I am not sure that you need likelihood profiling or any other
sophisticated procedures to study this particular problem. You can look
at relative standard errors of the parameter estimates: if one of the
ETAs is poorly estimated, this is the candidate for removal. For
two-compartment models, it is rarely possible to estimate ETAs on
peripheral compartment, and at least one of those can be removed (usually).
If the goal is to describe the data, you look for the simplest model
that allow you to fit the data. You may start with the model with all
random effects, but then try to reduce the number of random effect
(unless you use new IMP/SAEM/BAYES type procedures) to arrive at the
simpler model. You may use OF as a guide: if OF drop is small when you
remove the ETA, this ETA does not contribute to the fit (and the model
can equally well fit the data without this particular ETA). Alternative
procedure is to compare full (with ETAs) and reduced (with one ETA fixed
to zero) model using various diagnostic plots procedure (VPC in
particular), or plots of one model versus the other model: PRED vs PRED
and IPRED vs IPRED (where PRED and IPRED belog to two models that you
are comparing). If these plots looks like identity lines (both in normal
and log axes), you can safely use simpler model, especially if VPC
results are similar or identical.
As to the specific procedure that allowed you to fix the strange OF
behavior, even the simple problems (like two-compartment model that was
used) are highly nonlinear, and gradient methods cannot guarantee the
global minimum. The solution (local minimum) may depend on initial
conditions. By starting from the solution of the reduced problem, you
put the model in the vicinity of the correct local minimum, while when
you started from the larger model, it converged to the different
minimum. This is not a universal procedure, but it helps time to time if
the model has difficulties finding the solution.
Regards,
Leonid
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566
On 8/26/2013 9:58 AM, Denney, William S. wrote:
Hi Xinting,
This is a rather broad (and often highly-opinionated) topic. At the
highest level, you can only fit parameters in a model where you have
enough data to estimate the parameter. A simple example is that if you
have data that you want to fit an Emax model to with measurements only
up to the EC10, you don’t have enough data to estimate Emax and ED50; it
will look fully linear.
Due to data variability and the fact that Q and V3 are less correlated
with the measurements than other parameters (Ka, V2, and CL have a
stronger effect on the measurements than Q and V3), the estimates will
be more difficult. A good example of how to evaluate this would be what
Peter Bonate just suggested: do likelihood profiling on each of the
parameters (especially the ETAs) to estimate the certainty (peakedness)
or uncertainty (flatness) in the parameter estimates.
Thanks,
Bill
*From:*Xinting Wang [mailto:wxinting1...@gmail.com]
*Sent:* Monday, August 26, 2013 9:27 AM
*To:* Leonid Gibiansky
*Cc:* nmusers@globomaxnm.com; Denney, William S.
*Subject:* Re: [NMusers] Reducing ETAs actually decreased OFV
Dear Bill,
Appreciate your reply a lot. The issue is from KA. Adding KA or not did
have this problem. However, regarding your statement "it is rare to have
enough data to fit true IIV", can you explain more about this. My data
set is from Phase I studies, and I thought this should be enough for
this simulation.
Dear Leonid,
Thanks very much for your detailed suggestion. I followed the steps you
listed above, and did find that the OFV decreased in step 2, just as you
predicted. Then using the estimation to replace the initial values for
all of the THETA, OMEGA and SIGMA, the OFV stabilized. However, I am
curious about the explanation for this. And, is this a universal method
for estimation of initial values? Thank you.
The change of OFV was around 100 (the OFV was ~114300). I am pasting the
OMEGA matrix below for your information.
ETA1 ETA2 ETA3 ETA4 ETA5
ETA1
+ 4.08E-02
ETA2
+ 0.00E+00 1.57E-01
ETA3
+ 0.00E+00 0.00E+00 1.30E-01
ETA4
+ 0.00E+00 0.00E+00 0.00E+00 4.07E-01
ETA5
+ 0.00E+00 0.00E+00 0.00E+00 0.00E+00 2.19E-02
ETA5 (0.0219) is the one caused the problem.
