From: Martin Fransson <*marfr*>

Date: Fri, 13 Apr 2007 11:05:35 +0200

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 -----

From: Silke.Dittberner

To: nmusers

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

Received on Fri Apr 13 2007 - 05:05:35 EDT

Date: Fri, 13 Apr 2007 11:05:35 +0200

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 -----

From: Silke.Dittberner

To: nmusers

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

Received on Fri Apr 13 2007 - 05:05:35 EDT