Dear NMUSERS,
I wanted to investigate the dose-response relationship (Emax model) of a
drug with NONMEM, based on data from literature (i.e. a meta-analysis).
However, I am not quite sure how to deal with the different levels of
random effects. Suppose I have 10 studies of different size where
different doses were given and the response is presented as average change
of a biomarker +/- standard deviation for each dose level. How would I
incorporate the standard deviation of the biomarker measurements reported
in each study for each dose level and how would I account for the
different number of patients in the study?
I would greatly appreciate your help, maybe with a NM-code snippet or
reference to a paper where something similar has been done.
Thanks in advance, Andreas.
Andreas Lindauer
Pharmacokineticist
Pharmacokinetics and Metabolism
R&D Center. Ferrer Internacional S.A.
Juan de Sada 32, 08028 Barcelona
[email protected]
www.ferrergrupo.com
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Meta-analysis with Nonmem
Andreas,
I think if you have only study-level data, you can treat each study as a "subject", build meta-population dose-PD model in the usual way,
IPRED=Emax (or some other) function of DOSE
and modify the error part as follows: For each data point, you know the mean value (DV), SD, and N. From SD and N you can get an estimate of standard error of the mean as SE=SD/sqrt(N) (computed for each data point and included into the data file). Then your error model would include
Y=IPRED+SE*EPS(1)
I am not sure whether you need to fix SIGMA
$SIGMA
1 FIXED ; for EPS(1)
thus assuming that all error in your model comes from the "assay", or estimate it thus allowing for unexplained model misspecification and extra error. I would try both ways to see the difference.
This is the simplest version that can be further improved (? or at least, made more complicated) by adding the study effect on error (thus accounting for possible differences in study populations; Y=IPRED+SE*EXP(ETA(1))*EPS(1)), etc.
Leonid
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566
[email protected] wrote:
> Dear NMUSERS,
>
> I wanted to investigate the dose-response relationship (Emax model) of a drug with NONMEM, based on data from literature (i.e. a meta-analysis). However, I am not quite sure how to deal with the different levels of random effects. Suppose I have 10 studies of different size where different doses were given and the response is presented as average change of a biomarker +/- standard deviation for each dose level. How would I incorporate the standard deviation of the biomarker measurements reported in each study for each dose level and how would I account for the different number of patients in the study? I would greatly appreciate your help, maybe with a NM-code snippet or reference to a paper where something similar has been done.
>
> Thanks in advance, Andreas.
> Ferrer
> Andreas Lindauer
> Pharmacokineticist
> Pharmacokinetics and Metabolism
> R&D Center. Ferrer Internacional S.A.
> Juan de Sada 32, 08028 Barcelona
> [email protected]
> www.ferrergrupo.com
>
> Recicla ¿Necesita imprimir este mensaje? Protejamos el medio ambiente. Li cal imprimir aquest missatge? Protegim el medi ambient. Do you need to print this message? Let's protect the environment.
>
> Este mensaje, y en su caso, cualquier fichero anexo al mismo, puede contener información confidencial, siendo para uso exclusivo del destinatario, quedando prohibida su divulgación, copia o distribución a terceros sin la autorización expresa del remitente. Si Vd. ha recibido este mensaje erróneamente, se ruega lo notifique al remitente y proceda a su borrado. Gracias por su colaboración.
>
> This message and its annexed files may contain confidential information which is exclusively for the use of the addressee. It is strictly forbidden to distribute copies to third parties without the explicit permission of the sender. If you receive this message by mistake, please notify it to the sender and make sure to delete it. Thank you for your kind cooperation.
Thank you Leonid and Dirk for your replies. They were very helpful.
Leonid, what would you think about the following:
Y=IPRED+SE*EPS(1)+ETA(1)
With SIGMA fixed to 1 and OMEGA being the inter-study standard-deviation?
What would be the interpretation of SIGMA if it were not fixed to 1?
You wrote:
>>Y=IPRED+SE*EXP(ETA(1))*EPS(1)), etc.
Wouldn't this be somehow transformed by NONMEM because of the
linearization process? Similarly to why we cannot use the exponential
residual error model directly in NONMEM, but have to do the
transform-both-sides approach.
Dirk, good idea. However, estimation of the simulated datasets might
become very time consuming when you combine data from several large
studies. And, as you said:
>> If the number of subjects in a study is small, it might be useful to
repeat the simulation and produce different combined datasets.
I would even go further and say, that it is absolutly necessary to repeat
the simulation-reestimation procedure many times in order to get "stable"
results.
Best regards, Andreas.
Andreas Lindauer
Pharmacokineticist
Pharmacokinetics and Metabolism
R&D Center. Ferrer Internacional S.A.
