Further to today's interchange of emails:
Weiya Zhang has suggested turning NNTs back into absolute risk
reductions. Rolf Engel responded, wouldn't it be easier to work
with ARRs from the beginning? I'd certainly go along with that.
Indeed, it's the ARR that is the basic quantity calculated - in the
simple case, just the difference between two proportions, p1=r1/n1 in
sample 1 and p2=r2/n2 in sample 2. The NNT then comes from inverting
the ARR, and a CI for the NNT is obtained by inverting the CI for the
ARR.
But this is the rub. Doug Altman's article (referred to by Zhang)
shows how to do this, and shows how it leads to a doubly infinite CI
for the NNT when the CI for the ARR spans 0, i.e. when p>0.05.
I don't think most clinicians can cope with this (I'd love to
have more than anecdotal evidence to base this on, but I'm scared of
risking mailbox overflow if I ask for a straw poll of you guys out
there). I'm sure it's easier to give point and interval estimates
for the ARR - which will be asymmetrical or more nearly symmetrical
anyway - preferably expressed on a percent scale. For example, the
ARR might be +10%, with 95% CI from -5% to +25%. The NNT is then 10,
with CI from -infinity to -20 and from -4 to +infinity. I know
which looks simpler to me. See
http://www.bmj.com/cgi/eletters/317/7168/1309#EL2
Robert Newcombe.
..........................................
Robert G. Newcombe, PhD, CStat, Hon MFPHM
Senior Lecturer in Medical Statistics
University of Wales College of Medicine
Heath Park
Cardiff CF4 4XN, UK.
Phone 01222 742329 or 742311
Fax 01222 743664
Email [log in to unmask]
Macros for good methods for confidence intervals
for proportions and their differences available at
http://www.uwcm.ac.uk/uwcm/ms/Robert.html
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|