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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)?

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  • $\begingroup$ You could just do a test of proportions between each group and use a Bonferonni correction, but I think there might be better things to do. Would it be reasonable to assume there is a trend in disease stages as a function of smoking status (e.g. more people are moderately diseased if they smoke more)? There is also the issue of your first group having only 4 patients, which is extremely small. $\endgroup$
    – Demetri Pananos
    Nov 13, 2018 at 16:14
  • $\begingroup$ I was a bit worried about doing a Bonferroni correction for a Fisher with such low counts in 3 cells. I've done it for a Chi-squared with higher cell counts and I'm not sure it can be applied the same way to a Fisher. Yes, I assume there is an association between disease and smoking but not sure how to express this with categorical variables $\endgroup$
    – Mia
    Nov 13, 2018 at 16:20
  • $\begingroup$ I think testing for a relationship between the ordinal variables and the outcome would be more informative than doing multiple comparisons (and would likely have better statistical power). Most tests are asymptotic tests though, so that first group is a real problem. I'd have to know more about the problem and your goal in order to recommend something. Is this homework or something, or is this a clinical investigation? $\endgroup$
    – Demetri Pananos
    Nov 13, 2018 at 16:28
  • $\begingroup$ Yes the first group is very small because it is rare for elderly diseased patients to be active smokers. I'm not sure if collapsing to only 2 levels: exposed to smoke (active smokers and ex-smokers) and not exposed to smoke would help or make things worse $\endgroup$
    – Mia
    Nov 13, 2018 at 16:30
  • $\begingroup$ It's a clinical investigation $\endgroup$
    – Mia
    Nov 13, 2018 at 16:31

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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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  • $\begingroup$ Thank you Demetri. The clinical reason for an ordinal smoking variable is that the exposure significantly changes between active smokers and ex-smokers. I assume that those who are still active when elderly have been exposed to smoke for much longer (they haven't started smoking in their 70s of age), ex-smokers after 10 years of quitting are regarded as never smokers (ex-smokers is a heterogeneous group who have stopped smoking at various times). Would it be reasonable to say that smoke is associated with disease but for further analyses a continuous var (smoking years) would be needed? $\endgroup$
    – Mia
    Nov 13, 2018 at 17:49
  • $\begingroup$ I think that is a reasonable conclusion. $\endgroup$
    – Demetri Pananos
    Nov 13, 2018 at 18:01

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