Juan de Sada 32, 08028 Barcelona
[email protected]
www.ferrergrupo.com
¿Necesita imprimir este mensaje? Protejamos el medio ambiente.
Li cal imprimir aquest missatge? Protegim el medi ambient.
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Este mensaje, y en su caso, cualquier fichero anexo al mismo, puede
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terceros sin la autorización expresa del remitente. Si Vd. ha recibido
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Andreas,
I am not sure that I understood your idea
Y=IPRED+SE*EPS(1)+ETA(1)
What is ETA(1)? It would be added to the model part, with the new prediction being:
IPRED'=IPRED+ETA(1)
As to the code
Y=IPRED+SE*EXP(ETA(1))*EPS(1))
it will be interpreted correctly (make sure you use INTERACTION option). Linearization is done for the EPS() part, and the function above is linear over EPS.
If SIGMA is not fixed, you treat the entire combination
SE^2*SIGMA(1,1) as the variance (study-specific or even point-specific) of the residual error, with SE being the weighting function that takes care about differences in the number of patients and the variability of the patient population (between study and/or points).
Leonid
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566
[email protected] wrote:
> Thank you Leonid and Dirk for your replies. They were very helpful.
>
> Leonid, what would you think about the following:
> Y=IPRED+SE*EPS(1)+ETA(1)
>
> With SIGMA fixed to 1 and OMEGA being the inter-study standard-deviation? What would be the interpretation of SIGMA if it were not fixed to 1?
>
> You wrote:
> >>Y=IPRED+SE*EXP(ETA(1))*EPS(1)), etc.
>
> Wouldn't this be somehow transformed by NONMEM because of the linearization process? Similarly to why we cannot use the exponential residual error model directly in NONMEM, but have to do the transform-both-sides approach.
>
> Dirk, good idea. However, estimation of the simulated datasets might become very time consuming when you combine data from several large studies. And, as you said: >> If the number of subjects in a study is small, it might be useful to repeat the simulation and produce different combined datasets. I would even go further and say, that it is absolutly necessary to repeat the simulation-reestimation procedure many times in order to get "stable" results.
>
> Best regards, Andreas.
>
> Ferrer
> Andreas Lindauer
> Pharmacokineticist
> Pharmacokinetics and Metabolism
> R&D Center. Ferrer Internacional S.A.
> Juan de Sada 32, 08028 Barcelona
> [email protected]
> www.ferrergrupo.com
>
> Recicla ¿Necesita imprimir este mensaje? Protejamos el medio ambiente. Li cal imprimir aquest missatge? Protegim el medi ambient. Do you need to print this message? Let's protect the environment.
>
> Este mensaje, y en su caso, cualquier fichero anexo al mismo, puede contener información confidencial, siendo para uso exclusivo del destinatario, quedando prohibida su divulgación, copia o distribución a terceros sin la autorización expresa del remitente. Si Vd. ha recibido este mensaje erróneamente, se ruega lo notifique al remitente y proceda a su borrado. Gracias por su colaboración.
>
> This message and its annexed files may contain confidential information which is exclusively for the use of the addressee. It is strictly forbidden to distribute copies to third parties without the explicit permission of the sender. If you receive this message by mistake, please notify it to the sender and make sure to delete it. Thank you for your kind cooperation.
Dear Dirk,
I haven't fully understood your idea. Mean value, SD, and N can be
collected from literature. But if we don't have a model, how can we
simulate one individual with many observations?
I met a problem and haven't got a solution. I chose change from baseline
as endpoint. But some literatures didn't provide CFB. The CFB and SD of CFB
calculated from mean value and SD are different from the values calculated
from individual data. Your suggestion will be highly appreciated. Thanks.
Best regards,
Guangli
Dear Dirk,
I haven't fully understood your idea. Mean value, SD, and N can be
collected from literature. But if we don't have a model, how can we
simulate one individual with many observations?
I met a problem and haven't got a solution. I chose change from baseline
as endpoint. But some literatures didn't provide CFB. The CFB and SD of CFB
calculated from mean value and SD are different from the values calculated
from individual data. Your suggestion will be highly appreciated. Thanks.
Best regards,
Guangli
Guangli,
Change from baseline (CFB) is commonly done -- but like other common statistical practices such as LOCF -- it is not a good idea if you really want to learn something (see Chan & Holford 2001). CFBis a naive approach focussed on getting small P values rather than understanding how disease changes with time and how treatments might modify it.
One key issue that CFB ignores is the correlation between the baseline value and the rate of progression. This is often quite an important random effect correlation and should not be ignored (e.g. see Holford et al 2006).
