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

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

De inhoud van dit bericht is vertrouwelijk en alleen bestemd voor de gead=

resseerde(n). Anderen dan de geadresseerde mogen geen gebruik maken van d=

it bericht, het openbaar maken of op enige wijze verspreiden of vermenigv=

uldigen. Het UMCG kan niet aansprakelijk gesteld worden voor een incomple=

te aankomst of vertraging van dit verzonden bericht.

The contents of this message are confidential and only intended for the e=

yes of the addressee(s). Others than the addressee(s) are not allowed to =

use this message, to make it public or to distribute or multiply this mes=

sage in any way. The UMCG cannot be held responsible for incomplete recep=

tion or delay of this transferred message.

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