It seems my mails are not appearing on nmusers – maybe a sign that the thread
has gone on too long. Anyway the one below is from yesterday.
/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
From: Mats Karlsson [mailto:mats.karls...@farmbio.uu.se]
Sent: Tuesday, June 01, 2010 4:03 PM
To: 'Nick Holford'; 'nmusers@globomaxnm.com'
Subject: RE: [NMusers] distribution assumption of Eta in NONMEM
Nick,
I don’t think the design was bad at all. Two very precisely measured
observations per subject with 100 subjects for determining one THETA, one OMEGA
and one sigma is indeed a much more informative design than we ever get in real
life. I’m not sure what you try to achieve with these simulations. The question
of sensitivity to the underlying distribution and a preference for
transformations that result in normally distributed ETAs (ie differences
between the individual parameters and the typical parameters under the model) I
think has been shown. You may find situations where it is more or less
sensitive, but that does not alter the fact.
You don’t provide information about estimated sigma in your example below. Was
the estimate unbiased?
When you compare your original uniform eta distribution with the
logit-transformation, you have to look at the transformed etas.
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
From: Nick Holford [mailto:n.holf...@auckland.ac.nz]
Sent: Tuesday, June 01, 2010 3:23 PM
To: Mats Karlsson; nmusers@globomaxnm.com
Cc: 'Marc Lavielle'
Subject: Re: [NMusers] distribution assumption of Eta in NONMEM
Mats,
Thanks for the suggestion to try a more complex model. I agree there might be
some bias in the OMEGA(1,1) estimate from uniform simulated ETA when SIGMA is
estimated with 2 obs/subject.
In case this was due to a rather poor design (which is not what we are trying
to test) I tried your example with 10 obs/subject. Although the OMEGA(1,1)
(PPV_HILL) is indeed larger than the true value the 95% parametric bootstrap
confidence interval includes the true value so I would not conclude this was a
significant bias.
Uniform
Statistic
HILL
PPV_HILL
Obj
TRUE
5
0.08
.
average
4.9583
0.093377
-16926.4
CV
0.033317
0.102836
-0.00066
0.025
4.66
0.074833
-16950.2
0.975
5.25
0.11005
-16907.7
SD
0.165194
0.009603
11.15514
N
100
I also tried using the logistic transform you suggested and got these estimates:
Logistic
Statistic
HILL
LGPAR1
LGPAR2
PPV_HILL
OBJ
TRUE
.
.
.
.
.
average
5.0926
0.58006
1.6117
1.214079
-16938.7
CV
0.049328
0.121019
0.678749
0.432531
-0.00059
0.025
4.65475
0.47075
1.15475
0.321125
-16959.9
0.975
5.45575
0.6923
2.68925
2.1435
-16920.7
SD
0.251206
0.070198
1.09394
0.525127
10.05781
N
100
As you noted the OBJ was lower on average (12.3) with the LGST model.
I tried simulating from the average estimates above using these two models. The
distribution for the simulated uniform UNIETA value looked reasonably flat and
within -0.5 to 0.5 as expected. The ETA1 distribution simulated from the
uniform model was more or less normal with most of the values between -0.5 and
0.5. However the ETA1 distribution simulated from the logistic estimation
model, while also more or less normal, had most of the values lying between -2
and 2 and more than 66% outside the range -0.5 to 0.5. So although the OFV was
lower with the logistic transformation this would not be a good way to simulate
the original data.