Nick
1. Chan PLS, Holford NHG. Drug treatment effects on disease progression. Annu Rev Pharmacol Toxicol. 2001;41:625-59. 2. Holford NHG, Chan PL, Nutt JG, Kieburtz K, Shoulson I. Disease progression and pharmacodynamics in Parkinson disease - evidence for functional protection with levodopa and other treatments. J Pharmacokinet Pharmacodyn. 2006 Jun;33(3):281-311.
Guangli Ma wrote:
> Dear Dirk,
>
> I haven't fully understood your idea. Mean value, SD, and N can be collected from literature. But if we don't have a model, how can we simulate one individual with many observations? I met a problem and haven't got a solution. I chose change from baseline as endpoint. But some literatures didn't provide CFB. The CFB and SD of CFB calculated from mean value and SD are different from the values calculated from individual data. Your suggestion will be highly appreciated. Thanks. Best regards, Guangli
--
Nick Holford, Professor Clinical Pharmacology
Dept Pharmacology & Clinical Pharmacology
University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand
tel:+64(9)923-6730 fax:+64(9)373-7090 mobile:+64(21)46 23 53
email: [email protected]
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
Dear Andreas,
An approach you may consider is to model both the standard deviation and the
average as dependent variables:
SD=THETA(1)*EXP(ETA(1))
AV=(THETA(2)+DOSE*THETA(3))*EXP(ETA(2))
SESD=SD/(2*(N-1)**.5)
SEAV=SD/N**.5
IF(FLAG.EQ.0) THEN
Y = SD+SESD*EPS(1)
ELSE
Y = AV+SEAV*EPS(1)
ENDIF
$SIGMA 1 FIX
Your dataset would treat study as individuals, include N the number of
individuals in the study arm and incorporate a flag, so would look like:
STUD=ID DV N FLAG DOSE
1 SD1 N1 0 D1
1 AV1 N1 1 D1
1 SD2 N2 0 D2
1 AV2 N2 1 D2
Note: this is only valid when there was only 1 endpoint per subject.
Hope this helps.
Best regards,
Elodie, Martin and Mats
Elodie L. Plan, PharmD, MSc, PhD student
********************************************
Uppsala Pharmacometrics Research Group,
Department of Pharmaceutical Biosciences,
P.O. Box 591, SE-751 24 Uppsala, SWEDEN
Office +46 18-471 4385, Fax +46 18-471 4003
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of [email protected]
Sent: Friday, February 26, 2010 10:26 AM
To: [email protected]
Subject: Re: [NMusers] Meta-analysis with Nonmem
Thank you Leonid and Dirk for your replies. They were very helpful.
Leonid, what would you think about the following:
Y=IPRED+SE*EPS(1)+ETA(1)
With SIGMA fixed to 1 and OMEGA being the inter-study standard-deviation?
What would be the interpretation of SIGMA if it were not fixed to 1?
You wrote:
>>Y=IPRED+SE*EXP(ETA(1))*EPS(1)), etc.
Wouldn't this be somehow transformed by NONMEM because of the linearization
process? Similarly to why we cannot use the exponential residual error model
directly in NONMEM, but have to do the transform-both-sides approach.
Dirk, good idea. However, estimation of the simulated datasets might become
very time consuming when you combine data from several large studies. And,
as you said:
>> If the number of subjects in a study is small, it might be useful to
repeat the simulation and produce different combined datasets.
I would even go further and say, that it is absolutly necessary to repeat
the simulation-reestimation procedure many times in order to get "stable"
results.
Best regards, Andreas.
Ferrer
Andreas Lindauer
Pharmacokineticist
Pharmacokinetics and Metabolism
R&D Center. Ferrer Internacional S.A.
Juan de Sada 32, 08028 Barcelona
[email protected]
www.ferrergrupo.com
Recicla
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Gracias por su colaboración.
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Hi Elodie, Martin and Mats,
Thanks for your suggestion, a very interesting approach. So, THETA1 would
give me an estimate of the global between patient variability, expressed
as SD, across all studies and OMEGA1 would be an estimate of the between
study variability (BSV) of this SD. OMEGA2 would be the BSV of the average
response. Is this interpretation correct? I suppose the number of studies
has to be quite large to get precise estimates of the BSV.
Best regards, Andreas.
Andreas Lindauer
Pharmacokineticist
Pharmacokinetics and Metabolism
R&D Center. Ferrer Internacional S.A.
Juan de Sada 32, 08028 Barcelona
[email protected]
www.ferrergrupo.com
¿Necesita imprimir este mensaje? Protejamos el medio ambiente.
