```From: "Bonate, Peter" pbonate@ilexonc.com
Subject: [NMusers] Decrease in OFV with a fixed effect
Date: Mon, August 23, 2004 9:06 am

Hi, everyone.

I am having trouble understanding how something could happen.
Perhaps I am having a brain hiccup.  I don't know.  I fit a
2-compartment model to data from 97 subjects (2 to 9 observations per
subject) using FOCE-I.  Abbreviated NONMEM code:

TVCL  = THETA(1)*(CRCL/7.2)**THETA(5)*EXP(ETA(1))
V1  = THETA(2)
Q   = THETA(3)
V2 = THETA(4)

The variance associated with V1, Q2, and V2 was small, <1E-4, and so I removed these
from the model.  The remaining variance component on CL was ~30% with 15% IOV.  Residual
error was an exponential error model (15%).  The OFV was -134.

With this class of drugs, weight has been shown to be a consistent predictor of V1.
Now in my model, V1 is a fixed effect.  Just to see what would happen I modeled V1
using the following

TVCL  = THETA(1)*(CRCL/7.2)**THETA(5)*EXP(ETA(1))
V1  = THETA(2)*(WGT/60)**THETA(6)
Q   = THETA(3)
V2 = THETA(4)

Theta(6) was 1.19 +/- 0.551.  The OFV for this model was -155, a decrease of
21 points.  Imagine my surprise.

At first I thought maybe I was at a local minima with the reduced model.  I
perturbed the estimates of the reduced model a few times but consistently obtained
-134 as the OFV.  I don't think local minima explains this.

I am having a hard time understanding this.  How can a covariate explain a fixed
effect when the effect is a constant?

Any thoughts on this would be appreciated.

As an aside, how many people reduce their base model, removing small variance
components, prior to moving on towards covariate model development?  I can see
arguments for and against both practices.  I'd be interested in hearing arguments
for and against both sides.

Thanks alot.

Pete Bonate

Peter L. Bonate, PhD, FCP
Director, Pharmacokinetics
ILEX Oncology
4545 Horizon Hill Blvd
San Antonio, TX  78229
phone: 210-949-8662
fax: 210-949-8219
email: pbonate@ilexonc.com
_______________________________________________________

From: "Leonid Gibiansky" lgibiansky@emmes.com
Subject: RE: [NMusers] Decrease in OFV with a fixed effect
Date: Mon, August 23, 2004 9:30 am

Hi Peter,
Although I do not have any good statistical explanation for this effect
I've seen it several times: covariate on fixed effect may decrease OF and
improve fit even if random effect is absent (small or does not improve the
OF).
Leonid

_______________________________________________________

From: "Xiao, Alan" alan_xiao@merck.com
Subject: RE: [NMusers] Decrease in OFV with a fixed effect
Date: Mon, August 23, 2004 10:03 am

I saw this before too. Sometime, you could estimate the random effect again.

Alan
_______________________________________________________

From: "Mats Karlsson" mats.karlsson@farmbio.uu.se
Subject: RE: [NMusers] Decrease in OFV with a fixed effect
Date: Mon, August 23, 2004 10:12 am

Hi Pete,

The fact that you get an estimate of 10-4 for V1 variance,
may be because variance is truly small (in which case adding
covariate should not improve OFV), or because it is downwards
biased due to model misspecification (e.g. through a diagonal
omega structure). In the latter case, you can well expect an
improvement in OFV if you add a true covariate (and maybe if
you add a false one too – it is difficult to know what can
happen in misspecified models).

Mats

--

Mats Karlsson, PhD
Professor of Pharmacometrics
Div. of Pharmacokinetics and Drug Therapy
Dept. of Pharmaceutical Biosciences
Faculty of Pharmacy
Uppsala University
Box 591
SE-751 24 Uppsala
Sweden
phone +46 18 471 4105
fax   +46 18 471 4003
mats.karlsson@farmbio.uu.se
_______________________________________________________

From: "Kowalski, Ken" Ken.Kowalski@pfizer.com
Subject: RE: [NMusers] Decrease in OFV with a fixed effect
Date: Mon, August 23, 2004 11:46 am

Hi Pete,

To expand on Mats' comments you should be careful not to over-interpret
a variance component that is estimated near zero to mean that there is
no interindividual variability.  It may be that there is insufficient
information in the design to accurately estimate this variance component
(I note that you indicate that for some subjects you only had 2 observations).
