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RE: BSV and BOV interaction

From: Mats Karlsson <mats.karlsson>
Date: Mon, 21 Dec 2009 11:31:26 +0100

Jia,

I don't see any indication that your first model is problematic. A strong
correlation between BSV and BOV ETA for CL is to be expected when you have
shrinkage in your individual etas (see e.g. Savic & Karlsson AAPS J. 2009
Sep;11(3):558-69). This does not mean that the population model should
include such a correlation. If shrinkage is high (>20% or so) I would tend
to use simulation-based or CWRES based diagnostics instead of posthoc eta's.

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
Behalf Of andreas.krause
Sent: Monday, December 21, 2009 10:41 AM
To: Nick Holford
Cc: nmusers
Subject: Re: [NMusers] BSV and BOV interaction

Nick,

overparameterization refers to the parameters, the variances play only an
indirect role. Putting the SAME constraint on the covariance thus
restricts the set of random effects but not necessarily the set of random
effects for, say, subject i.
The SAME option thus might keep the estimation process a bit more under
control but I still think there is an overparameterization problem for
each individual subject.

It should be interesting to take out those ETA values containing the SAME
lines by specifying 0.0 FIX instead of SAME and comparing the results.

        Andreas


PS. Shouldn't we all be off for some holidays?





Nick Holford <n.holford
Sent by: owner-nmusers
12/21/2009 09:52 AM

To
nmusers <nmusers
cc

Subject
Re: [NMusers] BSV and BOV interaction






Andreas,

The code is not overparameterized because the SAME option is used for the
OMEGA block defining ETA(6). This means that there is only one parameter
being estimated for the variance of the distribution from which ETA(5) and
ETA(6) are sampled i.e. ETA(5) and ETA(6) come from an eta distribution
with the SAME variance.

Best wishes,

Nick

andreas.krause
Jia,

you are overparameterized. Take this snippet from your code:

  IOV2=0
  IF (DESC.EQ.1) IOV2=ETA(5)
  IF (DESC.EQ.2) IOV2=ETA(6)

  ETCL = ETA(1)+IOV1

Now consider the two possibilites:
a) DESC.EQ.1: ETCL = ETA(1) + ETA(5)
b) DESC.EQ2.2: ETCL = ETA(1) + ETA(6)

In other words, you have two equations to identify 3 parameters.
Usually you associate the "base" random effect with one case and add a
deviation parameter to the other case.
An example would be

  IOV2=0
  IF (DESC.EQ.2) IOV2=1
  ETCL = ETA(1)+IOV2*ETA(5)

Thus, ETA(1) estimates your random effect variation for the case DESC.EQ.1

and ETA(1) + ETA(5) is the random effect variation for the case DESC.EQ.2.
ETA(5) is thus the additional random effect variation for the second case
compared to the first.
Watch out that this implies that the random effect variation is larger for

DESC.EQ.2 than for DESC.EQ.1 since ETA(5) is (hopefully) not negative.
You could multiply the two to allow for the variation being smaller or
larger in the latter case but multiplication makes the estimation more
unstable.

Why do you see the need to link the two? Why don't you define
IF(DESC.EQ.1) ETCL=ETA(5)
IF(DESC.EQ.2) ETCL=ETA(6)
CL=THETA(1)*EXP(ETCL)

and get rid of ETA(1)? That decouples the two estimates entirely.

        Andreas







Jia Ji <jackie.j.ji
Sent by: owner-nmusers
12/19/2009 12:32 AM

To
nmusers
cc

Subject
[NMusers] BSV and BOV interaction






Dear All,
 
I am trying to model our data with a two-compartment model now. In our
trial, some patients received escalated dose at the second cycle so they
have one more set of kinetics data. So there were BSV and BOV on PK
parameters in the model. Objective function value is
significantly improved (compared with the model not having BOV) and SE of
ETAs are around 40% or less. The code is as below:
 