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"Elodie Plan" <[email protected]>
04/03/2010 14:33
Para
<[email protected]>, <[email protected]>
cc
Asunto
RE: [NMusers] Meta-analysis with Nonmem
Dear Andreas,
An approach you may consider is to model both the standard deviation and
the average as dependent variables:
SD=THETA(1)*EXP(ETA(1))
AV=(THETA(2)+DOSE*THETA(3))*EXP(ETA(2))
SESD=SD/(2*(N-1)**.5)
SEAV=SD/N**.5
IF(FLAG.EQ.0) THEN
Y = SD+SESD*EPS(1)
ELSE
Y = AV+SEAV*EPS(1)
ENDIF
$SIGMA 1 FIX
Your dataset would treat study as individuals, include N the number of
individuals in the study arm and incorporate a flag, so would look like:
STUD=ID DV N FLAG DOSE
1 SD1 N1 0 D1
1 AV1 N1 1 D1
1 SD2 N2 0 D2
1 AV2 N2 1 D2
…
Note: this is only valid when there was only 1 endpoint per subject.
Hope this helps.
Best regards,
Elodie, Martin and Mats
Elodie L. Plan, PharmD, MSc, PhD student
********************************************
Uppsala Pharmacometrics Research Group,
Department of Pharmaceutical Biosciences,
P.O. Box 591, SE-751 24 Uppsala, SWEDEN
Office +46 18-471 4385, Fax +46 18-471 4003
Quoted reply history
From: [email protected] [mailto:[email protected]]
On Behalf Of [email protected]
Sent: Friday, February 26, 2010 10:26 AM
To: [email protected]
Subject: Re: [NMusers] Meta-analysis with Nonmem
Thank you Leonid and Dirk for your replies. They were very helpful.
Leonid, what would you think about the following:
Y=IPRED+SE*EPS(1)+ETA(1)
With SIGMA fixed to 1 and OMEGA being the inter-study standard-deviation?
What would be the interpretation of SIGMA if it were not fixed to 1?
You wrote:
>>Y=IPRED+SE*EXP(ETA(1))*EPS(1)), etc.
Wouldn't this be somehow transformed by NONMEM because of the
linearization process? Similarly to why we cannot use the exponential
residual error model directly in NONMEM, but have to do the
transform-both-sides approach.
Dirk, good idea. However, estimation of the simulated datasets might
become very time consuming when you combine data from several large
studies. And, as you said:
>> If the number of subjects in a study is small, it might be useful to
repeat the simulation and produce different combined datasets.
I would even go further and say, that it is absolutly necessary to repeat
the simulation-reestimation procedure many times in order to get "stable"
results.
Best regards, Andreas.
Andreas Lindauer
Pharmacokineticist
Pharmacokinetics and Metabolism
R&D Center. Ferrer Internacional S.A.
Juan de Sada 32, 08028 Barcelona
[email protected]
www.ferrergrupo.com
¿Necesita imprimir este mensaje? Protejamos el medio ambiente.
Li cal imprimir aquest missatge? Protegim el medi ambient.
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Este mensaje, y en su caso, cualquier fichero anexo al mismo, puede
contener información confidencial, siendo para uso exclusivo del
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This message and its annexed files may contain confidential information
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Dear Elodie,
Thank you for your example.
Could you please further comment on why you used the same EPS(1) for
fitting both AV and SD instead of writing:
IF(FLAG.EQ.0) THEN
Y = SD+SESD*EPS(1)
ELSE
Y = AV+SEAV*EPS(2)
ENDIF
$SIGMA 1 FIX
$SIGMA 1 FIX
Many thanks
Ciao
Marco
------------------------------------------------------------------------------
Marco Campioni, PhD
Modelling & Simulations
Exploratory Medicine
Merck Serono S.A. - Geneva
9, Chemin des Mines
1202 Geneva, Switzerland
Location: B1.4
Phone: +41 22 414 4554
Fax: +41 22 414 3059
Email: marco.campioni
"Elodie Plan" <elodie.plan
Sent by: owner-nmusers
04/03/2010 14:33
To
<alindauer-research m.com>
cc
Subject
RE: [NMusers] Meta-analysis with Nonmem
Dear Andreas,
An approach you may consider is to model both the standard deviation and
the average as dependent variables:
SD=THETA(1)*EXP(ETA(1))
AV=(THETA(2)+DOSE*THETA(3))*EXP(ETA(2))
SESD=SD/(2*(N-1)**.5)
SEAV=SD/N**.5
IF(FLAG.EQ.0) THEN
Y = SD+SESD*EPS(1)
ELSE
Y = AV+SEAV*EPS(1)
ENDIF
$SIGMA 1 FIX
Your dataset would treat study as individuals, include N the number of
individuals in the study arm and incorporate a flag, so would look like:
STUD=ID DV N FLAG DOSE
1 SD1 N1 0 D1
1 AV1 N1 1 D1
1 SD2 N2 0 D2
1 AV2 N2 1 D2
…
Note: this is only valid when there was only 1 endpoint per subject.
