From: "INTV (Ivan Nestorov)" nestorvi@zgi.com
Subject: [NMusers] Bootstrap question
Date: Fri, 22 Sep 2006 15:30:23 -0700

Dear NONMEM,

I would like to bootstrap a dataset that includes 4 dosing
arms with 15, 20, 15, and 25 subjects in each arm respectively.

Do I bootstrap from within each arm so that I have the above
sample sizes per arm in each bootstrap file or I just bootstrap
the data as a whole and leave the distribution of subjects across
the four arms to the random number generators.

Thanks.

Ivan Nestorov 
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From: Nick Holford n.holford@auckland.ac.nz
Subject: Re: [NMusers] Bootstrap question
Date: Sat, 23 Sep 2006 10:55:39 +1200

Ivan,

If the purpose of the BS is to estimate the uncertainty in the parameter estimates
obtained from a particular data set then (e.g. 90% confidence interval [CI]) then
the BS should try to retain the original design i.e. you should bootstrap from each
arm separately. Note that in theory one should also maintain the same within subject
design i.e. the same sampling times. With a non-parametric bootstrap the latter is
quite hard to do (if you use actual rather than nominal times) and most people
(including me) ignore this requirement. 

In fact, I would not worry too much about maintaining the original number of subjects
per arm. I doubt if it would make much difference which way you did it when it came to
interpreting the results. Ignoring the treatment design and doing a non-parametric bootstrap
across the whole data set would probably inflate the CI a bit. For typical quantitative
applications of the CI (e.g. testing hypotheses for model building) then this bias would
tend to make you be a little bit more parsiminous and conservative before accepting new
parameters in the model.

In my experience it is unusual that anyone would really care much about the bias of a CI
for the parameter estimates. Its just something one does to get some rough idea of the
uncertainty and to satisfy obsessional journal reviewers/editors.

Nick
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/
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From: Leonid Gibiansky leonidg@metrumrg.com
Subject: Re: [NMusers] Bootstrap question
Date: Fri, 22 Sep 2006 19:03:13 -0400

If kinetics is linear, it should not matter. If you observe (or would like to
investigate) dose effect, I would keep relative fractions of arm relatively
stable, for example by sampling within each group as you suggested

Leonid 
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From: Chuanpu.Hu@sanofi-aventis.com
Subject: Re: [NMusers] Bootstrap question
Date: Tue, 26 Sep 2006

Very well said, Nick. Although when we did this, we really cared.  :-) 
 
Chuanpu
 
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From: Nick Holford n.holford@auckland.ac.nz
Subject: Re: [NMusers] Bootstrap question
Date: Tue, 26 Sep 2006 08:32:00 +1200

Chuanpu,

I'd be interested to know why you really cared about the bias in a bootstrap CI.
Its hard to imagine a situation when one might care for the CI on PK parameters
but perhaps you were really interested in a PD parameter?

Nick
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/
_______________________________________________________

From: Mark Sale - Next Level Solutions mark@nextlevelsolns.com
Subject: Re: [NMusers] Bootstrap question 
Date: Tue, 26 Sep 2006

Nick,

I can think of two:

1. PPC - including uncertainty of parameters, although
yours and Jogas work suggests it doesn't matter.

2. Bayesian dose adjustment

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From: Nick Holford n.holford@auckland.ac.nz
Subject: Re: [NMusers] Bootstrap question
Date: Tue, 26 Sep 2006 10:40:52 +1200

Mark,

Your responses are too short for me to understand why bias in a bootstrap CI is important in
these cases. Can you explain in each case (with an explicit example) why you think bias would
be important and giving an idea of what magnitude of bias you would consider important?

It should be kept firmly in mind that CIs obtained with the asymptotic standard error method
are likely to be biased because 1) they are asymptotic and 2) the CI calculation nearly always
is based on assuming a normal distribution and thus symmetry of the interval.

Nick
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/
_______________________________________________________