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RE: Questions about identifiability

From: Eleveld, DJ <d.j.eleveld>
Date: Mon, 16 Apr 2007 12:03:50 +0200

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

________________________________

Van: owner-nmusers
Namens Silke.Dittberner
Verzonden: vrijdag 13 april 2007 9:01
Aan: nmusers
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



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Received on Mon Apr 16 2007 - 06:03:50 EDT

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