Hope this helps.
Best regards,
Elodie, Martin and Mats
Elodie L. Plan, PharmD, MSc, PhD student
********************************************
Uppsala Pharmacometrics Research Group,
Department of Pharmaceutical Biosciences,
P.O. Box 591, SE-751 24 Uppsala, SWEDEN
Office +46 18-471 4385, Fax +46 18-471 4003
Quoted reply history
From: owner-nmusers xnm.com [mailto:owner-nmusers
On Behalf Of alindauer-research
Sent: Friday, February 26, 2010 10:26 AM
To: nmusers
Subject: Re: [NMusers] Meta-analysis with Nonmem
Thank you Leonid and Dirk for your replies. They were very helpful.
Leonid, what would you think about the following:
Y=IPRED+SE*EPS(1)+ETA(1)
With SIGMA fixed to 1 and OMEGA being the inter-study standard-deviation?
What would be the interpretation of SIGMA if it were not fixed to 1?
You wrote:
>>Y=IPRED+SE*EXP(ETA(1))*EPS(1)), etc.
Wouldn't this be somehow transformed by NONMEM because of the
linearization process? Similarly to why we cannot use the exponential
residual error model directly in NONMEM, but have to do the
transform-both-sides approach.
Dirk, good idea. However, estimation of the simulated datasets might
become very time consuming when you combine data from several large
studies. And, as you said:
>> If the number of subjects in a study is small, it might be useful to
repeat the simulation and produce different combined datasets.
I would even go further and say, that it is absolutly necessary to repeat
the simulation-reestimation procedure many times in order to get "stable"
results.
Best regards, Andreas.
Andreas Lindauer
Pharmacokineticist
Pharmacokinetics and Metabolism
R&D Center. Ferrer Internacional S.A.
Juan de Sada 32, 08028 Barcelona
alindauer-research ferrergrupo.com
www.ferrergrupo.com
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Dear Dirk,
Thanks. Now I understand that it is one observation per individual. The
reason why I mentioned CFB is not to ask how to use it but to show if CFB
can not be derived from simulation, there is no additional benefit.
Your results hightly depend on N, because simulation introduces random
errors for observed SD/SE.
Best regards,
Guangli
Dear Andreas,
Your interpretation is the same as mine (correct or not). My guessing is that
you are actually never all that interested in precisely estimating BSV in this
type of analysis. The approach nevertheless has advantages in assessing the
overall between subject variability and average response. One advantage is that
you could also include measurements of average response where the SD is
unknown.
One thing worth considering will be if it is geometric means or arithmetic
means that you are dealing with. The example in Elodies example assumes
arithmetic means but geometric means could easily be handled with Y = AV *
EXP(SEAV*EPS(1)).
Best regards,
Martin Bergstrand, MSc, PhD student
-----------------------------------------------
Pharmacometrics Research Group,
Department of Pharmaceutical Biosciences,
Uppsala University
-----------------------------------------------
<mailto:[email protected]> [email protected]
-----------------------------------------------
Work: +46 18 471 4639
Mobile: +46 709 994 396
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of [email protected]
Sent: den 4 mars 2010 16:21
To: Elodie Plan
Cc: [email protected]
Subject: RE: [NMusers] Meta-analysis with Nonmem
Hi Elodie, Martin and Mats,
Thanks for your suggestion, a very interesting approach. So, THETA1 would give
me an estimate of the global between patient variability, expressed as SD,
across all studies and OMEGA1 would be an estimate of the between study
variability (BSV) of this SD. OMEGA2 would be the BSV of the average response.
Is this interpretation correct? I suppose the number of studies has to be quite
large to get precise estimates of the BSV.
Best regards, Andreas.
Ferrer
Andreas Lindauer
Pharmacokineticist
Pharmacokinetics and Metabolism
R&D Center. Ferrer Internacional S.A.
Juan de Sada 32, 08028 Barcelona
[email protected]
www.ferrergrupo.com
Recicla
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and make sure to delete it. Thank you for your kind cooperation.
"Elodie Plan" <[email protected]>
04/03/2010 14:33
Para
<[email protected]>, <[email protected]>
cc
Asunto
RE: [NMusers] Meta-analysis with Nonmem
Dear Andreas,
An approach you may consider is to model both the standard deviation and the
average as dependent variables:
SD=THETA(1)*EXP(ETA(1))
AV=(THETA(2)+DOSE*THETA(3))*EXP(ETA(2))
SESD=SD/(2*(N-1)**.5)
SEAV=SD/N**.5
IF(FLAG.EQ.0) THEN
Y = SD+SESD*EPS(1)
ELSE
Y = AV+SEAV*EPS(1)
ENDIF
$SIGMA 1 FIX
Your dataset would treat study as individuals, include N the number of
individuals in the study arm and incorporate a flag, so would look like:
STUD=ID DV N FLAG DOSE
1 SD1 N1 0 D1
1 AV1 N1 1 D1
1 SD2 N2 0 D2
1 AV2 N2 1 D2
…
Note: this is only valid when there was only 1 endpoint per subject.
