StATS: Calculating NNT for observational studies (March 3, 2008).

Recent discussion at the Evidence Based health list centered on the calculation of NNT in a case-control study. While it is indeed possible to do so,  I have always been a bit curious why NNT and NNH are computed almost exclusively for randomized studies and why they are rarely used for observational studies. No one says this explicitly, but I suspect that the reason is that the NNT and NNH lead to problematic interpretations in observational studies.

For example, I use a data set on mortality onboard the Titanic to illustrate the concept of odds ratios and relative risks, but it is possible to compute a NNT for this data set as well. Among the Titanic passengers, the mortality rate was 83% for men and 33% for women. The NNT is 2. What does this mean?

It produces a counterfactual statement. If you could change someone's gender from male to female, then for every two gender changes, there would be one additional life saved on average. It is not realistic to change genders, but there are stories of some men who dressed up in women's clothes in order to be part of the "women and children first" ethic that existed at the time of the Titanic. So perhaps the NNT should really be called the NNCD (Number Needed to Cross-Dress).

In a study looking at age groups (you obviously can't randomly assign people to age groups unless you have access to the carousel ride in Ray Bradbury's Something Wicked This Way Comes), the NNT calculation might be more accurately called the NNA (Number Needed to Age).

If the groups being studied in an observational design involve weight, then NNT might better be called NNS (Number Needed to Shink). If the groups included psychiatrists and non-psychiatrics, then NNT might also be called the NNS.

I'm thinking that an article along these lines might be good for the holiday issue of BMJ.

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