Hi,
We would like to compute a covariate inclusion statistical power based on the Wald test and using SE given by the fisher information matrix.
Is there any method to implement this directly in NONMEM or is there at least a way to output the Fisher Information matrix in NONMEM?
Thank you.
Statistical power computation based on the wald test
Hi,
We would like to compute a covariate inclusion statistical power based on the
Wald test and using SE given by the fisher information matrix.
Is there any method to implement this directly in NONMEM or is there at least a
way to output the Fisher Information matrix in NONMEM?
Thank you.
Dear Hammami,
Do you mean starting from a so-called full (pre-specified) model, and
approximate which covariates in the nonmem model would reach statistical
significance?
See the publication by Kowalski:
https://ascpt.onlinelibrary.wiley.com/doi/abs/10.1016/j.clpt.2003.11.158
https://ascpt.onlinelibrary.wiley.com/doi/abs/10.1016/j.clpt.2003.11.158
Best regards
Jakob
Jakob Ribbing, Ph.D.
Senior Consultant, Pharmetheus AB
Cell/Mobile: +46 (0)70 514 33 77
[email protected]
www.pharmetheus.com
Phone, Office: +46 (0)18 513 328
Uppsala Science Park, Dag Hammarskjölds väg 36B
SE-752 37 Uppsala, Sweden
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Quoted reply history
> On 22 Mar 2021, at 14:22, Hammami, Ibtihel /FR <[email protected]>
> wrote:
>
> Hi,
> We would like to compute a covariate inclusion statistical power based on
> the Wald test and using SE given by the fisher information matrix.
> Is there any method to implement this directly in NONMEM or is there at least
> a way to output the Fisher Information matrix in NONMEM?
>
> Thank you.
Hi Ibtihel,
I think you are probably asking for covariance matrix of the parameter
estimates. This should automatically be outputted as the .cov file assuming
that the $COV step runs successfully. Note that since NONMEM minimizes a
function related to -2LL, the Hessian (R matrix) in NONMEM is equivalent to
Fisher's Informaton matrix. I know you can print the R matrix in the NONMEM
output and I assume this can also be outputted to a file.perhaps others
might know
I'll leave it for you to decide whether you really want to perform power
calculations say to design/justify a sample size to detect the covariate
effect using a Wald-based test as opposed to performing simulations and
relying on a likelihood ratio test.
Ken
Kenneth G. Kowalski
Kowalski PMetrics Consulting, LLC
Email: <mailto:[email protected]> [email protected]
Cell: 248-207-5082
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Hammami, Ibtihel /FR
Sent: Monday, March 22, 2021 9:22 AM
To: [email protected]
Subject: [NMusers] Statistical power computation based on the wald test
Hi,
We would like to compute a covariate inclusion statistical power based on
the Wald test and using SE given by the fisher information matrix.
Is there any method to implement this directly in NONMEM or is there at
least a way to output the Fisher Information matrix in NONMEM?
Thank you.
--
This email has been checked for viruses by Avast antivirus software.
https://www.avast.com/antivirus
This is a related article using Monte Carlo Power Mapping (MCPM) that I
recently used. It is time efficient and takes the spirit of simulation and LLR
test.
Vong C, Bergstrand M, Nyberg J, Karlsson MO. Rapid sample size calculations for
a defined likelihood ratio test-based power in mixed-effects models. AAPS J.
2012 Jun;14(2):176-86. doi: 10.1208/s12248-012-9327-8. Epub 2012 Feb 17. PMID:
22350626; PMCID: PMC3326172.
https://pubmed.ncbi.nlm.nih.gov/22350626/
Regards,
Ayyappa
Quoted reply history
> On Mar 22, 2021, at 9:41 AM, Ken Kowalski <[email protected]> wrote:
>
>
> Hi Ibtihel,
>
> I think you are probably asking for covariance matrix of the parameter
> estimates. This should automatically be outputted as the .cov file assuming
> that the $COV step runs successfully. Note that since NONMEM minimizes a
> function related to -2LL, the Hessian (R matrix) in NONMEM is equivalent to
> Fisher’s Informaton matrix. I know you can print the R matrix in the NONMEM
> output and I assume this can also be outputted to a file…perhaps others might
> know
>
> I’ll leave it for you to decide whether you really want to perform power
> calculations say to design/justify a sample size to detect the covariate
> effect using a Wald-based test as opposed to performing simulations and
> relying on a likelihood ratio test.
