Just a couple more comments. This may be boring to some people, but I have
strong opinions about this issue. We are all awash in a sea of numbers (I've
contributed a few drops to this sea, myself). The trick is to present all
these numbers in a way that doesn't drown our readers.
Point #1. Rory O'Conor talks about rounding. A good reference for rounding
is Ehrenberg, A.S.C. (1981) "The Problem of Numeracy," The American
Statistician, 35(2), 67-71.
Ehrenberg stresses that you should never display three significant figures.
Always display only one or two figures. There are several reasons for this.
One that I remember is that quite often we want to compare two numbers by
subtracting one from another. It's a whole lot easier to do the subtraction
with numbers like 550 and 480, than with numbers like 549 and 482. Our short
term memory can only hold 3-4 pieces of information, and trying to
manipulate a pair of three digit numbers will overload short term memory.
In the context of NNTs, you might want to do division instead of
subtraction, but the same principle applies.
It is difficult emotionally to round to two significant digits, and I find
myself wanting to include that third digit (as I did in an earlier e-mail).
But that third digit is rarely helpful and it can hinder comprehension.
Point #2. Robert Newcombe argues that with the proper adjustment, small
fractions are easily assimilable. So even though .00235 is hard to work
with, 2.35 per thousand is easy to work with. I may be nitpicking, but I
still disagree. I always prefer working with whole numbers and the NNT is
usually a nice whole number. Also, I am indecisive by nature, and I hate to
choose between reporting 2.35 per thousand or 235 per hundred thousand.
Point #3. The idea of inverting an absolute risk reduction seems unnatural,
but there is a lot of precedent for such manipulation. We normally think
nothing of using logarithmic scales for measuring noise and earthquake
intensity, and the log transformation is a lot more difficult to explain
than an inverse transformation.
We also use an inverse transformation in other areas. When measuring how
long it takes for someone to perform a task, we can talk either about time
(the task takes five minutes) or speed (you complete 12 items every hour). I
switched units on you, but the second number is the inverse of the first
(and vice versa).
Perhaps this confusion about a confidence interval for NNT containing
infinity would be less problematic when we remind ourselves that someone
working at a speed of zero will take an infinite amount of time to complete
the task.
Point #4. When you are trying to decide between an absolute risk reduction
and a number needed to treat, why not present it both ways? It doesn't add
that much to the length of a paper, and most of us don't have a calculator
handy when we are reading JAMA.
Disclaimer#1. Effective presentation of research data is an art more than a
science, and I'm a lousy artist. So take everything I say with a grain of
salt.
Disclaimer #2. I think the issue of what patients comprehend is an important
one, but this is one area I can't comment on intelligently as I don't see
patients as part of my job. I'm not qualified to provide health care, but my
Ph.D. in Statistics does allow me to doctor numbers.
Final disclaimer. I don't disagree in substance with what most of the others
have written on this subject. If I do disagree, it is a question of degree.
It's a "yes, but" rather than a "no".
Steve Simon, [log in to unmask], Standard Disclaimer.
STATS - Steve's Attempt to Teach Statistics: http://www.cmh.edu/stats
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