How to obtain NNT from Cohen's d: comparison of two methods

In the literature we find many indices of size of treatment effect (effect size: ES). The preferred index of treatment effect in evidence-based medicine is the number needed to treat (NNT), while the most common one in the medical literature is Cohen's d when the outcome is continuous. There is confusion about how to convert Cohen's d into NNT.

We conducted meta-analyses of individual patient data from 10 randomized controlled trials of second generation antipsychotics for schizophrenia (n = 4278) to produce Cohen's d and NNTs for various definitions of response, using cutoffs of 10% through 90% reduction on the symptom severity scale. These actual NNTs were compared with NNTs calculated from Cohen's d according to two proposed methods in the literature (Kraemer, et al., Biological Psychiatry, 2006; Furukawa, Lancet, 1999).

NNTs from Kraemer's method overlapped with the actual NNTs in 56%, while those based on Furukawa's method fell within the observed ranges of NNTs in 97% of the examined instances. For various definitions of response corresponding with 10% through 70% symptom reduction where we observed a non-small number of responders, the degree of agreement for the former method was at a chance level (ANOVA ICC of 0.12, p = 0.22) but that for the latter method was ANOVA ICC of 0.86 (95%CI: 0.55 to 0.95, p<0.01).

Furukawa's method allows more accurate prediction of NNTs from Cohen's d. Kraemer's method gives a wrong impression that NNT is constant for a given d even when the event rate differs.