# RE: Statistical power of covariate inclusion in popPK models

From: Ken Kowalski <kgkowalski58>
Date: Wed, 24 Mar 2021 09:35:14 -0400

Hi Ibtihel,

Ken

From: owner-nmusers
Behalf Of Hammami, Ibtihel /FR
Sent: Wednesday, March 24, 2021 5:47 AM
To: nmusers
Subject: [NMusers] Statistical power of covariate inclusion in popPK models

Hi,

1. Is it mandatory to use the matrix R as a variance co-variance
matrix to obtain the FIM? In case we have already used other type of
variance co-variance matrix, should we rerun the model with matrix R
setting?

Ken: The Hessian (or R matrix) is the 2nd derivative matrix of -LL which
is equivalent to the FIM. However, you don't have to invert the Hessian to
obtain the covariance matrix. For example, in NONMEM the default estimator
is the sandwich estimator, (R^-1)S(R^-1), where S is the 1st derivative
(gradient) cross-product matrix. Note that R^-1 as well as (R^-1)S(R^-1)
are consistent estimators of the covariance matrix and thus asymptotically,
both should converge to the same result as the sample size increases.
However, most nonlinear regression packages invert the Hessian (R matrix) as
the default estimate of the covariance matrix of the parameter estimates.

2. How critical is the estimation method for the computed SE? In other
words, is it relevant to compare two powers computed based on two standard
errors givens by different estimation algorithms?

For example, if we used FOCE-INTER to minimize our model, could we compare
the power (based on the Wald test) to results given by PFIM which is based
on FO ?

Ken: The R and S matrices involve taking 1st and 2nd derivatives of the
log-likelihood and evaluating them at the final estimates of the parameters.
Thus, if you use different approximations of the likelihood (e.g., FOCEI or
FOCE or FO) and you get different final estimates of the population
parameters you will also get different values for the R and S matrices.

Just for a little bit of background to clarify why we are interested in the
Wald test.

We are working on the comparison of different methods to compute the
statistical power of covariate inclusion in popPK models (SSE (gold
standard), MCMP, PPE , and Wald test). We have also included the Wald test
in our comparison because it is the fastest method and mostly because it
used by optimal designs software. R Therefore, the evaluation of the
accuracy of the power derived by this method could facilitate the bridging
step between model validation and the design of upcoming clinical trials
using optimal design software.

Ken: Most optimal design software (e.g., D-optimality) I imagine would
use the Hessian (R matrix) rather than the sandwich estimator, however, I'm
not familiar with what PFIM uses. You may want to follow up with the PFIM
developers to find out what they use.

Cordially.

Ibtihel HAMMAMI.

--
This email has been checked for viruses by Avast antivirus software.
https://www.avast.com/antivirus

Received on Wed Mar 24 2021 - 09:35:14 EDT

The NONMEM Users Network is maintained by ICON plc. Requests to subscribe to the network should be sent to: nmusers-request@iconplc.com.

Once subscribed, you may contribute to the discussion by emailing: nmusers@globomaxnm.com.