>
> Ken
>
> Kenneth G. Kowalski
> Kowalski PMetrics Consulting, LLC
> Email: [email protected]
> Cell: 248-207-5082
>
>
>
> From: [email protected] [mailto:[email protected]] On
> Behalf Of Hammami, Ibtihel /FR
> Sent: Monday, March 22, 2021 9:22 AM
> To: [email protected]
> Subject: [NMusers] Statistical power computation based on the wald test
>
> Hi,
> We would like to compute a covariate inclusion statistical power based on
> the Wald test and using SE given by the fisher information matrix.
> Is there any method to implement this directly in NONMEM or is there at least
> a way to output the Fisher Information matrix in NONMEM?
>
> Thank you.
>
>
> Virus-free. www.avast.com
Hello all:
I would just like to add some information to help the discussion along.
In addition to the variance-covariance matrix that is outputted in the .cov
file that Ken mentioned, the Fisher information matrix itself (inverse of
variance-covariance) is also outputted in the .coi file. Additional files,
such as .rmt (R matrix), and .smt (S matrix) are also outputted upon user
request ($COV PRINT=RS, for example)
A test related to Wald and log-likelihood ratio tests is the Lagrange
Multiplier test. For this purpose, NONMEM outputs the following in the .ext
file:
Iteration -1000000008 lists the partial derivative of the log likelihood (-1/2
OFV) with respect to each estimated parameter.
PFIM, POPED, and NONMEM's $DESIGN calculate the expected FIM with respect to
the data, and the expected value R matrix is equivalent to the expected value
of the S matrix. That is, Ey(R)= Ey(S).
Several companion/interface software to NONMEM have additional model evaluation
facilities, such as stepwise covariate model (scm) building in Perl Speaks
NONMEM, and Wald test in PDxPop.
Robert J. Bauer, Ph.D.
Senior Director
Pharmacometrics R&D
ICON Early Phase
820 W. Diamond Avenue
Suite 100
Gaithersburg, MD 20878
Office: (215) 616-6428
Mobile: (925) 286-0769
[email protected]<mailto:[email protected]>
http://www.iconplc.com
Hi Bob,
Just a point of clarification. If the default sandwich estimator is used to
estimate the covariance matrix then the .coi file outputs the inverse of this
sandwich estimator, ie., R(S^-1)R …correct? If so, and maybe this is just
semantics but I don’t think we would refer to R(S^-1)R as the Fisher
information matrix. However, both R and S can be considered equivalent FIM
under certain regularity conditions. Nevertheless, if one wanted to determine
a D-optimal design I suppose maximizing the determinant of R(S^-1)R could be a
reasonable thing to do. Your thoughts?
Ken
Kenneth G. Kowalski
Kowalski PMetrics Consulting, LLC
Email: <mailto:[email protected]> [email protected]
Cell: 248-207-5082
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Bauer, Robert
Sent: Wednesday, March 24, 2021 2:18 PM
To: [email protected]
Subject: RE: [EXTERNAL] RE: [NMusers] Statistical power computation based on
the wald test
Hello all:
I would just like to add some information to help the discussion along.
In addition to the variance-covariance matrix that is outputted in the .cov
file that Ken mentioned, the Fisher information matrix itself (inverse of
variance-covariance) is also outputted in the .coi file. Additional files,
such as .rmt (R matrix), and .smt (S matrix) are also outputted upon user
request ($COV PRINT=RS, for example)
A test related to Wald and log-likelihood ratio tests is the Lagrange
Multiplier test. For this purpose, NONMEM outputs the following in the .ext
file:
Iteration -1000000008 lists the partial derivative of the log likelihood (-1/2
OFV) with respect to each estimated parameter.
PFIM, POPED, and NONMEM’s $DESIGN calculate the expected FIM with respect to
the data, and the expected value R matrix is equivalent to the expected value
of the S matrix. That is, Ey(R)= Ey(S).
Several companion/interface software to NONMEM have additional model evaluation
facilities, such as stepwise covariate model (scm) building in Perl Speaks
NONMEM, and Wald test in PDxPop.
Robert J. Bauer, Ph.D.
