Interpreting Fisher's exact test OR, CI and p-values

Question

In the context of Fisher's exact test results, it seems that a bunch of online tutorials mainly focus on interpreting the p-value exclusively, without considering the confidence intervals or the odds ratio.
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Based on those results, I cannot state that there is a significant association between the variant and the phenotype, because:

• the confidence interval does not include a 1, indicating no significance?

Thanks a lot.

Answer 1

If you take a look at the wikipedia article on odds ratio, the value of an odds ratio simply means the following:

An odds ratio greater than 1 indicates that the condition or event is more likely to occur in the first group. And an odds ratio less than 1 indicates that the condition or event is less likely to occur in the first group.

You'll notice that this quote says nothing about p-values, confidence intervals, or statistical significance.

So on its own, the value of an odds-ratio observed in a sample won't tell you if you can infer something about your population of interest, relative to the true odds ratio. It means that you can't say just from the odds ratio if it is "statistically significant" or not. For that, you have to look at the p-value (is it smaller than your alpha level?) or at the confidence interval (does it exclude the null hypothesis? in your case, does it exclude the value 1?).

You say:

the confidence interval does not include a 1, indicating no significance

Your statement is incorrect. Think about a confidence interval including 1: it shows uncertainty about whether the true value of the odds ratio in your population of interest is larger or smaller than 1 (i.e. uncertainty on whether the event is less or more likely to occur in the first group).

So a confidence interval excluding 1 is consistent with having a small p-value. In your case, there does not seem to be an problem relative to that (the p-value is quite small, and the confidence interval excludes 1).

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As a side note, the sample contingency table from your question gives the following output in R, which is not in line with the OR, p-value, and confidence interval you mention (this is incidentally an example of a confidence interval including 1, with a large p-value):

tab = rbind(c(15835, 923),
            c(1867425, 111832))
fisher.test(tab)

    Fisher's Exact Test for Count Data

data:  tab
p-value = 0.4396
alternative hypothesis: true odds ratio is not equal to 1
95 percent confidence interval:
 0.9611067 1.0993676
sample estimates:
odds ratio 
    1.0274