Also, if there is model misspecification in omega by using a diagonal omega
structure when there is a true non-zero correlation between parameters (say
CL and V) it may be that NONMEM will partition the interindividual variability
into only one of these components.  I have observed that variance components
estimated near zero (say for V) for a diagonal omega will no longer be
estimated near zero when fitting a block omega that allows for the covariance
to be estimated (say between CL and V).  Based on these observations I have
a couple of suggestions/questions:

1)  If you fit a block omega structure does NONMEM still want to estimate
the variance components for V1, Q2, and V2 near zero?

2) For the model fit you describe below with a 21 point drop in OFV did you
ee a reduction in the omega for CL relative to the estimate when you did not
include the WT effect on V1?  It may be that some of the interindividual
variability is getting partitioned into the random effect for CL due to
misspecification of omega.  If so, then I would expect that the fixed effect
for WT on V1 would to some extent reduce the omega estimate for CL.

Ken
_______________________________________________________

From: "Serge Guzy" GUZY@xoma.com
Subject: RE: [NMusers] Decrease in OFV with a fixed effect
Date: Mon, August 23, 2004 1:26 pm

May be I did not understand but if you model V1 the way you did, V1 across
individuals will be different because of their difference in weight. Your
first model will give you the same V1 for everybody. If I am right, the two
models are different.
If there is a real correlation between V1 and weight, the latter could be
bigger than the remaining random effect which then can be ignored.

Serge Guzy
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Subject: RE: [NMusers] Decrease in OFV with a fixed effect
Date: Tue, August 24, 2004 6:16 am

Pete,

I would recommend to keep all BIV-related random effects in
the model until the full covariate model is finalized.
Usually, due to practical reasons the base model (w/o covariate
effects) implements a diagonal random effect matrix. It is not
uncommon the data do not support estimation of BIV in all parameters,
however, before you build the covariate model you cannot say, which
component of the matrix is not estimable. If you drop one or more
ETAs based on the fact that the corresponding OMEGAs are negligible
in the base model you are at risk of selecting a wrong matrix for
the final model.
Best regards,

-----------------------------------------------------------------

Research Fellow, Advanced PK-PD Modeling & Simulation
Global Clinical Pharmacokinetics and Clinical Pharmacology (ext. 5463/151)
Johnson & Johnson Pharmaceutical Research & Development
Turnhoutseweg 30
B-2340 Beerse
Belgium
_______________________________________________________

From:"Vanapalli_Sreenivasa" Vanapalli_Sreenivasa@allergan.com
Subject: RE: [NMusers] Decrease in OFV with a fixed effect
Date: Tue, August 24, 2004 11:05 am

Peter,

Looks like you've fixed THETA(2), which was V1 in the first model and
your assumption of fixing V1 was right. However, you have incorporated
other variables in the equation in the second model which is 'body weight'
and also THETA(6). Now you are computing V1 based on all these parameters
not just with 'fixed THETA(2)'. I don't see V1 fixed anymore with all
these new variables into equation. With changing body weights the fit
looks much better (not fixed) resulting in decreased OBJ value.

I may be wrong with my explanation.

Regards,

Sreenivasa Rao Vanapalli, Ph.D.
Scientist, Clinical Pharmacokinetics
Allergan Inc.
2525 Dupont Drive, RD2-2B
Irvine, CA 92623-9534
E-mail: vanapalli_sreenivasa@allergan.com
Phone: (714) 246-4325
Fax: (714) 246-5538
_______________________________________________________

From: "Serge Guzy" GUZY@xoma.com
Subject: RE: [NMusers] Decrease in OFV with a fixed effect
Date: Tue, August 24, 2004 12:18 pm

You are right about V1 not being fixed and therefore you
The issue was that without covariate, V1 does not have random
effect associated with it (eta is very very small). This seems to
suggest that V1 is the same across all individual and therefore we
should not expect a correlation between weight and V1.
However, confounding factors that flip flop random effects with covariate
effect is not uncommon. When there are no covariate, most of the interindividual
variability can be found in some of the parameters and not in V1(may be by
chance only). When assuming a correlation (without random effect), a flip flop
between 2 different effects occur. I am pretty sure that at least one random
effect from all other parameters (except V1) is different in the covariate
model and the one without covariate.

Serge Guzy
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