Senior Director
Pharmacometrics R&D
ICON Early Phase
820 W. Diamond Avenue
Suite 100
Gaithersburg, MD 20878
Office: (215) 616-6428
Mobile: (925) 286-0769
[email protected] <mailto:[email protected]>
www.iconplc.com http://www.iconplc.com
Thanks, Bob. This makes sense.
Ken
Sent from my iPhone
Quoted reply history
> On Mar 24, 2021, at 5:27 PM, Bauer, Robert <[email protected]> wrote:
>
>
> Ken:
>
> Yes, if $COV MATRIX is not specified, then .cov and .coi contain the
> respective sandwich versions.
>
> According to Wikipedia ( https://en.wikipedia.org/wiki/Fisher_information )
> the proper Fisher information matrix is defined as
>
> “Formally, it is the variance of the score, or the expected value of the
> observed information”
>
> which is E(S) (at the maximum likelihood positon), and it is equivalent to
> E(R) (at the maximum likelihood position). So, it seems that neither a
> finite data R nor finite data S are formally a FIM, but if one is going to
> use a practically assessed (on finite data) FIM, R is preferred when there
> are few subjects. With sufficient data available, S approaches R, so that S
> and R*Sinv*R may be used as well.
>
> Robert J. Bauer, Ph.D.
> Senior Director
> Pharmacometrics R&D
> ICON Early Phase
> 820 W. Diamond Avenue
> Suite 100
> Gaithersburg, MD 20878
> Office: (215) 616-6428
> Mobile: (925) 286-0769
> [email protected]
> www.iconplc.com
>
> From: Ken Kowalski <[email protected]>
> Sent: Wednesday, March 24, 2021 1:34 PM
> To: Bauer, Robert <[email protected]>; [email protected]
> Subject: RE: [EXTERNAL] RE: [NMusers] Statistical power computation based on
> the wald test
>
> Hi Bob,
>
> Just a point of clarification. If the default sandwich estimator is used to
> estimate the covariance matrix then the .coi file outputs the inverse of this
> sandwich estimator, ie., R(S^-1)R …correct? If so, and maybe this is just
> semantics but I don’t think we would refer to R(S^-1)R as the Fisher
> information matrix. However, both R and S can be considered equivalent FIM
> under certain regularity conditions. Nevertheless, if one wanted to
> determine a D-optimal design I suppose maximizing the determinant of R(S^-1)R
> could be a reasonable thing to do. Your thoughts?
>
> Ken
>
> Kenneth G. Kowalski
> Kowalski PMetrics Consulting, LLC
> Email: [email protected]
> Cell: 248-207-5082
>
>
>
> From: [email protected] [mailto:[email protected]] On
> Behalf Of Bauer, Robert
> Sent: Wednesday, March 24, 2021 2:18 PM
> To: [email protected]
> Subject: RE: [EXTERNAL] RE: [NMusers] Statistical power computation based on
> the wald test
>
> Hello all:
> I would just like to add some information to help the discussion along.
>
> In addition to the variance-covariance matrix that is outputted in the .cov
> file that Ken mentioned, the Fisher information matrix itself (inverse of
> variance-covariance) is also outputted in the .coi file. Additional files,
> such as .rmt (R matrix), and .smt (S matrix) are also outputted upon user
> request ($COV PRINT=RS, for example)
>
> A test related to Wald and log-likelihood ratio tests is the Lagrange
> Multiplier test. For this purpose, NONMEM outputs the following in the .ext
> file:
> Iteration -1000000008 lists the partial derivative of the log likelihood
> (-1/2 OFV) with respect to each estimated parameter.
>
> PFIM, POPED, and NONMEM’s $DESIGN calculate the expected FIM with respect to
> the data, and the expected value R matrix is equivalent to the expected value
> of the S matrix. That is, Ey(R)= Ey(S).
>
> Several companion/interface software to NONMEM have additional model
> evaluation facilities, such as stepwise covariate model (scm) building in
> Perl Speaks NONMEM, and Wald test in PDxPop.
>
>
> Robert J. Bauer, Ph.D.
> Senior Director
> Pharmacometrics R&D
> ICON Early Phase
> 820 W. Diamond Avenue
> Suite 100
> Gaithersburg, MD 20878
> Office: (215) 616-6428
> Mobile: (925) 286-0769
> [email protected]
> www.iconplc.com
>
>
>
>