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RE: st: Number Needed to be Treated (NNT)


From   "Newson, Roger B" <r.newson@imperial.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Number Needed to be Treated (NNT)
Date   Thu, 2 Aug 2007 21:59:36 +0100

Thanks to Anders for telling us all about this paper, which is in a
special issue of Statistics in Medicine with special papers on the
Mann-Witney test.

A possible way to get a confidence interval for the NNT, based on this
method, might involve using -somersd- together with -parmest- to produce
an output dataset (or resultsset) of confidence intervals for Somers' D,
and then carrying out an end-point transformation on the confidence
interval for Somers' D to derive a confidence interval for the NNT.

Best wishes

Roger


Roger Newson
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: r.newson@imperial.ac.uk 
Web page: www.imperial.ac.uk/nhli/r.newson/
Departmental Web page:
http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/pop
genetics/reph/

Opinions expressed are those of the author, not of the institution.

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Anders
Alexandersson
Sent: 02 August 2007 21:20
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: Number Needed to be Treated (NNT)

Svend Juul and then Nick Cox wrote a small program to calculate number
needed to be treated (NNT) based on -cs- and this was one example
output:
>     NNT = 15.230769  (95% CI: 5.0701399; -15.169883)

NNT is also related to the probability that variable for first group
is larger than for second group, P(X>Y). For a reference, see Acion,
L. et al. 2006. "Probabilistic index: an intuitive non-parametric
approach to measuring the size of treatment effects". Statistics in
Medicine 25(4): 591-602. There was a follow-up with reply later on
pages 3944-3948.
It seems to me that NNT = -(1/(2P(X>Y)-1)).

Therefore, you can also calculate NNT quickly using either -ranksum-
with the porder option or Roger Newson's command -somersd- with the
tr(c) option:
. ranksum low, by(x) porder-
[output ommitted]
. di -(1/((2*0.467)-1))
15.151515

or, more precise and automated:
. somersd  x low, tr(c)
. di -(1/((2*(1-_b[low]))-1))
15.230769

This does not give a 95% confidence interval (yet) but is another way
of calculating NNT.

Anders Alexandersson
andersalex@gmail.com
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