# 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 -
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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Cary, NC 27511

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-----Original Message-----
From: owner-nmusers
[mailto:owner-nmusers
Sent: Thursday, June 18, 2009 2:4 AM
To: Mats Karlsson; 'Ribbing, Jakob'; '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

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:stephen.duffull

P: +64 3 479 5044

F: +64 3 479 7034

Design software: <http://www.winpopt.com> www.winpopt.com

From: owner-nmusers
On Behalf Of Mats Karlsson
Sent: Thursday, 18 June 2009 9:17 a.m.
To: 'Ribbing, Jakob'; '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

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: 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.

Cheers

Jakob

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

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