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

Date: Sat, 14 Apr 2007 10:33:03 +1200

Hi Silke

A couple of quick comments.

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