identifiability?
> 2. Does it make sense that the fixed effect parameters differ from the
> original ones when IIV and IOV are omitted in the estimation step in
> constrast to when they are included in the simulation step? Shouldn't the
> structure of the model remain stable?
>
> 3. How often would you simulate and re-estimate the third experiment?
> 4. Would you vary the initial estimates to check for any potential
> other set of parameters? (If yes how often?)
> 5. One problem is that the complete model with IIV and IOV has quite
> long run times (around 24h), do you think checking the model with just IIV
> would be enough?
>
> 6. Do you have any other proposal to check for the identifiability of a
> model?
>
> Your help is highly appreciated, thank you in advance,
>
> Silke
>
>
>
> Silke Dittberner
> PhD student
> Institute of Pharmacy
> University Bonn
> Germany
--
Hi Silke
A couple of quick comments.
> The questions we have are:
> 1. Are these experiments sufficient to conclude on the
> model identifiability?
Yes and no.
Technically speaking what you have done is not sufficient to show
identifiability of your model. You can either do a formal identifiability
analysis or alternatively compute the expected Fisher information matrix for
the parameters given your design. In the latter case if the information
matrix is rank deficient or the determinant of the matrix is close to zero
then you have some level of identifiability problem. The latter method
cannot distinguish between structural identifiability (i.e. that the model
has 2 or more parameters that cannot be locally identified irrespective of
your design) from deterministic identifiability (i.e. your model is
structurally identifiable but your design is insufficient to allow all of
your parameters to be precisely estimated). The Fisher information matrix
can be computed for any design using a variety of "optimal" design programs
include WinPOPT (www.winpopt.com).
It should be noted that being able to simulate and estimate model parameters
under a particular design does not mean the model is structurally
identifiable. I have seen several cases where precise parameter estimates
occurred under a structurally non-identifiable model.
However, I think it does provide reasonable evidence that all is well :-)
Whether it is sufficient evidence depends on what you are developing the
model for...
I'll leave the other questions for the time being.
Steve
--
Professor Stephen Duffull
Chair of Clinical Pharmacy
School of Pharmacy
University of Otago
PO Box 913 Dunedin
New Zealand
E: [EMAIL PROTECTED]
P: +64 3 479 5044
F: +64 3 479 7034
Design software: www.winpopt.com
sorry that I followed with the wrong email.
Alan
Quoted reply history
-----Original Message-----
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] Behalf Of Amy
Cheung
Sent: Friday, April 13, 2007 8:56 AM
To: Xiao, Alan
Cc: [EMAIL PROTECTED]
Subject: Re: [NMusers] Questions about identifiability
Dear Alan,
The problem was originally posted by Silke Dittberner. I am just
helping in solving the problem and my email was to express interest to
the nature of the model in order to answer the structural
identifiability problem. I think you should email your comment
addressed to Silke Dittberner at
[EMAIL PROTECTED] instead of me.
Many thanks,
Amy
On 13/04/07, Xiao, Alan <[EMAIL PROTECTED]> wrote:
> Amy,
>
> Just one comment about identifiability. A very simple and efficient way to
> see whether your model has identifiability problem is to randomly change your
> initial guesses to see whether your parameter estimates are stable. In
> addition, that your simulation proves no identifiability problem does not
> necessarily mean your model will not have identifiability problem to your
> real data.
>
> Alan
>
> -----Original Message-----
> From: [EMAIL PROTECTED]
> [mailto:[EMAIL PROTECTED] Behalf Of Amy Cheung
> Sent: Friday, April 13, 2007 4:45 AM
> To: [EMAIL PROTECTED]
> Cc: [EMAIL PROTECTED]
> Subject: Re: [NMusers] Questions about identifiability
>
>
> Dear Silke,
>
> Before looking into the identifiability question, it is useful to know
> what the differential equations and the dosing route are, please?
>
> Kind regards,
>
> Amy
>
> -------------------------------------------------------------------------------
> S.Y.A. Cheung
> Postgraduate Research Student
> The Centre for Applied Pharmacokinetic Research (CAPKR)
> School of Pharmacy and Pharmaceutical Sciences
> University of Manchester
> Stopford Building
> Oxford Road
> Manchester
> U.K.
