From: Mats Karlsson <*mats.karlsson*>

Date: Mon, 24 Aug 2009 04:01:55 +0200

Hi Steve,

I think you're missing an important point. As I wrote to Nick, you will

never get concentrations reported regardless of their value. At some point,

you will only get the information that concentration is below a limit

(LOQ,LOD,LO?). This you should take into account in your design. Error

models for concentrations below LO? are not entirely unimportant, but will

not have the properties you mention below.

Best regards,

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

-----Original Message-----

From: Stephen Duffull [mailto:stephen.duffull

Sent: Monday, August 24, 2009 2:49 AM

To: Mats Karlsson; 'Nick Holford'; 'Leonid Gibiansky'

Cc: 'nmusers'

Subject: RE: [NMusers] Linear VS LTBS

Mats

Just a comment on your comments below:

"All models are wrong and I see no reason why the exponential error model

would be different although I think it is better than the proportional error

for most situations. "

"Why would you not be able to get sensible information from models that

don't have an additive error component?"

I agree that for estimation purposes a purely proportional or exponential

error model often seems to work well and under the principles of "all models

are wrong" it may well be appropriately justified. This is probably because

estimation processes that we use in standard software are fairly robust to

trivial solutions. The theory of optimal design is less forgiving in this

light and if you stated that your error was proportional to the observation

then it would conclude that there would be no error when there is no

observation (which we know is not true due to LOD issues). All designs are

optimal when there is zero error since the information matrix would be

infinite. Practically, the smallest observation will have least error and

hence be in some sense close to optimal.

So, a proportional or exponential only error model should be used with

caution in anything other than estimation and not used for the purposes of

optimal design.

Steve

--

Received on Sun Aug 23 2009 - 22:01:55 EDT

Date: Mon, 24 Aug 2009 04:01:55 +0200

Hi Steve,

I think you're missing an important point. As I wrote to Nick, you will

never get concentrations reported regardless of their value. At some point,

you will only get the information that concentration is below a limit

(LOQ,LOD,LO?). This you should take into account in your design. Error

models for concentrations below LO? are not entirely unimportant, but will

not have the properties you mention below.

Best regards,

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

-----Original Message-----

From: Stephen Duffull [mailto:stephen.duffull

Sent: Monday, August 24, 2009 2:49 AM

To: Mats Karlsson; 'Nick Holford'; 'Leonid Gibiansky'

Cc: 'nmusers'

Subject: RE: [NMusers] Linear VS LTBS

Mats

Just a comment on your comments below:

"All models are wrong and I see no reason why the exponential error model

would be different although I think it is better than the proportional error

for most situations. "

"Why would you not be able to get sensible information from models that

don't have an additive error component?"

I agree that for estimation purposes a purely proportional or exponential

error model often seems to work well and under the principles of "all models

are wrong" it may well be appropriately justified. This is probably because

estimation processes that we use in standard software are fairly robust to

trivial solutions. The theory of optimal design is less forgiving in this

light and if you stated that your error was proportional to the observation

then it would conclude that there would be no error when there is no

observation (which we know is not true due to LOD issues). All designs are

optimal when there is zero error since the information matrix would be

infinite. Practically, the smallest observation will have least error and

hence be in some sense close to optimal.

So, a proportional or exponential only error model should be used with

caution in anything other than estimation and not used for the purposes of

optimal design.

Steve

--

Received on Sun Aug 23 2009 - 22:01:55 EDT