NONMEM Users Network Archive

Hosted by Cognigen

RE: BSV and BOV interaction

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


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

This first equation that you suggest is this:
  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


-----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


you are overparameterized. Take this snippet from your code:

  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

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

Thus, ETA(1) estimates your random effect variation for the case
and ETA(1) + ETA(5) is the random effect variation for the case
ETA(5) is thus the additional random effect variation for the second
compared to the first.
Watch out that this implies that the random effect variation is larger
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

Why do you see the need to link the two? Why don't you define

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


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


[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
ETAs are around 40% or less. The code is as below:
  IF (TIME.GE.100) DESC=2
  IF (DESC.EQ.1) IOV1=ETA(2)
  IF (DESC.EQ.2) IOV1=ETA(3)
  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)

;OMEGA initial estimates
  $OMEGA 0.0529
  $OMEGA BLOCK(1) 0.05
  $OMEGA 0.318
  $OMEGA BLOCK(1) 0.05
  $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
same thing happened to BSV and BOV of Q. Worrying about
over-parameterization (I am not NONMEM 7 user), I tried to define a
for this correlation as the code below (just test on CL only first):
  IF (TIME.GE.100) DESC=2
  ETCL = ETA(1)+IOV1
  ETQ = ETA(2)
  ETV2 = ETA(3)

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

;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,
not working when putting SAME here
  $OMEGA 0.318
  $OMEGA 0.711
This time I got significantly decreased objective function value,
with the model not having IOV. But, SE of ETA(1), ETA(2) and ETA(3) are
All together, does it mean that there is no need to have BOV on CL and
Or I don't get the right solution to solve correlation problem? Any
suggestion is highly appreciated! Thank you so much!
Happy Holidays!

The information of this email and in any file transmitted with it is
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
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
Received on Mon Dec 21 2009 - 04:21:35 EST

The NONMEM Users Network is maintained by ICON plc. Requests to subscribe to the network should be sent to:

Once subscribed, you may contribute to the discussion by emailing: