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Re: [EXTERNAL] RE: Statistical power computation based on the wald test

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

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