Best Regards
On 26 August 2013 07:06, Leonid Gibiansky <lgibian...@quantpharm.com
<mailto:lgibian...@quantpharm.com>> wrote:
Hi Xinting,
You should be able to do it. Let's check it again this way
1. You run the model with all ETAs included, but one ETA (the one that
was excluded in the reduced model) is fixed to zero. You should be able
to reproduce your "reduced ETA" result (OF)
2. You take the same control stream, and set all initial values to the
final parameter estimates of model (1) above, except you use the small
value (may be not 0.01 but 0.000001) as the initial value of the ETA
that was fixed to zero in model (1).
Model (2) is the not-reduced model, and it's OF should be less or equal
to the OF of model (1). If this is not the case, increase the number of
significant digits in the initial estimates of model (2) - take those
from the final estimates of model 1.
Without data, it is very difficult to offer more specific advice.
Also, what is the magnitude of the OF change? What is the estimate of
the OMEGA for the ETA in question?
Regards,
Leonid
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com <http://www.quantpharm.com>
e-mail: LGibiansky at quantpharm.com <http://quantpharm.com>
tel: (301) 767 5566 <tel:%28301%29%20767%205566>
On 8/25/2013 8:42 AM, Xinting Wang wrote:
Dear Leonid,
I tried with your method and found the same result. The initial
estimation of the added ETA was set at 0.01, and the result showed an
increase of OFV. Please see below the $PK part of the control file for
more information. Many thanks.
Dear Bill,
Could you please explain that in a little bit more detail? I am pasting
the $PK part of the control file in case you could find the useful
information. Thanks a lot.
$PK
FA1=0
FA2=0
FA3=0
FA4=0
IF(DOSE.EQ.250) THEN
FA1=1
ENDIF
IF(DOSE.EQ.500) THEN
FA2=1
ENDIF
IF(DOSE.EQ.850) THEN
FA3=1
ENDIF
IF(DOSE.EQ.1000) THEN
FA4=1
ENDIF
F1=FA1+FA2*THETA(6)+FA3*THETA(7)+FA4*THETA(8)
TVCL=THETA(1)
TVV2=THETA(2)
TVKA=THETA(3)
TVQ=THETA(4)
TVV3=THETA(5)
CL=TVCL*EXP(ETA(1))
V2=TVV2*EXP(ETA(2))
KA=TVKA*EXP(ETA(5))
Q=TVQ*EXP(ETA(3))
V3=TVV3*EXP(ETA(4))
S2=V2/1000
S3=V3/1000
$ERROR
IPRE=F
IRES=DV-IPRE
W=F
IF(W.EQ.0) W = 1
IWRE = IRES/W
Y=F*(1+EPS(1))+EPS(2)
Best Regards
On 12 August 2013 20:50, Denney, William S.
<william.s.den...@pfizer.com <mailto:william.s.den...@pfizer.com>
<mailto:william.s.den...@pfizer.com
<mailto:william.s.den...@pfizer.com>>> wrote:
Hi Xinting,
In a few rare cases, I've seen this happen if the model is
approaching nonconvergence. In those cases, typically the RSE on
one or more parameters will increase and the ratio of max to min
eigenvalues will increase substantially. Are you seeing either of
these?
Thanks,
Bill
On Aug 11, 2013, at 21:56, "Leonid Gibiansky"
<lgibian...@quantpharm.com <mailto:lgibian...@quantpharm.com>
<mailto:lgibian...@quantpharm.com
<mailto:lgibian...@quantpharm.com>>> wrote:
Xinting,
Try to start from the initial conditions of your "reduced"
model but
add that "reduced" ETA with the corresponding OMEGA equal to
0.01 or
other small number. If the control stream code is correct, the
objective function should decrease or retain the same value.
Leonid
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com <http://www.quantpharm.com>
<http://www.quantpharm.com>
e-mail: LGibiansky at quantpharm.com <http://quantpharm.com>
<http://quantpharm.com>
tel: (301) 767 5566 <tel:%28301%29%20767%205566>
<tel:%28301%29%20767%205566>
On 8/10/2013 10:23 PM, Xinting Wang wrote:
> Dear all,
>
> Does anyone witnessed such a phenomenon in NONMEM as when you
reduced an
> ETA, the OFV value, rather than increase, actually decreased?
It's quite
> against intuition, as individual estimation should be better
than
> population estimation in that particular parameter. Both models,
whether
> having this ETA, converged very well.
>
> Best
>
> --
> Xinting
--
Xinting
--
Xinting
