```From: Xiaofeng Wang - xiaofeng.wang@bms.com
Subject: [NMusers] simulation
Date: 1/27/2004 10:50 AM

Colleagues:
If I know the PK model, the matrix of Omega, Sigma, also the
covariate models,  how can I predict the time-concentration of a
particular subject with 95% confidence interval using NONMEM?
xiaofeng
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From: Xiaofeng Wang - xiaofeng.wang@bms.com
Subject: RE: [NMusers] simulation
Date: 1/27/2004 11:27 AM

Hello again:
I would like to calculate the 95% confident interval through
variance matrix, C.  Since I already know Omega, Sigma, the PK
models, and the covariate model, mathematically the
variance-covariance matrix of yi, Ci, can be calculated.  In this
case, I don't have to simulate 1000 times and then calculate the
mean and 95% confident interval.
xiaofeng
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From: "Kowalski, Ken" - Ken.Kowalski@pfizer.com
Subject: RE: [NMusers] simulation
Date: 1/27/2004 1:10 PM

Xiaofeng,

Essentially what you are asking for are the standard errors (SEs) for the
IPREDs.  These SEs are not easy to get as they involve a second level of
estimation provided by the empirical Bayes predictions of the ETAs.  You
might be able to trick NONMEM to provide the covariance matrix for the ETA
predictions by constructing single subject datasets where the ETAs are the
parameters you want to estimate to minimize the OFV and the \$COV output from
such NONMEM runs would provide the covariance matrix of these ETA
predictions.  I believe examples of this are provided somewhere in the
NONMEM manuals and/or one of the NONMEM workshop course notes.  However, I
don't know if this approach gives you the same ETA predictions as what
NONMEM provides directly from the posthoc and/or conditional estimation
methods when fitting the population model.  Even so, once you get the
covariance matrix of the ETA predictions for a given subject you still need
to do some sort of linearization to get the SEs for the IPREDs
(incorporating both the uncertainty in the population estimates and the ETA
predictions).

A few years ago I was interested in looking at whether an improvement could
be made on the original GAM procedure by using the covariance matrix of the
ETA predictions to properly weight them in the GAM estimation.  I came to
the conclusion that estimating these covariance matrices for the ETA
predictions was more trouble than its worth.

I'm interested if anyone else in Nmusers has tried to do this and whether
they have a slicker approach to obtain these SEs.

Regards,

Ken
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From: Xiaofeng Wang - xiaofeng.wang@bms.com
Subject: RE: [NMusers] simulation
Date: 1/27/2004 2:14 PM

Hi Ken:
Thank you for message and elaboration of the question I have.
yes, you are right that I was asking for the SEs for the IPREDs.
I tried to go in this direction:
for example, from FO, the PK model can be linearized as yij=fi(Theta1, ...)
+gij etai +hij epij, where gij is the partial derivative of the model at etai=0.
then the variance of yij is G'i Omega Gi +diag (Hi'Sigma Hi).  If I have
the PK model, the covariate model, as well as Omega and Sigma, the
variance (or SEs) of yij can be calculated and then the 95% CI of yij.
From NONMEN manual, the matrix G and H can be obtained when running
estimation (I don't know how to write the code to get these two matrix,
if anyone can point it out for me).  I dont' know in the simulation mode,
if G and H can be also obtained.  In fact, H is easy to obtained once the
error model was determined.  However, G is involved the estimate of all
the partial derivative at eta.
xiaofeng
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From: "Hutmacher, Matt" - mhutmach@amgen.com
Subject: RE: [NMusers] simulation
Date: 1/27/2004 3:46 PM

Xiaofeng,

As Ken stated, it is a bit of work to try and get the covariance matrix of
estimates for the empirical Bayes predictions of the etas.  If you are able
to use SAS (or know someone that does), it is much simpler to get the
standard errors you desire.  These quantities are computed by the delta
method and can be output using a single line of code.  However, if you have
a complex model or a nonstandard dosing history, it will require some effort
to program the model for fitting.

Matt
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