In a study which analyses the effect of Lithium on suicide rates, the results were the following:
- Placebo group: 3 suicides in 83 patients
- Lithium group: 0 suicides in 84 patients
My first approach would be to apply the Chi Square test, which does not result in a significant difference (chi=3.0184).
The authors however, suggest the following, finding a significant difference between the groups (p=0.049):
As a post hoc analysis, differences between intervention groups with regard to completed suicides were examined based on determining the probability of zero events in the lithium group on the expectation of 3 ⁄ 83 events in the placebo group on grounds of a Poisson distribution
Is this a valid approach, what am I missing?