>
> -----------------------------------------------------------------------------------------------------------------------
>
> On 13/04/07, [EMAIL PROTECTED]
> <[EMAIL PROTECTED]> wrote:
> >
> >
> > Dear NONMEM users,
> >
> > The PK of the compound we are working on can be described by a 2-compartment
> > model with non–linear protein binding in the central and in the peripheral
> > compartment, which from a physiological point of view makes complete sense.
> > The question we have is whether such model is identifiable having just total
> > plasma concentration (no binding information is available).
> >
> > Therefore we want to simulate different kind of datasets and check if NONMEM
> > is able to re-estimate them properly.
> >
> >
> > · Our first question was: "Is the structure itself in principle
> > identifiable?"
> >
> > We simulated a dataset with 100 time points per subject and no
> > intra- or inter-individual variability and no residual error. ('ideal' data:
> > plenty time points, no random error) Since under these conditions the
> > parameters could be re-estimated (parameter estimates were nearly identical
> > to the original ones, %SE is very small) we concluded that the structure
> > in principle is identifiable.
> >
> >
> >
> > · Our second question was: "Are the time points of the given study
> > sufficient to estimate all parameters assuming 'ideal' data?"
> >
> > We simulated the given dataset assuming no intra- or
> > inter-individual variability and no residual error. The parameter estimates
> > were again nearly identical to the original ones and %SE is still very
> > small (below 0.3 %).
> >
> > · Our third question was: "Could the parameters still be re-estimated
> > if we assume inter- and intra-subject variability for the simulation step?"
> >
> > We simulated the given dataset assuming IIV, IOV and residual error.
> > Under these conditions, the parameter (fixed and random effect) estimates
> > are again similar, but not identical to the original ones, %SE increased to
> > about 9% (one exception is the SE% of the parameter for the amount of
> > peripheral binding sites which were estimated to be 16%). However, when we
> > re-estimate omitting the IIV and IOV, the estimated parameters differ from
> > the original ones and estimates for the peripheral binding becomes difficult
> > to estimate.
> >
> > The questions we have are:
> > 1. Are these experiments sufficient to conclude on the model
> > identifiability?
> > 2. Does it make sense that the fixed effect parameters differ from the
> > original ones when IIV and IOV are omitted in the estimation step in
> > constrast to when they are included in the simulation step? Shouldn't the
> > structure of the model remain stable?
> >
> > 3. How often would you simulate and re-estimate the third experiment?
> > 4. Would you vary the initial estimates to check for any potential
> > other set of parameters? (If yes how often?)
> > 5. One problem is that the complete model with IIV and IOV has quite
> > long run times (around 24h), do you think checking the model with just IIV
> > would be enough?
> >
> > 6. Do you have any other proposal to check for the identifiability of a
> > model?
> >
> > Your help is highly appreciated, thank you in advance,
> >
> > Silke
> >
> >
> >
> > Silke Dittberner
> > PhD student
> > Institute of Pharmacy
> > University Bonn
> > Germany
>
>
> --
>
--
-------------------------------------------------------------------------------
S.Y.A. Cheung
Postgraduate Research Student
The Centre for Applied Pharmacokinetic Research (CAPKR)
School of Pharmacy and Pharmaceutical Sciences
University of Manchester
Stopford Building
Oxford Road
Manchester
U.K.
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
"For beautiful eyes, look for the good in others;
for beautiful lips, speak only words of kindness;
and for poise, walk with the knowledge that you are
never alone. People, even more than things, have to
be restored, renewed, revived, reclaimed, and redeemed;
never throw out anyone. Remember, if you ever need a
helping hand, it's at the end of your arm, as you get
older, remember you have another hand: The first is to
help yourself, the second is to help others."
Audrey hepburn
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/
Hi Silke,
If you are looking at model indentifiability, regardless of in-principle
or in-practice, you absolutely must use a range of initial estimates.
Minimization algorithms can converge to a minimum or a saddle point
close to the initial estimates. If your model always finds the 'right'
answer even when you start with a (number of) 'wrong' estimates then
this is usually what people mean when they talk about identifiability.
In real-life you are *guaranteed* to start with incorrect initial
estimates anyway...
