From: Ken Kowalski <*kgkowalski58*>

Date: Wed, 24 Mar 2021 16:33:46 -0400

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 =

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:kgkowalski58

Cell: 248-207-5082

From: owner-nmusers

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 .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 Multi=

plier 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 ex=

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

Several companion/interface software to NONMEM have additional model evalua=

tion 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 <http://www.iconplc.com>

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Thank You,

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Ireland

Registered number: 145835

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Received on Wed Mar 24 2021 - 16:33:46 EDT

Date: Wed, 24 Mar 2021 16:33:46 -0400

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 =

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:kgkowalski58

Cell: 248-207-5082

From: owner-nmusers

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 .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 Multi=

plier 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 ex=

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

Several companion/interface software to NONMEM have additional model evalua=

tion 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 <http://www.iconplc.com>

ICON plc made the following annotations.

---------------------------------------------------------------------------=

---

This e-mail transmission may contain confidential or legally privileged inf=

ormation 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 notifie=

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

of this e-mail is strictly prohibited. If you have received this e-mail tr=

ansmission in error, please reply to the sender, so that ICON plc can arran=

ge for proper delivery, and then please delete the message.

Thank You,

ICON plc

South County Business Park

Leopardstown

Dublin 18

Ireland

Registered number: 145835

--

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Received on Wed Mar 24 2021 - 16:33:46 EDT