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RE: estimating Ka from dataset combining rich sample study and sparse sampling study

From: Bob Leary <bleary>
Date: Fri, 19 Jun 2009 16:08:00 -0400

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 = =
(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

Pharsight - A Certara(tm) Company
5625 Dillard Dr., Suite 205
Cary, NC 27511

Phone/Voice Mail: (919) 852-4625, Fax: (919) 859-6871
Email: bleary

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-----Original Message-----
From: owner-nmusers
Sent: Thursday, June 18, 2009 2:4 AM
To: Mats Karlsson; 'Ribbing, Jakob'; 'Ethan Wu'; 'Jurgen Bulitta'; =
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




Professor Stephen Duffull

Chair of Clinical Pharmacy

School of Pharmacy

University of Otago

PO Box 913 Dunedin

New Zealand

E: <mailto:stephen.duffull

P: +64 3 479 5044

F: +64 3 479 7034


Design software: <>







From: owner-nmusers
On Behalf Of Mats Karlsson
Sent: Thursday, 18 June 2009 9:17 a.m.
To: 'Ribbing, Jakob'; 'Ethan Wu'; 'Jurgen Bulitta'; =
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 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: owner-nmusers
On Behalf Of Ribbing, Jakob
Sent: Wednesday, June 17, 2009 10:43 PM
To: Ethan Wu; Jurgen Bulitta; nmusers
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.







Received on Fri Jun 19 2009 - 16:08:00 EDT

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