Andreas,
I doubt that one can give a general answer (without looking on the
specific model) but here is my understanding of the situation:
In over-parametrized models, there is one or more degenerate directions
(in the parameter space) where changes of the parameters do not change
the fit (i.e., where there is no data to estimate each parameter, only
some combination). The model can be well-defined in the orthogonal
directions. The simplest example is oral absorption: without IV data, F(
bioavaialbility), CL and V are not definable. However, CL/F and V/F can
be estimated. This leads to two different situations: if your critical
parameter is in the "well-defined" space, then you may use it as a
biomarker. If, on the other hand, this parameter is in the degenerate
space, it cannot be used since its value is not stable. The burden of
proof is of course on the presenter. One can support it by
- small RSEs on the parameter of interest, if you can get them;
- no correlation with other parameters (either in bootstrap samples,
or in the history of SAEM iterations, or by investigation the
variance-covariance matrix of the parameter estimates);
- starting the model run with perturbed values of this parameter to
show that the final estimate does not depend on the initial values;
- etc.
Alternative is to try to make the entire model stable by fixing some
parameters at the biologically plausible values: if the model with fixed
parameters is still flexible enough to describe the entire range of
available data, one can use this model until some experimental results
provide the data (and the need) to free and estimate those fixed parameters.
Thanks
Leonid
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566
On 9/7/2010 2:42 AM, Steingötter Andreas wrote:
Hello Nick, Leonid, Dieter
As a beginner in NONMEM society, I am becoming very curious in your
current discussion. In a related situation I may need some helpful
comments and already excuse myself if this question has been answered
many times before.
THE SITUATION: We have tissue (let's say tumor tissue) that has some
anatomical structure known by histology. So we know roughly how many
blood vessels (to get an idea on blood flow/perfusion), how many vital
tissue (to get an idea where the blood can distribute or perfuse into)
and how many dead tissue (where only blood diffusion can take place)
is present. We inject a substance (i.v. bolus) and macroscopically
follow its kinetics through this tissue, i.e. have a concentration
curve of this tissue. At the same time we can also measure the
kinetics of other (neighboring) healthy tissues to generate additional
concentration curves. All these curves exhibit bi- or
multi-exponential behavior.
First PROBLEM: We only observe on the macroscopic scale and therefore
we have a mixture of tissue kinetics for each concentration curve.
However, we are able to create a model that perfectly describes the
concentration curves of all tissues as Dieter has done. This model is
very likely to be over-parameterized.
In a SECOND STEP we treat this tumor tissue and see some changes in
tumor structure. But don't have clue how these changes in structure
relate to changes in function, e.g. what rate constant, volume flow or
distribution volume is most sensitive to such a change in blood
vessels. For later purpose and to omit the need for histology the aim
is to identify this sensitive parameter and use it as some kind of
biomarker.
NOW THE QUESTION: How to best proceed to (numerically) find this most
sensitive parameter in the model? Do we start from the model that best
describes the concentration curves and go backwards again. Do we pick
a first potential parameter and reduce the model until this parameter
is robust (shows no correlation) and do the same again for other
possible candidates? Do we then end up with one model for each
parameter of interest (which does not make sense to me)?
To my understanding, for a given (rich) data set there can only be a
compromise between model fit and robustness of parameter estimation
and finally someone has to decide what that is. This compromise then
needs to be tested and validated again and again by generating or
including new data.
BEGINNER's QUESTION: If we show that we have done the testing and
tweaking with regard to what we (pretend to) know from
physiology/biology/histology and are aware of (and describe) the
uncertainty in parameter estimates for the selected, probably over
parameterized model, would expert reviewers of your caliber still ask
for more model simplification?
Sorry for being so elaborate and many thanks for comments and critics
of every description.
Andreas
Andreas Steingötter, PhD
Division for Gastroenterology and Hepatology
Department of Internal Medicine
University Hospital Zurich
*Von:* [email protected]
[mailto:[email protected]] *Im Auftrag von *Nick Holford
*Gesendet:* Dienstag, 7. September 2010 04:19
*An:* nmusers
*Betreff:* Re: [NMusers] How serious are negative eigenvalues?
Dieter,
You ask:
My question: can we trust this fit?
The answer depends on why you are doing the modelling.
If your goal is to describe the time course of concentrations then the
overall ability of the model to describe what you saw depends on the
totality of the model and its parameters. The model may be
overparameterized but it may still do what you want it to do i.e.
describe (and predict) the time course of concentrations in each
compartment. If you are satisfied with the VPC showing that
simulations from the model appropriately describe the observed
concentrations then I think the answer to your question is yes.
On the other hand if the goal is to estimate the size of one or more
critical parameters then you will need to pay attention to how well
these parameters are estimated. As Leonid has pointed out it seems
that at least some of the model parameters are not well identified.
This may be unimportant if the parameters you want to describe are
robustly estimated.
For example, if you had a simple PK model with samples mainly taken at
steady state with few observations during absorption then you may get
a good estimate of clearance but a rather poor estimate of KA. You
cannot simply remove a parameter such as KA (you have to describe the
sparse absorption somehow) but it will have little impact on the
clearance estimate. Thus the model can be trusted for the purpose of
estimating clearance but not absorption rate.
Nick
On 7/09/2010 12:11 a.m., Dieter Menne wrote:
Dear Nmusers,
we have very rich data from MRI concentration measurements, with 11
compartments and multiple compartments observed. The model is fit via SAEM
(nburn=2000), and followed by an IMPMAP as in the described in the 7.1.2
manual. OMEGA is band with pair-wise block correlations in the following
style:
$OMEGA BLOCK(2)
.02 ;CL
0.01 0.06 ; VC
$OMEGA BLOCK(2)
5.4 ; QMVP
0.001 0.05 ;VMVP
$OMEGA BLOCK(2)
0.06 ; QTVP
0.001 0.25 ;VTPV
$EST PRINT=1 METHOD=SAEM INTERACTION NBURN=2000 NITER=200 CTYPE=2 NSIG=2
FILE=SAEM.EXT
$EST METHOD=IMPMAP EONLY = 1 INTERACTION ISAMPLE=1000 NITER=5 FILE=IMP.EXT
$COV PRINT=E UNCONDITIONAL
Fits and CWRES diagnostics are perfect, and VPC checks are good.
However, we have negative eigenvalues (the following example has been edited
by removing digits)
ETAPval = 0.2 0.2 0.3 0.04 0.8 0.95 0.003 0.1 0.6 0.4 0.9 0.1 0.5 0.4 0.2
0.8 0.3 0.3 0.4 0.01 0.8
ETAshr% = 13. 0.4 38 20 23 33 46 30 18 41 54 22 2. 26. 49. 12. 0.07 24. 18.
35. 2.5
EPSshr% = 7.5 8.1
Number of Negative Eigenvalues in Matrix= 7
Most negative value= -65339.
Most positive value= 88796185.9
Forcing positive definiteness
Root mean square deviation of matrix from original= 1.37E-003
My question: can we trust this fit?
Dieter Menne
Menne Biomed/University Hospital of Zürich
--
Nick Holford, Professor Clinical Pharmacology
Dept Pharmacology& Clinical Pharmacology
University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand
tel:+64(9)923-6730 fax:+64(9)373-7090 mobile:+64(21)46 23 53
email:[email protected] <mailto:[email protected]>
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
