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RE: time-dependent residual error models

From: Chan, Phylinda <Phylinda.Chan>
Date: Fri, 25 Sep 2009 11:08:04 +0100

Hi Nick,

Being a substrate of P-gp and CYP3A4, the compound itself has a very
complex absorption profile including dose non-linearity, double peaks,
food effects as well as high between individual and within individual
variability. Barry Weatherley has spent a substantial amount of time
and effort in understanding the dose non-linearity and some covariate
effects on the PK of this compound, including development of a very
complex flexible input model which was presented at PKUK in 2004. More
details of some of this modelling work can be found in a recent
publication.

http://www3.interscience.wiley.com/journal/122386172/abstract


The main objective of the meta-analysis was to develop a compartmental
model which would be useful in identifying significant covariates
explaining inter-individual variability and was simple enough to be used
in the later modelling of sparsely sampled PK in phase 2b/3 studies
where a full time profile and samples were likely to be clustered in the
elimination phase of the PK. We felt the first-order input with dose
and food effects on Ka in addition to the time-dependent residual error
model was adequate for this purpose.


For those who interested in the coding of the time-dependent residual
error model:
$ERROR
IPRED = F+.00001
LPRED = 0
IF(IPRED.GT.0) LPRED = LOG(IPRED)

PMAX=THETA(7)
TMAX=THETA(8)
K=THETA(9)
BASE=THETA(10)

P=K*TMAX
A=EXP(P)/TMAX**P

W= PMAX*A*(TAD+.01)**P*EXP(-K*(TAD+.01))+BASE
IRES= DV-LPRED
IWRES= IRES/W
Y= LPRED+EPS(1) * W

Note:
i) $SIGMA (1 FIX)
ii) TAD=time after dose

Phylinda.


-----Original Message-----
From: owner-nmusers
On Behalf Of Nick Holford
Sent: 24 September 2009 08:42
To: nmusers
Subject: Re: [NMusers] time-dependent residual error models

Mats,

I agree with your general idea but in this particular case there is no
description in the paper of efforts made to test structural models for
absorption apart from first order input with dose and food effects on
Ka. There seems to be quite a lot of time related structure in the
residual error model function that Phylinda reported and I would have
thought that at least some of this could have been explored via another
structural model e.g. involving parallel or sequential zero-order
inputs. It struck me as a rather unusual approach and I wondered what
the reasons for it were.

It does not really bother me which approach is used when describing
absorption (fancy structure+vanilla residual or vanilla structure+fancy
residual) because the details of the rate of absorption rarely have any
clinical relevance (Justin Wilkins may want to disagree <grin>). Of
course, as you point out the errors may often arise from poorly
reproducible fixed effects such as timing errors etc. and thus the goal
may be to describe the error adequately and not the structure because
the structure is not really fixed or of any interest.

Nick


Mats Karlsson wrote:
> Hi Nick,
>
> I can't answer for Phylinda, but the general idea is to build the most
> appropriate structural model that is supported by data. However, after
that
> is done, if there still is variation in residual error magnitude one
should
> take that into account and not ignore it. All models are wrong, and I
would
> say that in general our models for absorption are more wrong than our
models
> for disposition. That is not just because we have focused more on the
> latter, but because the underlying processes governing absorption are
of a
> different nature (e.g. with discrete events like food intake, gastric
> emptying, bile release and formulation disintegration and movement).
Further
> often part of the error magnitude is from timing errors. Such errors
are
> more pronounced when concentrations are changing fast (normally
fastest
> changes in absorption phase). We wrote on time-varying residual errors
(and
> alternatives such as residual error magnitude related to rate of
change) in
> these publications:
> J Pharmacokinet Biopharm. 1995 Dec;23(6):651-72.
> J Pharmacokinet Biopharm. 1998 Apr;26(2):207-46
>
> 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
>
>
> -----Original Message-----
> From: owner-nmusers
[mailto:owner-nmusers
> Behalf Of Nick Holford
> Sent: Thursday, September 24, 2009 7:46 AM
> To: nmusers
> Subject: Re: [NMusers] time-dependent residual error models
>
> Hi,
>
> If Phylinda reads this I'd be interested to hear why she choose to use
a
> plain vanilla first-order absorption model and a fancy time-dependent
> residual error model rather than trying to model a fancy absorption
> process with a plain vanilla residual error model?
>
> Nick
>
> Joseph Standing wrote:
>
>> Xiang,
>>
>>
>>
>> There is a rather elegant time-dependent residual error model
>> described by Phylinda Chan et al in:
>>
>> BJCP, 2008;65(S1):76-85.
>>
>>
>>
>> BW,
>>
>> Joe
>>
>>
>
>

--
Nick Holford, Professor Clinical Pharmacology
Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New
Zealand
n.holford
mobile: +64 21 46 23 53
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
Received on Fri Sep 25 2009 - 06:08:04 EDT

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