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

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