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Re: Questions about identifiability

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

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