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
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
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
(with no apologies for bringing rhetoric into EBM)