From: Paul Hutson prhutson@pharmacy.wisc.edu
Subject: [NMusers] Incorporating duplicate assays
Date: Wed, 16 Nov 2005 12:04:28 -0600

Am I correct in including all assay results in my data set when I
have duplicate or triplicate analyses of a sample so that the assay
variability can be incorporated into the residual error?  It seemed
logical to do so, but I could not find anything in the Archives or
the easily searched Users Manual to support this.
Thanks in advance
Paul

-- 

Paul R. Hutson, Pharm.D.

Associate Professor

UW School of Pharmacy

777 Highland Avenue

Madison WI 53705-2222

Tel  608.263.2496

Fax 608.265.5421

Pager 608.265.7000, p7856 

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From: "Mats Karlsson" mats.karlsson@farmbio.uu.se
Subject: RE: [NMusers] Incorporating duplicate assays
Date: Wed, 16 Nov 2005 20:59:58 +0100

Hi Paul,

It is best done by using the L2 data item. We illustrated how that could be
done in


Karlsson
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=8733951&query_hl=2  MO, Beal SL, Sheiner LB.
 

Three new residual error models for population PK/PD analyses.
J Pharmacokinet Biopharm. 1995 Dec;23(6):651-72.
 

Best regards,

Mats

--

Mats Karlsson, PhD

Professor of Pharmacometrics

Div. of Pharmacokinetics and Drug Therapy

Dept. of Pharmaceutical Biosciences

Faculty of Pharmacy

Uppsala University

Box 591

SE-751 24 Uppsala

Sweden

phone +46 18 471 4105

fax   +46 18 471 4003

mats.karlsson@farmbio.uu.se

 
_______________________________________________________

From: "Piotrovskij, Vladimir [PRDBE]" VPIOTROV@PRDBE.jnj.com
Subject: RE: [NMusers] Incorporating duplicate assays
Date: Wed, 16 Nov 2005 21:09:29 +0100

Paul,
 
Besides the assay variability the residual error includes imprecision in
dosing and sampling times, and model misspecification error. If you use raw
data with multiple measurements per time point you have to modify the
residual error structure. The concept of nested random effects may suite.
Below is an example of the $ERROR block that you can try: 
 
; REPEATED OBS
 OBS1 = 0
 OBS2 = 0
 OBS3 = 0
  IF(OBSN.EQ.1) OBS1=1
  IF(OBSN.EQ.2) OBS2=1
  IF(OBSN.EQ.3) OBS3=1
 ASSERR = OBS1*ERR(1) + OBS2*ERR(2) + OBS3*ERR(3)
 Y = F * (1 + ASSERR + ERR(4))
.....
 
$SIGMA BLOCK(1) .1
$SIGMA BLOCK(1) SAME
$SIGMA BLOCK(1) SAME
$SIGMA .2

Best regards, 
Vladimir 

----------------------------------------------------------------- 

Vladimir Piotrovsky, Ph.D. 
Research Fellow, Advanced PK-PD Modeling & Simulation 
Clinical Pharmacology and Experimental Medicine
Johnson & Johnson Pharmaceutical Research & Development 
B-2340 Beerse 
Belgium 

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From: Leonid Gibiansky leonidg@metrumrg.com
Subject: Re: [NMusers] Incorporating duplicate assays
Date: Wed, 16 Nov 2005 15:25:21 -0500

Hi Paul,
Technically, this is correct. I had duplicate measurements in some of the NONMEM
runs, and there were no complaints from the program concerning the duplicate times.
For the actual data set, residual error consists of the assay error + unexplained
error. I think that the second component is usually larger. Repeated measurements
at the same point cannot help with that part. If you have the same number of
measurement for the majority of points, you can average before running the model
(thus creating the new more precise and less variable assay as an average of x
number of measurements at each point).
Thanks
Leonid 
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From: "Hutmacher, Matt" Matt.Hutmacher@pfizer.com
Subject: RE: [NMusers] Incorporating duplicate assays
Date: Wed, 16 Nov 2005 15:33:57 -0500

Paul and Vladimir,
 
Adding in misspecification is a good point to consider.  Also, it should be
noted that if the re-assay comes from the same sample, the experimental unit
becomes the blood draw - potentially inducing correlation between these
observations (similar to parent-metabolite correlation).  Thus, the L2 data
item and a $SIGMA block could be evaluated.
 
Matt  

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From: "Piotrovskij, Vladimir [PRDBE]" VPIOTROV@PRDBE.jnj.com
Subject: RE: [NMusers] Incorporating duplicate assays
Date: Fri, 18 Nov 2005 10:14:28 +0100

Matt,
 
I don't think there is any correlation in the case of duplicated assays. In
the model Yijk = Fij * (1 + ETAij + ETAijk) higher ETAij is not necessarily
accociated with systematically higher (or lower) ETAijk. I do not see any
reason of using L2 data item. The situation is completely different compared
to the parent-metabolite correlation you mention. There are here 2 analytes.
BTW, an example of using L2 presented in the NONMEM user guide V includes
simultaneous analysis of PK and PD data; it is also an example of 2 types of
observations that may indeed correlate.
 
Best regards, 
Vladimir 

_______________________________________________________

From: "Mats Karlsson" mats.karlsson@farmbio.uu.se
Subject: RE: [NMusers] Incorporating duplicate assays
Date: Fri, 18 Nov 2005 11:05:49 +0100

Hi Vladimir,
 
The L2 data item is necessary as the duplicates will share a common residual
error (due to error in dosing history, sampling time, model misspecification
etc). The only way to have two observations share an EPS is by using the L2
data item. There is however no need to estimate off-diagonal elements of the
SIGMA matrix.
 
Best regards,
Mats
 

--

Mats Karlsson, PhD

Professor of Pharmacometrics

Div. of Pharmacokinetics and Drug Therapy

Dept. of Pharmaceutical Biosciences

Faculty of Pharmacy

Uppsala University

Box 591

SE-751 24 Uppsala

Sweden

phone +46 18 471 4105

fax   +46 18 471 4003

mats.karlsson@farmbio.uu.se
_______________________________________________________

From: "Hutmacher, Matt" Matt.Hutmacher@pfizer.com
Subject: RE: [NMusers] Incorporating duplicate assays
Date: Mon, 21 Nov 2005 12:40:45 -0500

Hello,
 
Vladimir, let me be more specific about my response.  As per your formulation below, let
Yijk=Fij+EPS1ij+EPS2ijk and Var(EPS1ij)=s12, Var(EPS2ijk)=s22, where all the EPS are independent. 
Let Rijk=Yijk-Fij.  For two replicates (i.e. k=1,2 for simplicity), the correlation of Rij1 and
Rij2 is s12/(s12+s22) for this model, with a variance-covariance matrix (lower triangle),
[s12+s22,s12,s12+s22]. So, even though the EPS are independent, the Rijk's are not.  My indication
that this is similar to a parent-metabolite correlation stems from the implication that the assay
results all stem from one blood sample, which is the experimental unit for the replicate (analogous
in some sense to a patient being the experimental unit for single blood samples). The variance
structure (compound symmetric) in the case above is a special case of a more general $SIGMA block
in which the variances can be different and the correlation is not tied to the variances. The
formulation in Mats' paper is a very parsimonious model (and very cleverly developed given the
coding in NONMEM which would be necessary for similar variances parameters with a general covariance),
which might be very appropriate for PK replicates.  This structure might not be appropriate for QT
sampling replicates (temporally ordered) and could be tested relative to a general structure.
 
Matt  
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