Exactly how many to use is a harder question. As many as possible
doesnt really answer your question I think. On the order of thousands
would satisfy almost everyone, but it likely depends on the number of
model parameters and how many runs are possible given your problem,
computing power and patience.
hope this helps,
Doug Eleveld
________________________________
Quoted reply history
Van: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]
Namens [EMAIL PROTECTED]
Verzonden: vrijdag 13 april 2007 9:01
Aan: [email protected]
Onderwerp: [NMusers] Questions about identifiability
Dear NONMEM users,
The PK of the compound we are working on can be described by a
2-compartment model with non-linear protein binding in the central and
in the peripheral compartment, which from a physiological point of view
makes complete sense. The question we have is whether such model is
identifiable having just total plasma concentration (no binding
information is available).
Therefore we want to simulate different kind of datasets and check if
NONMEM is able to re-estimate them properly.
* Our first question was: "Is the structure itself in
principle identifiable?"
We simulated a dataset with 100 time points per subject
and no intra- or inter-individual variability and no residual error.
('ideal' data: plenty time points, no random error) Since under
these conditions the parameters could be re-estimated (parameter
estimates were nearly identical to the original ones, %SE is very
small) we concluded that the structure in principle is identifiable.
* Our second question was: "Are the time points of the
given study sufficient to estimate all parameters assuming 'ideal'
data?"
We simulated the given dataset assuming no intra- or
inter-individual variability and no residual error. The parameter
estimates were again nearly identical to the original ones and %SE
is still very small (below 0.3 %).
* Our third question was: "Could the parameters still be
re-estimated if we assume inter- and intra-subject variability for the
simulation step?"
We simulated the given dataset assuming IIV, IOV and
residual error. Under these conditions, the parameter (fixed and random
effect) estimates are again similar, but not identical to the
original ones, %SE increased to about 9% (one exception is the SE% of
the parameter for the amount of peripheral binding sites which were
estimated to be 16%). However, when we re-estimate omitting the IIV and
IOV, the estimated parameters differ from the original ones and
estimates for the peripheral binding becomes difficult to estimate.
The questions we have are:
1. Are these experiments sufficient to conclude on the model
identifiability?
2. Does it make sense that the fixed effect parameters differ from
the original ones when IIV and IOV are omitted in the estimation step in
constrast to when they are included in the simulation step? Shouldn't
the structure of the model remain stable?
3. How often would you simulate and re-estimate the third
experiment?
4. Would you vary the initial estimates to check for any potential
other set of parameters? (If yes how often?)
5. One problem is that the complete model with IIV and IOV has
quite long run times (around 24h), do you think checking the model with
just IIV would be enough?
6. Do you have any other proposal to check for the identifiability
of a model?
Your help is highly appreciated, thank you in advance,
Silke
Silke Dittberner
PhD student
Institute of Pharmacy
University Bonn
Germany
Dear Silke
Usually the parameter structural identifiability problem is dealt with
in terms of local identifiability (see Grewal MS, IEEE
Trans.Autom.Control, 21:833-837, 1976) and less often in terms of global
identifiability (by Laplace transformation, Taylor series expansion or
similarity transformation/reparametrization). Different issues pertain
to structural admissibility, reachability and observability. Keith
Godfrey has researched extensively on these topics (start maybe with
Godfrey KR and DiStefano JJ, 'Identifiability of model parameters' in
'Identifiability of parametric models', Walter E, Ed. 1987, Pergamon
Press).
IMHO, dealing with biological data, the identifiability problem becomes
essentially local and is always pragmatic in nature. Hat matrix entries,
information matrices and sensitivity to different initial estimates are
usually valuable, but no warranty for structural identifiability
(particularly global). Simulation exercises are always prone to what I
use to call the 'mirror syndrome' and you may just get what you put in,
ending up biased.
Realization theory based on Markov parameters provides usually good
insights for time-invariant finite-dimensional linear systems. My
preferred approach is Information theory based on the concept that each
observation has an intrinsic amount of information (Shannon Information)
which is the upper bound for every inference exercise. But again, with
routinely encountered problems we usually get away with small enough
confidence intervals for our adjustable parameters.
Cheers
Luis
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Luis M. Pereira, Ph.D.
Assistant Professor, Biopharmaceutics and Pharmacokinetics
Massachusetts College of Pharmacy and Health Sciences
179 Longwood Ave, Boston, MA 02115
Phone: (617) 732-2905
Fax: (617) 732-2228
[EMAIL PROTECTED]