RE: estimating Ka from dataset combining rich sample study and sparse sampling study
Steve -
I agree with you that adding addtional data (in this case adding a sparse data
set to a dense data set)
ideally should result in better (more precise) estimates when the individuals
from the two data sets
are exchangeable, but only assuming the underlying estimation methodology is
well-behaved for
both the sparse and dense data. In the real world, and in particular
with the FOCE approximation, sparse data may not be well estimated by FOCE and
merging sparse data with
dense data may contaminate the dense data rather than enhance it.
As an example, I ran a simulation using an Emax Hill coefficient model with
gamma=4.5 (this is the same
model that appears in Mats' 2007 Pharm Res paper Hooker et al, "Conditional
Weighted Residuals (CWRES):
A Diagostic For the FOCE Method)". Using dense data (25 observations per
subject) and 200 subjects
simulated from the true model, all parameters all well estimated. In
particular, gamma is estimated at
4.38 (std err = 0.069)
For an equivalent amount of sparse data (2000 subjects, average of 2.5
obs/susbject, also simulated from the same
model and the same design except that observations were removed at random with
a 90% probability of removal for
any given observation), the FOCE estimate of gamma is 3.51 (std err = 0.060)
(all other parameters are reasonably estimated by the sparse data).
When the data sets are combined, the gamma estimate is 3.69 (std err =0.104 )
. Thus merging the dense data with
the sparse data has resulted in a good estimate being converted to a relatively
poor one. Moreover,
the std error (albeit from a Hessian based computation) has increased in the
merged set relative to both
separate individual sets.
I agree with Jurgen that nonparametric estimation is much less susceptible to
this contamination
effect. For the merged data set, the nonparametric
method will likely simply use the sharply defined support points from the
dense data, (assuming there are a reasonable number
of these and they cover the region of interest). Individuals from the dense
data set will be modeled with very large
probabilities associated with their single corresponding support point, while
individuals from the sparse set will
have probabilities spread out over several supports.
Bob Leary
Robert H. Leary, PhD
Fellow
Pharsight - A Certara(tm) Company
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Quoted reply history
-----Original Message-----
From: [email protected] [mailto:[email protected]]on
Behalf Of Stephen Duffull
Sent: Thursday, June 18, 2009 2:4 AM
To: Mats Karlsson; 'Ribbing, Jakob'; 'Ethan Wu'; 'Jurgen Bulitta';
[email protected]
Cc: 'Roger Jelliffe'; 'Neely, Michael'
Subject: RE: [NMusers] estimating Ka from dataset combining rich sample study
and sparse sampling study
Dear Ethan
I concur with Mats's comments below.
As a note, from a design perspective adding additional data to an experiment
cannot result in less precise parameter estimates under the assumption that the
individuals from the two data sets are exchangeable. Under this assumption
therefore the Sparse data should merely add information to the Rich data. That
the Sparse data is affecting the parameter estimates from the Rich data
suggests that the two data sets are not exchangeable (different centre,
different assay, different covariates ...).
Another possible way to investigate the differences between the two data sets
would be to analyse them sequentially, perhaps with consideration for using the
analysis from the Rich data as an informative prior for the analysis of the
Sparse data and see where this leads you.
Kind regards
Steve
--
Professor Stephen Duffull
Chair of Clinical Pharmacy
School of Pharmacy
University of Otago
PO Box 913 Dunedin
New Zealand
E: <mailto:[email protected]> [email protected]
P: +64 3 479 5044
F: +64 3 479 7034
Design software: http://www.winpopt.com www.winpopt.com
From: [email protected] [mailto:[email protected]] On
Behalf Of Mats Karlsson
Sent: Thursday, 18 June 2009 9:17 a.m.
To: 'Ribbing, Jakob'; 'Ethan Wu'; 'Jurgen Bulitta'; [email protected]
Cc: 'Roger Jelliffe'; 'Neely, Michael'
Subject: RE: [NMusers] estimating Ka from dataset combining rich sample study
and sparse sampling study
Dear Ethan,
Variances estimated to be zero may result from fixing off-diagonal variances to
zero (i.e. not using BLOCKs in IIV). Here, however, it may be that there are
systematic differences between the sparse and the rich data experiments. Maybe
fasting/fed status or something else is different. If the fit to the rich data
is markedly worse when including the rich data, at least one parameter is
different between the two situations. I would explore what parameter(s) that
would be. In addition to Jakob's suggestions below, the two data sets together
may indicate a more complex structural model that a single profile indicated.
Maybe you need to go to a two-compartment for example.
Best regards,
Mats
Mats Karlsson, PhD
Professor of Pharmacometrics
Dept of Pharmaceutical Biosciences
Uppsala University
Box 591
751 24 Uppsala Sweden
phone: +46 18 4714105
fax: +46 18 471 4003
From: [email protected] [mailto:[email protected]] On
Behalf Of Ribbing, Jakob
Sent: Wednesday, June 17, 2009 10:43 PM
To: Ethan Wu; Jurgen Bulitta; [email protected]
Cc: Roger Jelliffe; Neely, Michael
Subject: RE: [NMusers] estimating Ka from dataset combining rich sample study
and sparse sampling study
Hi Ethan,
If OMEGA(?) for KA is drastically reduced when including the sparse data, then
something is wrong with your model and in this case it is not the estimation
method or assumption on distribution of individual parameter). Eta-shrinkage
would not drastically reduce the estimate of OMEGA, since this estimate is
driven by the subjects/studies which contain information on the parameter.
If the sparse data is multiple dosing it may be that KA is variable between
occasions, rather than between subjects (assuming the sparse data contain some
information on KA). Or if the sparse data is from a less well-controlled study
or a different population, it may be that increased IIV in other parts of the
model (e.g. OMEGA on V) is making IIV in KA appear low for the rich study, when
fitting the two studies together. If you get the covariate model in place this
problem will be solved. For the simple model you have it should be quick to
start out assuming that most parameters (THETAs and OMEGAs) are different
between the two studies and then reduce down to a model which is stable and
parsimonious. Obviously, if you eventually can explain the differences using
more mechanistic covariates than study number that is of more use.
Cheers
Jakob