# RE: How to calculate confidence interval (CI) and prediction interval (PI) of individual prediction (IPRED) in NONMEM

From: Bauer, Robert <Robert.Bauer>
Date: Thu, 19 Jul 2018 18:50:07 +0000

NONMEM 7.4 provides a straight-forward means of evaluating the standard error of IPRED and other table outputted parameters, by use of the option \$TABLE … VARCALC=1. Please see nm743.pdf for more information on this, located at

https://nonmem.iconplc.com/nonmem743

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 c.com>
www.iconplc.com<http://www.iconplc.com/>

From: owner-nmusers
Sent: Wednesday, July 18, 2018 8:56 PM
To: nmusers
Subject: [NMusers] How to calculate confidence interval (CI) and prediction interval (PI) of individual prediction (IPRED) in NONMEM

Dear NMusers,

Someone (several months ago via email) asked me how to calculate a confidence interval and prediction interval for individual prediction using R (might be with my “wnl" package”).

At that time, I suggested the delta method for a confidence interval and simulation for prediction interval like visual predictive check (VPC).

He/She then asked me how about using NONMEM script in p220 (for the prediction interval) and p221 (for the confidence interval) of Ette and William's ‘Pharmacometrics: The Science of Quantitative Pharmacology’(2007), when I could not answer about that and still recommended to use simulation technique.

Now I can answer a little more about how to calculate those (although somewhat naïve way) in NONMEM (maybe in older versions only).

NONMEM code in p220 should be corrected like the following;

“VARCP = 2*G(1,1)*G(2,1)*OMEGAF(1,2) + VARCP

“VARCP = 2*G(1,1)*G(3,1)*OMEGAF(1,3) + VARCP

“VARCP = 2*G(2,1)*G(3,1)*OMEGAF(2,3) + VARCP

“VARCP = VARCP + IPRED**2*SIGMAF(1,1) + VARCP*SIGMAF(1,1) + SIGMAF(2,2)

And, NONMEM code in p221 should be corrected like the following;

“VARCP = 2*G(1,1)*G(2,1)*OMEGAF(1,2) + VARCP

“VARCP = 2*G(1,1)*G(3,1)*OMEGAF(1,3) + VARCP

“VARCP = 2*G(1,1)*G(4,1)*OMEGAF(1,4) + VARCP

“VARCP = 2*G(2,1)*G(3,1)*OMEGAF(2,3) + VARCP

“VARCP = 2*G(2,1)*G(4,1)*OMEGAF(2,4) + VARCP

“VARCP = 2*G(3,1)*G(4,1)*OMEGAF(3,4) + VARCP

One of the references for the biggest different line is p180 of <Mood AM, Graybill F, Boes DC. Introduction to the theory of statistics. 3e. 1974>.

Sincerely,

Kyun-Seop Bae MD PhD

Professor

Department of Clinical Pharmacology and Therapeutics

Asan Medical Center, University of Ulsan, Republic of Korea
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