Solved – Significant Fisher’s exact test, post hoc analysis for subgroup comparisons

contingency tablesfishers-exact-testpost-hoc

I'm analysing 2 groups of patients with 2 different DISEASE_STAGES: MILD disease and MODERATE disease, as defined by a complex clinical diagnosis. The sample size is relatively small: a total of 80 patients characterised by SMOKING_STATUS with 3 levels: active smoker, ex-smoker and never smoked.

I've performed a Fisher exact test because one cell has a frequency of 1

fisher.test(matrix(c(1, 5, 14, 3, 33, 22), nrow=2, ncol=3, byrow=TRUE))

Fisher's Exact Test for Count Data
p-value = 0.03039
alternative hypothesis: two.sided

I reject the null hypothesis that the disease is not affected by smoking status.

My question: Is it possible and how can I perform a post-hoc analysis with pairwise comparisons of the proportions for a Fisher exact test? How should I correct p-values to account for the multiple testing (what kind of statistical significance should I accept for these subgroup comparisons)?

Best Answer

After giving it some thought, I think the best approach is to combine the categories of active smoker and ex smoker into "exposed to smoke" unless there is a good clinical reason to suspect that actively smoking is different than having smoked. Combining the categories alleviates the troubles of multiple comparisons as well as the category with small sample size.

You could look to see what other people have done with respect to this problem. A quick google reveals a paper in PLOS one about post hoc and fisher tests. I've not read that paper, so I can't comment on its relevance. In any case I think a reviewer would look at that first category and take issue with the fact that you are making comparisons with so few observations.

I would also suggest making friends with a biostatistician if you have not already done so.

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