Some comments on NNT, NTN and ITI.
The paper by Bogaty with a proposal for a new statistic, the number
treated needlessly (NTN) or the index of therapeutic impotence (ITI), is
about an idea, rather than a method. So, when I proposed it, I was pushing
the limits of the inclusion criteria for best EBM methods paper. The
reason that I found the paper memorable is that it exposes an asymmetry in
the way that people react to statistics. Such asymmetries are well
documented and complicate decision-making. They are therefore important
tools in the spin doctor's toolkit.
What I mean by asymmetry is the psychological asymmetry in interpreting
information which can be presented as either a statement or
its "converse". There is a mathematical symmetry between a statement and
its "converse", similar to a mirror image. The "converse" carries exactly
the same information that the original statement did, but presents it in a
different way.
For example, I could say: "The probability of X happening is p". Or I
could say: "The probability of X not happenning is q".
Because we know that p + q = 1, the two statements carry exactly the same
information. Given one statement, we can work out what the other statement
must say. The 2 statements have a logical symmetry. But at the same time
they have a psychological asymmetry.
I think that NNT puts a positive spin on the facts. It seems to appeal to
the optimistic/gullable side of human nature. In contrast, NTN or ITI puts
a negative spin on the same facts. It seems to appeal to the
pessimistic/skeptical side of human nature. If you are trying sell the
benefits of a treatment, counter fears, and boost hopes, use the NNT. If
you are cost aware and risk averse, look at the NTN/ITI.
And, if you really want to make the "best" decision, based on the best
understanding of the best evidence, you need to look at the facts from all
angles.
Or do you?
Unfortunately a simple 2X2 table generates a lot more statistics than the
4 original data items. A paper that presented all the statistics from a
2X2 table would have an effect similar to looking at 4 simple coloured
shapes through a kaleidoscope. Amazing. Pretty. But concealing, rather
than revealing the underlying meaning.
The scientific community will have to decide through trial, error, and
debate what constitutes the best set of summary statistics. But I like the
idea of tying spin doctors in knots by coupling a positive spinning
statistic with a negative spinning statistic. E.g. RRR with ARR; NNT with
ITI.
Michael
(with no apologies for bringing rhetoric into EBM)
|