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RE: BSV and BOV interaction

From: Ribbing, Jakob <Jakob.Ribbing>
Date: Mon, 21 Dec 2009 09:21:35 -0000

Andreas,

The code snippet you picked out is not overparameterized, since the
assumption is made that the variance of eta 5 and 6 are the same:

  $OMEGA BLOCK(1) 0.05
  $OMEGA BLOCK(1) SAME

This first equation that you suggest is this:
  IOV2=0
  IF (DESC.EQ.2) IOV2=1
  ETCL = ETA(1)+IOV2*ETA(5)
As you note the equation you suggest implies that the between-subject
variability in CL will be larger for the first occasion than the second.
Unless inclusion criteria resulted in weird data that forced me to make
that assumption I would not feel comfortable using this
parameterisation. Also I do not fully understand this "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." Both eta 1
and eta 5 may be negative and positive, so if you are hoping for only
positive eta5 values it seems something is wrong with the structural
model. Or did you mean that you hope the variance of eta5 is positive
(ie. OMEGA(5,5))?

Finally, I also have my doubts about your last suggestion regarding how
to combine eta 1 and 5: "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." How would you interpret that model?
Subjects that have abnormally high CL at occasion 1 are likely to have
either abnormally high, or abnormally low CL at occasion 2. I think
simulations would give you patterns you do not see in real life with
such assumptions. Also, if data supports such a model, it may be more a
reflection of the error model. If some subjects have more error in their
observations a simple eta on epsilon may be more appropriate.

I hope everyone will have a nice break, both from nmusers and from work!
Best regards

Jakob

-----Original Message-----
From: owner-nmusers
On Behalf Of andreas.krause
Sent: 21 December 2009 08:18
To: Jia Ji
Cc: nmusers
Subject: Re: [NMusers] BSV and BOV interaction

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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Received on Mon Dec 21 2009 - 04:21:35 EST

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