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