From: kgkowalski58

Date: Wed, 24 Mar 2021 17:51:28 -0400

Thanks, Bob. This makes sense.

Ken

Sent from my iPhone

*> On Mar 24, 2021, at 5:27 PM, Bauer, Robert <Robert.Bauer *

e:

*>
*

*>
*

*> Ken:
*

*>
*

*> Yes, if $COV MATRIX is not specified, then .cov and .coi contain the respe=
*

ctive 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 o=
*

f 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 fi=

nite 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 f=

ew 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
*

*> Robert.Bauer *

*> www.iconplc.com
*

*>
*

*> From: Ken Kowalski <kgkowalski58 *

*> Sent: Wednesday, March 24, 2021 1:34 PM
*

*> To: Bauer, Robert <Robert.Bauer *

*> Subject: RE: [EXTERNAL] RE: [NMusers] Statistical power computation based o=
*

n the wald test

*>
*

*> Hi Bob,
*

*>
*

*> Just a point of clarification. If the default sandwich estimator is used t=
*

o estimate the covariance matrix then the .coi file outputs the inverse of t=

his sandwich estimator, ie., R(S^-1)R …correct? If so, and maybe th=

is 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 equ=

ivalent FIM under certain regularity conditions. Nevertheless, if one wante=

d 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: kgkowalski58 *

*> Cell: 248-207-5082
*

*>
*

*>
*

*>
*

*> From: owner-nmusers *

n Behalf Of Bauer, Robert

*> Sent: Wednesday, March 24, 2021 2:18 PM
*

*> To: nmusers *

*> Subject: RE: [EXTERNAL] RE: [NMusers] Statistical power computation based o=
*

n 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 .co=
*

v file that Ken mentioned, the Fisher information matrix itself (inverse of v=

ariance-covariance) is also outputted in the .coi file. Additional files, s=

uch as .rmt (R matrix), and .smt (S matrix) are also outputted upon user req=

uest ($COV PRINT=RS, for example)

*>
*

*> A test related to Wald and log-likelihood ratio tests is the Lagrange Mult=
*

iplier test. For this purpose, NONMEM outputs the following in the .ext fil=

e:

*> 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 r=
*

espect to the data, and the expected value R matrix is equivalent to the exp=

ected value of the S matrix. That is, Ey(R)= Ey(S).

*>
*

*> Several companion/interface software to NONMEM have additional model evalu=
*

ation facilities, such as stepwise covariate model (scm) building in Perl Sp=

eaks 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
*

*> Robert.Bauer *

*> www.iconplc.com
*

*>
*

*>
*

*>
*

*> ICON plc made the following annotations.
*

*> --------------------------------------------------------------------------=
*

----

*> This e-mail transmission may contain confidential or legally privileged in=
*

formation that is intended only for the individual or entity named in the e-=

mail address. If you are not the intended recipient, you are hereby notified=

that any disclosure, copying, distribution, or reliance upon the contents o=

f this e-mail is strictly prohibited. If you have received this e-mail trans=

mission in error, please reply to the sender, so that ICON plc can arrange f=

or proper delivery, and then please delete the message.

*>
*

*> Thank You,
*

*>
*

*> ICON plc
*

*> South County Business Park
*

*> Leopardstown
*

*> Dublin 18
*

*> Ireland
*

*> Registered number: 145835
*

*>
*

*>
*

*> <image001.jpg>
*

*> Virus-free. www.avast.com
*

*>
*

Received on Wed Mar 24 2021 - 17:51:28 EDT

Date: Wed, 24 Mar 2021 17:51:28 -0400

Thanks, Bob. This makes sense.

Ken

Sent from my iPhone

e:

ctive sandwich versions.

the proper Fisher information matrix is defined as

f the observed information”

E(R) (at the maximum likelihood position). So, it seems that neither a fi=

nite 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 f=

ew subjects. With sufficient data available, S approaches R, so that S and R=

*Sinv*R may be used as well.

n the wald test

o estimate the covariance matrix then the .coi file outputs the inverse of t=

his sandwich estimator, ie., R(S^-1)R …correct? If so, and maybe th=

is 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 equ=

ivalent FIM under certain regularity conditions. Nevertheless, if one wante=

d 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?

n Behalf Of Bauer, Robert

n the wald test

v file that Ken mentioned, the Fisher information matrix itself (inverse of v=

ariance-covariance) is also outputted in the .coi file. Additional files, s=

uch as .rmt (R matrix), and .smt (S matrix) are also outputted upon user req=

uest ($COV PRINT=RS, for example)

iplier test. For this purpose, NONMEM outputs the following in the .ext fil=

e:

-1/2 OFV) with respect to each estimated parameter.

espect to the data, and the expected value R matrix is equivalent to the exp=

ected value of the S matrix. That is, Ey(R)= Ey(S).

ation facilities, such as stepwise covariate model (scm) building in Perl Sp=

eaks NONMEM, and Wald test in PDxPop.

----

formation that is intended only for the individual or entity named in the e-=

mail address. If you are not the intended recipient, you are hereby notified=

that any disclosure, copying, distribution, or reliance upon the contents o=

f this e-mail is strictly prohibited. If you have received this e-mail trans=

mission in error, please reply to the sender, so that ICON plc can arrange f=

or proper delivery, and then please delete the message.

Received on Wed Mar 24 2021 - 17:51:28 EDT