Hope this helps.
Best regards,
Elodie, Martin and Mats
Elodie L. Plan, PharmD, MSc, PhD student
********************************************
Uppsala Pharmacometrics Research Group,
Department of Pharmaceutical Biosciences,
P.O. Box 591, SE-751 24 Uppsala, SWEDEN
Office +46 18-471 4385, Fax +46 18-471 4003
From: [email protected] [mailto:[email protected]] On
Behalf Of [email protected]
Sent: Friday, February 26, 2010 10:26 AM
To: [email protected]
Subject: Re: [NMusers] Meta-analysis with Nonmem
Thank you Leonid and Dirk for your replies. They were very helpful.
Leonid, what would you think about the following:
Y=IPRED+SE*EPS(1)+ETA(1)
With SIGMA fixed to 1 and OMEGA being the inter-study standard-deviation? What
would be the interpretation of SIGMA if it were not fixed to 1?
You wrote:
>>Y=IPRED+SE*EXP(ETA(1))*EPS(1)), etc.
Wouldn't this be somehow transformed by NONMEM because of the linearization
process? Similarly to why we cannot use the exponential residual error model
directly in NONMEM, but have to do the transform-both-sides approach.
Dirk, good idea. However, estimation of the simulated datasets might become
very time consuming when you combine data from several large studies. And, as
you said:
>> If the number of subjects in a study is small, it might be useful to repeat
>> the simulation and produce different combined datasets.
I would even go further and say, that it is absolutly necessary to repeat the
simulation-reestimation procedure many times in order to get "stable" results.
Best regards, Andreas.
Ferrer
Andreas Lindauer
Pharmacokineticist
Pharmacokinetics and Metabolism
R&D Center. Ferrer Internacional S.A.
Juan de Sada 32, 08028 Barcelona
<mailto:[email protected]> [email protected]
http://www.ferrergrupo.com/ www.ferrergrupo.com
Recicla
¿Necesita imprimir este mensaje? Protejamos el medio ambiente.
Li cal imprimir aquest missatge? Protegim el medi ambient.
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Este mensaje, y en su caso, cualquier fichero anexo al mismo, puede contener
información confidencial, siendo para uso exclusivo del destinatario, quedando
prohibida su divulgación, copia o distribución a terceros sin la autorización
expresa del remitente. Si Vd. ha recibido este mensaje erróneamente, se ruega
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This message and its annexed files may contain confidential information which
is exclusively for the use of the addressee. It is strictly forbidden to
distribute copies to third parties without the explicit permission of the
sender. If you receive this message by mistake, please notify it to the sender
and make sure to delete it. Thank you for your kind cooperation.
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<<image002.gif>>
Dear Elodie,
Thank you for your example.
Could you please further comment on why you used the same EPS(1) for
fitting both AV and SD instead of writing:
IF(FLAG.EQ.0) THEN
Y = SD+SESD*EPS(1)
ELSE
Y = AV+SEAV*EPS(2)
ENDIF
$SIGMA 1 FIX
$SIGMA 1 FIX
Many thanks
Ciao
Marco
------------------------------------------------------------------------------
Marco Campioni, PhD
Modelling & Simulations
Exploratory Medicine
Merck Serono S.A. - Geneva
9, Chemin des Mines
1202 Geneva, Switzerland
Location: B1.4
Phone: +41 22 414 4554
Fax: +41 22 414 3059
Email: [email protected]
"Elodie Plan" <[email protected]>
Sent by: [email protected]
04/03/2010 14:33
To
<[email protected]>, <[email protected]>
cc
Subject
RE: [NMusers] Meta-analysis with Nonmem
Dear Andreas,
An approach you may consider is to model both the standard deviation and
the average as dependent variables:
SD=THETA(1)*EXP(ETA(1))
AV=(THETA(2)+DOSE*THETA(3))*EXP(ETA(2))
SESD=SD/(2*(N-1)**.5)
SEAV=SD/N**.5
IF(FLAG.EQ.0) THEN
Y = SD+SESD*EPS(1)
ELSE
Y = AV+SEAV*EPS(1)
ENDIF
$SIGMA 1 FIX
Your dataset would treat study as individuals, include N the number of
individuals in the study arm and incorporate a flag, so would look like:
STUD=ID DV N FLAG DOSE
1 SD1 N1 0 D1
1 AV1 N1 1 D1
1 SD2 N2 0 D2
1 AV2 N2 1 D2
…
Note: this is only valid when there was only 1 endpoint per subject.
