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FW: distribution assumption of Eta in NONMEM

From: Mats Karlsson <mats.karlsson>
Date: Wed, 2 Jun 2010 13:27:38 +0200

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.karlsson
Sent: Tuesday, June 01, 2010 4:03 PM
To: 'Nick Holford'; 'nmusers
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.holford
Sent: Tuesday, June 01, 2010 3:23 PM
To: Mats Karlsson; nmusers
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

0.083333

.


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.




 

Received on Wed Jun 02 2010 - 07:27:38 EDT

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