I have followed with great interest the interchange of emails over
last weekend, involving Steve Simon, Brian Budenholzer, Kevork
Hopayian, Klasien Matter-Walstra and Michael Bigby.
Maybe I excessively censored my straw poll, possibly incurring
selection bias in the process, but it appears that 2 out of 2
respondents who expressed a preference (BB & MB) preferred the
singularity of the NNT as the method of expressing a treatment's
possible inefficacy! So be it.
Even away from the singularity, the ARR and NNT, though they contain
equivalent information, look rather different mathematically. I
wouldn't advocate bandying about small decimals like 0.00235,
but 2.35 per 1000 seems assimilable. A fair degree of rounding is
sensible, when professionals talk about study results informally
among themselves, but the definitive documentation should give things
to "about two-and-a-half" significant figures, whichever scale is
used. (I can't give a reference for this quote, I'm afraid.)
KH and KM-W extend the discussion to communication with patients. KH
asks whether there is evidence that NNT is superior to ARR in this
respect. First, I'd point out that on several occasions I've seen
reference made to evidence that professionals can form quite
different interpretations of the same data, presented in different
ways - though I haven't the reference to hand - I guess that it
follows that patients would do the same.
But the issue goes a lot deeper than this. The British education
system, at least, has always failed to instil basic statistical
numeracy into the population. The most persuasive evidence
for this is the tremendous success of the national lottery etc.
And from what I've seen, similar organisations in other countries
have no problem maintaining profitability. The national curriculum
is going some way to redress the balance, but it isn't easily
achieved. The upshot of all this is, not whether Joe or Jo Public
can understand an NNT of 9 better than an ARR of 11%, but just what
either of these expressions of difference in risk really means to
them. With a naturally totally selfish outlook here, as pointed out
by KM-W, your being the 1 in 9 doesn't disadvantage the other
patients in the queue as they're all independent, so "you're the only
one that matters" is unequivocally right. (Though they often can't
see this, and invoke the "law of averages".) And with a (generally)
very fatalistic, external locus of control - again, evidenced by the
success of the lottery - which is often why they persist in the
lifestyle that leads to "caseness". Sorry if this sounds very
right-wing - I believe fully in this half of the inverse care law, as
well as in the left-wing aspect, what Julian Tudor Hart meant in
terms of provision being inversely related to need - and which is
invariant under changes of colour of government which may be merely
cosmetic.
Furthermore, I'd question whether the ARR vs. NNT issue as we've
discussed it really carries across in the same way to discussions
with patients. I've been very scathing about the NNT, from the
standpoint that I'm a statistician and it is my professional role to
communicate with clinicians about how evidence should be expressed,
*together with an appropriate expression of sampling imprecision*. I
realise that many of those using these measures are clinicians, who
are in the *very different* business of explaining to patients and
relatives. In this situation, there does not appear to be a place
for putting a quantitative expression of uncertainty around the
estimated ARR or NNT - if the evidence is very poor, I guess you just
say it's very poor.
Also, even if you are basing your advice to the patient on a
meta-analysis rather than a single study, you probably won't want to
place too much emphasis on the exact ARR or NNT that was calculated,
but you'll tend to modify it on an ad-hoc basis, either upwards or
downwards, in the light of the great deal of information you already
know about the patient - even if only history, age and gender.
Traditionally, the reporting of calculated numerical risks to
patients has been the preserve of medical geneticists, where it is of
course appropriate. I think that in other contexts, notwithstanding
the availability of the evidence base, we should give careful thought
to whether it is really appropriate to do so.
Robert Newcombe.
..........................................
Robert G. Newcombe, PhD, CStat, Hon MFPHM
Senior Lecturer in Medical Statistics
University of Wales College of Medicine
Heath Park
Cardiff CF14 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
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