From:bgarcia@hsvo.insalud.es
Subject:[NMusers] Confidence interval
Date:Mon, 19 Aug 2002 12:25:56 +0200

I have a doubt about the lower bound of confidence interval of OMEGA and SIGMA. Is it possible to obtain a valid output when lower bound is less
than 0?. Thank you.

Benito García 
Pharmacy Service 
Hospital Severo Ochoa 
Leganés - Madrid - Spain 
bgarcia@hsvo.insalud.es
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From:Nick Holford 
Subject: Re: [NMusers] Confidence interval
Date:Mon, 19 Aug 2002 23:42:11 +1200

Benito,

You are quite correct to be worried about using the asymptotic standard errors produced by
NONMEM to construct a confidence interval. It is not unusual to find examples were such a
confidence interval is not possible e.g. negative $OMEGA.

The problem arises because the SEs produced by NONMEM are only asymptotic estimates BUT more
importantly you must assume a symmetrical distribution to construct a CI. When CIs are
constructed using methods such as the log likelihood profile or by non-parametric bootstrapping
they are often found to be assymetrical. If you really want to know the CI for your parameters
then I suggest you consider using the log likelihood profile method (5-10 NONMEM runs per
parameter) or bootstrapping (1000 NONMEM runs but this will let you construct CI on all
parameters in the model).

Nick

-- 
Nick Holford, Divn Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
email:n.holford@auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/

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