$PK
  DESC=1
  IF (TIME.GE.100) DESC=2
  IOV1=0
  IF (DESC.EQ.1) IOV1=ETA(2)
  IF (DESC.EQ.2) IOV1=ETA(3)
 
  IOV2=0
  IF (DESC.EQ.1) IOV2=ETA(5)
  IF (DESC.EQ.2) IOV2=ETA(6)

  ETCL = ETA(1)+IOV1
  ETQ = ETA(4)+IOV2
  ETV2 = ETA(7)

  CL=THETA(1)*EXP(ETCL)
  V1=THETA(2)
  Q=THETA(3)*EXP(ETQ)
  V2=THETA(4)*EXP(ETV2)
 
;OMEGA initial estimates
  $OMEGA 0.0529
  $OMEGA BLOCK(1) 0.05
  $OMEGA BLOCK(1) SAME
  $OMEGA 0.318
  $OMEGA BLOCK(1) 0.05
  $OMEGA BLOCK(1) SAME
  $OMEGA 0.711
 
When I looked at scatterplot of ETA, I found that there is strong
correlation between ETA(1) and ETA(2), which is BSV and BOV of CL. And the

same thing happened to BSV and BOV of Q. Worrying about
over-parameterization (I am not NONMEM 7 user), I tried to define a THETA
for this correlation as the code below (just test on CL only first):
 
$PK
  DESC=1
  IF (TIME.GE.100) DESC=2
  IOV1=0
  IF (DESC.EQ.1) IOV1=THETA(1)*ETA(1)
  IF (DESC.EQ.2) IOV1=THETA(1)*ETA(1)
 
  ETCL = ETA(1)+IOV1
  ETQ = ETA(2)
  ETV2 = ETA(3)

  CL=THETA(2)*EXP(ETCL)
  V1=THETA(3)
  Q=THETA(4)*EXP(ETQ)
  V2=THETA(5)*EXP(ETV2)
 
The objective function value is exactly the same as the model not having
IOV. BSV of CL is decreased and SE of THETAs are also improved,
though. The same thing happend to Q when tested individually. Then I tried

another way to account for this correlation:
 
$PK
  DESC=1
  IF (TIME.GE.100) DESC=2
  IOV1=0
  IF (DESC.EQ.1) IOV1=ETA(2)
  IF (DESC.EQ.2) IOV1=ETA(3)
 
  ETCL = ETA(1)+IOV1
  ETQ = ETA(4)
  ETV2 = ETA(5)

  CL=THETA(1)*EXP(ETCL)
  V1=THETA(2)
  Q=THETA(3)*EXP(ETQ)
  V2=THETA(4)*EXP(ETV2)
 
;OMEGA initial estimates
  $OMEGA BLOCK(2) 0.0529 0.01 0.05
  $OMEGA BLOCK(1) 0.05 ;BTW, I don't know how to do SAME here, it's

not working when putting SAME here
  $OMEGA 0.318
  $OMEGA 0.711
 
This time I got significantly decreased objective function value, compared

with the model not having IOV. But, SE of ETA(1), ETA(2) and ETA(3) are
huge!
 
All together, does it mean that there is no need to have BOV on CL and Q?
Or I don't get the right solution to solve correlation problem? Any
suggestion is highly appreciated! Thank you so much!
 
Happy Holidays!
 
Jia



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--
Nick Holford, Professor Clinical Pharmacology
Dept Pharmacology & Clinical Pharmacology
University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand
tel:+64(9)923-6730 fax:+64(9)373-7090 mobile:+64(21)46 23 53
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strictly confidential and may be legally privileged.
It is intended solely for the addressee. If you are not the intended
recipient, any copying, distribution or any other use of this email is
prohibited and may be unlawful. In such case, you should please notify the
sender immediately and destroy this email.
The content of this email is not legally binding unless confirmed by letter.
Any views expressed in this message are those of the individual sender,
except where the message states otherwise and the sender is authorised to
state them to be the views of the sender's company. For further information
about Actelion please see our website at http://www.actelion.com
Received on Mon Dec 21 2009 - 05:31:26 EST

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