From: "Robert L. James" rjames@rhoworld.com
Subject: [NMusers] How sparse is too sparse? 
Date: Thu, June 10, 2004 2:26 pm

Dear group,

I am a NONMEM user with some modeling experience (perhaps 8 PK publications
mostly 2-cpt models with time varying covariates). 

 A Pharm company has just approached me to do a simple PK analysis (Cmax,
Tmax, half-life, and AUC) on some VERY sparse data.  Although there are 150
patients, each patient has only one plasma conc sample following an oral
dose on two separate occasions spaced 2 weeks apart (the expected half life
of the drug is a few hours).  The timing of the single plasma sample
following the oral dose was appears to be randomly timed.  I don't have the
data and so I don't know how well spaced these single samples are.  Is this
hopeless?  The data has already been 80% collected.  There are no previous
human PK studies.  

The only plan of action I can think of is to pool the data across patients
and fit a simple one-compartment model with either zero- or first-order
absorption following an absorption lag.  I could also model interoccasion
variabilility into the model.  Has anyone tried to fit models to data this
sparse (1 sample following each of two dosing occasions).  Would I be just
spinning my electrons to accept this assignment?  

---Robert
Robert L. James, M.S., M.Stat.
Senior Biostatistician
Rho, Inc.
100 Eastowne Drive
Chapel Hill, NC 27514

(919) 408-8000 x 468
(919) 408-0999 (fax)

rjames@rhoworld.com

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From: Leonid Gibiansky lgibiansky@emmes.com
Subject: RE:[NMusers] How sparse is too sparse?
Date: Thu, June 10, 2004 2:58 pm

I think population PK would be more appropriate than pooling the data (If 
by pooling you mean just fitting all of them to one curve). I do not think 
that you will be able to estimate inter-occasion variability, I would 
ignore it. Two samples per person is not a lot, so you won't be able to 
investigate the model in details, but I would try it, population PK has 
more chances of success in this case than anything else.
Leonid
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From: fengyan yaf2+@pitt.edu
Subject: RE:[NMusers] How sparse is too sparse?
Date: Thu, June 10, 2004 3:39 pm

Population method should be better than pooling the data. Also for Pop PK, 
I doubt how precise you can estimate your parameters, because generally you 
need 1 sample /subject /parameter. So if you only have one sample per 
subject, then it will be hard to estimate every parameter, unless you fix 
some based on literature report and estimate part of parameter.

Yan Feng
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From: Nick Holford n.holford@auckland.ac.nz
Subject: RE:[NMusers] How sparse is too sparse? 
Date: Thu, June 10, 2004 3:46 pm

Robert,

Its unlikely you will be able to estimate much more than CL/F (and thus AUC if you
want) from this kind of data. This is especially so if you only have trough samples.
I cannot imagine that you would be able to estimate a lag time. At best you might be
able to get CL/F, V/F and Ka.

Perhaps this Pharm company would be better off Farming. 

Nick
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/
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From: "Kowalski, Ken" Ken.Kowalski@pfizer.com
Subject: RE: [NMusers] How sparse is too sparse? 
Date: Thu, June 10, 2004 3:51 pm

Robert,

As Leonid indicates, you won't be able to partition out inter-occasion
variability with only 1 sample per occasion per subject.  I agree with
Leonid that you should analyze it using a pop PK model rather than to
perform naive pooling.  Also, you should point out the limitations of the
design and clarify expectations with regards to estimating Tmax, Cmax, t1/2,
and AUC.  With such sparse sampling and depending on the timing of the
samples I suspect that you will get a lot of shrinkage (bias towards the
mean) in the empirical Bayes predictions for some of these parameters.  At
best you might be able to get a good population estimate of CL/F and its IIV
from which you can provide information on AUC.  Depending on the timing and
underlying true model (e.g., 2-comp vs 1-comp) your sparse design may not
provide reliable estimates of Tmax, Cmax and t1/2.

Ken

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From: "Serge Guzy" GUZY@xoma.com
Subject: RE:[NMusers] How sparse is too sparse?
Date: Thu, June 10, 2004 5:09 pm

Apparently, you will not be able to separate intra-individual
variability(I mean epsilon) from inter-individual variability(omega).
Therefore you will have to assume a fixed, known cste cv error (or any
other error model).
Serge Guzy;
PH.D
President POP-PHARM
Head Pharmacometrics and Preclinical Statistics;
Xoma
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From:"Serge Guzy" GUZY@xoma.com
Subject: RE:[NMusers] How sparse is too sparse? 
Date: Thu, June 10, 2004 5:29 pm 

I do not agree. (in reference to Yan Feng message, Date: Thu, June 10, 2004 3:39 pm [above])
If the sampling times are distributed in a clever fashion (usually log
uniform distributed is a good sampling), then population PK has the
ability to estimate all the parameters if you have enough patients. The
MCPEM algorithm (algorithm optimizing the same fct as FOCE with
interaction)has been tested on many models with more than 1 PK
parameters with 1 sample per patient and there were no problems as long
as the information was there. The only confounding factor I am pretty
sure is always present is the intra-individual variability confounded
with the inter-individual variability.
Serge Guzy
President POP-PHARM
Head Pharmacometrics and Preclinical Statistics;XOMA
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From: "Kowalski, Ken" Ken.Kowalski@pfizer.com
Subject: RE:[NMusers] How sparse is too sparse?
Date: Fri, June 11, 2004 8:10 am

Serge,

I can certainly understand that Robert won't be able to separate out
intra-individual variability in the PK parameters  with only 1 obs/visit
(i.e., inter-occasion or between-visit variability within a subject).  But
he should be able to separate out intra-individual variability in the
response (i.e., measurement variability or sigma^2) from the
inter-individual variability in the PK parameters since he is getting two
measurements on each individual (one measurement on each of two visits).  Of
course if there is true inter-occasion variability it will be confounded
with other sources and most likely will inflate the intra-individual
variability in the measured response (sigma^2).

Ken
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