RE: [EXTERNAL] RE: 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: <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