Hope this helps.
Best regards,
Elodie, Martin and Mats
Elodie L. Plan, PharmD, MSc, PhD student
********************************************
Uppsala Pharmacometrics Research Group,
Department of Pharmaceutical Biosciences,
P.O. Box 591, SE-751 24 Uppsala, SWEDEN
Office +46 18-471 4385, Fax +46 18-471 4003
Quoted reply history
From: [email protected] [mailto:[email protected]]
On Behalf Of [email protected]
Sent: Friday, February 26, 2010 10:26 AM
To: [email protected]
Subject: Re: [NMusers] Meta-analysis with Nonmem
Thank you Leonid and Dirk for your replies. They were very helpful.
Leonid, what would you think about the following:
Y=IPRED+SE*EPS(1)+ETA(1)
With SIGMA fixed to 1 and OMEGA being the inter-study standard-deviation?
What would be the interpretation of SIGMA if it were not fixed to 1?
You wrote:
>>Y=IPRED+SE*EXP(ETA(1))*EPS(1)), etc.
Wouldn't this be somehow transformed by NONMEM because of the
linearization process? Similarly to why we cannot use the exponential
residual error model directly in NONMEM, but have to do the
transform-both-sides approach.
Dirk, good idea. However, estimation of the simulated datasets might
become very time consuming when you combine data from several large
studies. And, as you said:
>> If the number of subjects in a study is small, it might be useful to
repeat the simulation and produce different combined datasets.
I would even go further and say, that it is absolutly necessary to repeat
the simulation-reestimation procedure many times in order to get "stable"
results.
Best regards, Andreas.
Andreas Lindauer
Pharmacokineticist
Pharmacokinetics and Metabolism
R&D Center. Ferrer Internacional S.A.
Juan de Sada 32, 08028 Barcelona
[email protected]
www.ferrergrupo.com
¿Necesita imprimir este mensaje? Protejamos el medio ambiente.
Li cal imprimir aquest missatge? Protegim el medi ambient.
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Este mensaje, y en su caso, cualquier fichero anexo al mismo, puede
contener información confidencial, siendo para uso exclusivo del
destinatario, quedando prohibida su divulgación, copia o distribución a
terceros sin la autorización expresa del remitente. Si Vd. ha recibido
este mensaje erróneamente, se ruega lo notifique al remitente y proceda a
su borrado. Gracias por su colaboración.
This message and its annexed files may contain confidential information
which is exclusively for the use of the addressee. It is strictly
forbidden to distribute copies to third parties without the explicit
permission of the sender. If you receive this message by mistake, please
notify it to the sender and make sure to delete it. Thank you for your
kind cooperation.
This message and any attachment are confidential and may be privileged or
otherwise protected from disclosure. If you are not the intended recipient, you
must not copy this message or attachment or disclose the contents to any other
person. If you have received this transmission in error, please notify the
sender immediately and delete the message and any attachment from your system.
Merck KGaA, Darmstadt, Germany and any of its subsidiaries do not accept
liability for any omissions or errors in this message which may arise as a
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<<image/gif>>
<<image/gif>>
Dear Marco,
Actually it does not matter the epsilons of Y(SD) and Y(AV) to be sampled from
the same distribution, since they are connected to 2 observations modeled
independently. As you noticed EPS(1) is not estimated but fixed, since the
magnitude of the variability actually comes from the SE multiplication part.
Best regards,
Elodie
Elodie L. Plan, PharmD, MSc, PhD student
********************************************
Uppsala Pharmacometrics Research Group,
Department of Pharmaceutical Biosciences,
P.O. Box 591, SE-751 24 Uppsala, SWEDEN
Office +46 18-471 4385, Fax +46 18-471 4003
Quoted reply history
From: [email protected] [mailto:[email protected]]
Sent: Friday, March 05, 2010 1:41 PM
To: Elodie Plan
Cc: [email protected]; [email protected];
[email protected]
Subject: RE: [NMusers] Meta-analysis with Nonmem
Dear Elodie,
Thank you for your example.
