I have performed bulk RNAsequencing of tissue (e.g. kidney) from patients with a disease (e.g. diabetes), and I would like to identify genes that correlate with a continuous clinical variable (e.g. Hemoglobin A1c). I can then obtain a Rho (correlation coefficient) and a p value for each gene.
As you can imagine, I am doing this for about 20,000 genes, and will get multiple p values. The knee-jerk reflex is to perform some sort of correction for multiple testing. But I can't help feeling that correlation tests are inherently descriptive, and should be able to stand on their own without requiring multiple testing correction. Maybe not so relevant, but given the fact that we're now dealing with two random variables (A1c and gene expression), each with their own noise, it seems much less likely that a "significant" correlation will appear by chance.
The null hypothesis is also different I think for these two tests - in a test of difference, we're asking whether the observed distributions of data could have arisen by chance given that there is no difference between the two groups. For correlation analysis, we ask whether the strength of the correlation could have arisen by chance alone given that there is no correlation between the two variables. This may appear to be a minor distinction, but I wonder whether it could influence the answer here.
Also, correlation p values for real world biological data involving humans in my experience generally do not sit in the ranges I see for differential gene expression, and performing p value adjustment often leads everything to be "non-significant", even when the Rho's are potentially meaningful (0.5+).
I'd like to do what is methodologically proper, and I'm wondering if anyone can give me a bit of a deeper explanation on whether the maxim "multiple testing requires p value correction" applies for descriptive statistics like P values.
Thanks in advance! Your comments are all very appreciated :)