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: [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
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