Could you please further comment on why you used the same EPS(1) for fitting
both AV and SD instead of writing:
IF(FLAG.EQ.0) THEN
Y = SD+SESD*EPS(1)
ELSE
Y = AV+SEAV*EPS(2)
ENDIF
$SIGMA 1 FIX
$SIGMA 1 FIX
Many thanks
Ciao
Marco
------------------------------------------------------------------------------
Marco Campioni, PhD
Modelling & Simulations
Exploratory Medicine
Merck Serono S.A. - Geneva
9, Chemin des Mines
1202 Geneva, Switzerland
Location: B1.4
Phone: +41 22 414 4554
Fax: +41 22 414 3059
Email: [email protected]
"Elodie Plan" <[email protected]>
Sent by: [email protected]
04/03/2010 14:33
To
<[email protected]>, <[email protected]>
cc
Subject
RE: [NMusers] Meta-analysis with Nonmem
Dear Andreas,
An approach you may consider is to model both the standard deviation and the
average as dependent variables:
SD=THETA(1)*EXP(ETA(1))
AV=(THETA(2)+DOSE*THETA(3))*EXP(ETA(2))
SESD=SD/(2*(N-1)**.5)
SEAV=SD/N**.5
IF(FLAG.EQ.0) THEN
Y = SD+SESD*EPS(1)
ELSE
Y = AV+SEAV*EPS(1)
ENDIF
$SIGMA 1 FIX
Your dataset would treat study as individuals, include N the number of
individuals in the study arm and incorporate a flag, so would look like:
STUD=ID DV N FLAG DOSE
1 SD1 N1 0 D1
1 AV1 N1 1 D1
1 SD2 N2 0 D2
1 AV2 N2 1 D2
…
Note: this is only valid when there was only 1 endpoint per subject.
Hope this helps.
Best regards,
Elodie, Martin and Mats
Elodie L. Plan, PharmD, MSc, PhD student
********************************************
Uppsala Pharmacometrics Research Group,
Department of Pharmaceutical Biosciences,
P.O. Box 591, SE-751 24 Uppsala, SWEDEN
Office +46 18-471 4385, Fax +46 18-471 4003
From: [email protected] [mailto:[email protected]] On
Behalf Of [email protected]
Sent: Friday, February 26, 2010 10:26 AM
To: [email protected]
Subject: Re: [NMusers] Meta-analysis with Nonmem
Thank you Leonid and Dirk for your replies. They were very helpful.
Leonid, what would you think about the following:
Y=IPRED+SE*EPS(1)+ETA(1)
With SIGMA fixed to 1 and OMEGA being the inter-study standard-deviation? What
would be the interpretation of SIGMA if it were not fixed to 1?
You wrote:
>>Y=IPRED+SE*EXP(ETA(1))*EPS(1)), etc.
Wouldn't this be somehow transformed by NONMEM because of the linearization
process? Similarly to why we cannot use the exponential residual error model
directly in NONMEM, but have to do the transform-both-sides approach.
Dirk, good idea. However, estimation of the simulated datasets might become
very time consuming when you combine data from several large studies. And, as
you said:
>> If the number of subjects in a study is small, it might be useful to repeat
>> the simulation and produce different combined datasets.
I would even go further and say, that it is absolutly necessary to repeat the
simulation-reestimation procedure many times in order to get "stable" results.
Best regards, Andreas.
Ferrer
Andreas Lindauer
Pharmacokineticist
Pharmacokinetics and Metabolism
R&D Center. Ferrer Internacional S.A.
Juan de Sada 32, 08028 Barcelona
<mailto:[email protected]> [email protected]
http://www.ferrergrupo.com/ www.ferrergrupo.com
Recicla
¿Necesita imprimir este mensaje? Protejamos el medio ambiente.
Li cal imprimir aquest missatge? Protegim el medi ambient.
Do you need to print this message? Let's protect the environment.
Este mensaje, y en su caso, cualquier fichero anexo al mismo, puede contener
información confidencial, siendo para uso exclusivo del destinatario, quedando
prohibida su divulgación, copia o distribución a terceros sin la autorización
expresa del remitente. Si Vd. ha recibido este mensaje erróneamente, se ruega
lo notifique al remitente y proceda a su borrado. Gracias por su colaboración.
This message and its annexed files may contain confidential information which
is exclusively for the use of the addressee. It is strictly forbidden to
distribute copies to third parties without the explicit permission of the
sender. If you receive this message by mistake, please notify it to the sender
and make sure to delete it. Thank you for your kind cooperation.
This message and any attachment are confidential and may be privileged or
otherwise protected from disclosure. If you are not the intended recipient, you
must not copy this message or attachment or disclose the contents to any other
person. If you have received this transmission in error, please notify the
sender immediately and delete the message and any attachment from your system.
Merck KGaA, Darmstadt, Germany and any of its subsidiaries do not accept
liability for any omissions or errors in this message which may arise as a
result of E-Mail-transmission or for damages resulting from any unauthorized
changes of the content of this message and any attachment thereto. Merck KGaA,
Darmstadt, Germany and any of its subsidiaries do not guarantee that this
message is free of viruses and does not accept liability for any damages caused
by any virus transmitted therewith.
Click http://disclaimer.merck.de to access the German, French, Spanish and
Portuguese versions of this disclaimer.
<<image001.gif>>
<<image002.gif>>