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RE: Questions about identifiability

From: Stephen Duffull <stephen.duffull>
Date: Sat, 14 Apr 2007 10:33:03 +1200

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: stephen.duffull
P: +64 3 479 5044
F: +64 3 479 7034

Design software: www.winpopt.com
 

Received on Fri Apr 13 2007 - 18:33:03 EDT

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