here is a response from doug altman, director of the centre for statistics
in medicine here in oxford, and a member of our centre.
cheers
dls
............................................................................
Prof David L. Sackett
Director, NHS R&D Centre for Evidence-Based Medicine
Consultant in Medicine Editor, Evidence-Based Medicine
Nuffield Department of Medicine, University of Oxford
Level 5, John Radcliffe Hospital, Oxford OX3 9DU, England
Phone: +44-(0)1865-221320 Fax: +44-(0)1865 222901
Email: [log in to unmask] WWW: http://cebm.jr2.ox.ac.uk
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Doug Altman writes:
Iain Buchan is right to draw attention to the improved formula developed
recently by Newcombe for the CI of the difference between two proportions.
This is a valuable advance, but the old (standard) formula works fine
except when the either the numbers of events or the observed proportions
are very small (or very near n or 1 respectively) - i.e it works most of
the time. I doubt whether the problems encountered by Tony Redmond are
related to this issue.
The primary reason for the discrepancies noted by Tony is likely to be the
fact that the formula given on the Bandolier web page is wrong (see PS
below). The simplest approach to getting the CI for the NNT is to calculate
the CI for the absolute risk difference (the difference between the
observed proportions) - which can be done using a simple formula found in
any good statistics book - and take reciprocals of these two values.
I might add that the Bandolier web page also says that when the difference
between the groups (the treatment effect) is not significant, then it is
'unwise to bother with the CI for the NNT'. I disagree - CIs are especially
useful when there is a so-called negative result, especially given that
trials tend to be too small to have adequate power to detect useful benefits.
@@@@ dls note: that's why, in the CATMaker, we calculate and display both
NNTs (e.g., 20 to infinity) and NNHs (e.g., 50 to infinity), recalling
that the "NN" when stated 20-50 gets between these two umbers via infinity
@@@@
The usual reason for not giving CIs for the NNT in such cases is that the
results may seem somewhat nonsensical. I have a paper due out soon in the
BMJ explaining how to calculate and present such confidence intervals even
when the treatment effect is not significant.
In this paper I also note that the term 'number needed to harm' (NNH) is
confusing and grammatically incorrect, and suggest that we use instead of
NNTB and NNTH - the number need to treat to benefit (or harm).
Doug Altman
PS The error in the formula on the Bandolier web page quoted is that there
should be yet another set of brackets around everything after 1/ at the
beginning. But the way of calculation given above is much simpler to follow.
_________________________________________________
Douglas G Altman Tel: +44 (0)1865 226799
ICRF Medical Statistics Group Fax: +44 (0)1865 226962
Centre for Statistics in Medicine
Institute of Health Sciences
Old Road, Headington email: [log in to unmask]
Oxford OX3 7LF, UK http://www.ihs.ox.ac.uk/csm
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