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RE: Splitting the residual error

From: Mats Karlsson <Mats.Karlsson>
Date: Fri, 13 May 2016 10:37:01 +0000

Dear Jon,

As you point out the concept of residual error magnitude being dependent on=
 anything else than the prediction itself is a straightforward. Yet it is, =
I think underused and that is why you may not see it much in the literature=
. In addition to what you mention, a large component is that model misspeci=
fication is not a homogeneous process. It is likely that most of our models=
 are more specified for absorption than disposition. Absorption contains ma=
ny processes that are discrete and difficult to easily capture in simple mo=
For most compunds, the absolute gradient is much higher during the absorpti=
on phase than the distribution phase and that is probably a contributing fa=
ctor to what experience. You would probably get as good an improvement if y=
ou had a separate error magnitude during the absorption phase.

The model you mentioned with were outlined in the 1998 article below. I als=
o add some other articles for the case you're further interested in residua=
l error modeling.

Best regards,


A strategy for residual error modeling incorporating scedasticity of varian=
ce and distribution shape.<>

Dosne AG, Bergstrand M, Karlsson MO.

J Pharmacokinet Pharmacodyn. 2016 Apr;43(2):137-51. doi: 10.1007/s10928-015=
-9460-y. Epub 2015 Dec 17.

PMID: 26679003 [PubMed - in process] Free PMC Article

Similar articles<


The impact of misspecification of residual error or correlation structure o=
n the type I error rate for covariate inclusion.<http://www.ncbi.nlm.nih.go=

Silber HE, Kjellsson MC, Karlsson MO.

J Pharmacokinet Pharmacodyn. 2009 Feb;36(1):81-99. doi: 10.1007/s10928-009-=
9112-1. Epub 2009 Feb 14.

PMID: 19219538 [PubMed - indexed for MEDLINE]

Similar articles<


Three new residual error models for population PK/PD analyses.<http://www.n=>

Karlsson MO, Beal SL, Sheiner LB.

J Pharmacokinet Biopharm. 1995 Dec;23(6):651-72.

PMID: 8733951 [PubMed - indexed for MEDLINE]

Similar articles<


Assumption testing in population pharmacokinetic models: illustrated with a=
n analysis of moxonidine data from congestive heart failure patients.<http:=

Karlsson MO, Jonsson EN, Wiltse CG, Wade JR.

J Pharmacokinet Biopharm. 1998 Apr;26(2):207-46.



Mats Karlsson, PhD
Professor of Pharmacometrics

Dept of Pharmaceutical Biosciences
Faculty of Pharmacy
Uppsala University
Box 591
75124 Uppsala

Phone: +46 18 4714105
Fax + 46 18 4714003<http://www.farmb=>

From: owner-nmusers
 Behalf Of Jonathan Moss
Sent: Friday, May 13, 2016 11:37 AM
To: nmusers
Subject: [NMusers] Splitting the residual error

Dear all,

I would like to share with you and get people's opinions on a recent issue =
I had.
I have a data set of 46 patients, orally dosed, with very dense sampling du=
ring absorption (0.25h, 0.5h, 0.75h, 1h, 1.5h, 2h, 3h, 4h, 6h, 8h, 12h, 24h=
, 36h), Cmax at around 4 hours.
During modelling, I found that the residual error was not evenly distribute=
d. Plotting CWRES against time after dose, the result looked like an "hourg=
lass" shape. I.e. A wide spread during absorption, narrower near Cmax time,=
 then wider at later time points.
My thinking was as follows: Residual error contains both the assay / model =
spec. error, and the error in recorded observation time. When the gradient =
of the PK curve is large, any error in recorded observation time equals a l=
arge error in the recorded concentration, whereas if the gradient is small =
then the recorded concentration error will be small.
I "split" the residual error into its assay/model spec and time-error parts=
 in the $ERROR block:

GRAD = KA*A(2) - K20*A(3)


C_1 = A(3)/V ; Concentration in the =
central compartment
SD = SQRT(EPROP*C_1**2) ; Standard deviation of=
 predicted concentration


Note: Sigma is fixed to one and EPROP is estimated as a theta. Here, GRAD i=
s the right hand side of the differential equation for A(3), in order to re=
cover the gradient. Val is estimated by NONMEM.

This approach vastly improved the model fit (OFV drop of around 350!). All =
GOF plots, VPCs, NPCs, NPDEs, individual fits looked good. This got me thin=
king, and I tried this approach on some of my other popPK models. I found f=
or the simpler models, the result was nearly always a significant improveme=
nt in the model fit. For the more complicated models, NONMEM had trouble fi=
nishing the runs.

I struggled to find any approach like this in the literature, which leads m=
e to believe that there is something wrong, as it is a relatively simple co=
ncept. Please, what are peoples thoughts on this?


Jon Moss, PhD
BAST Inc Limited
Loughborough Innovation Centre
Charnwood Wing
Holywell Park
Ashby Road
Loughborough, LE11 3AQ, UK
Tel: +44 (0)1509 222908

Received on Fri May 13 2016 - 06:37:01 EDT

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