How to test assumptions for a large number of statistical tests? I am running a logistic regression. The outcome is a clinical variable, and there are two predictors: gene expression (continuous), hormone levels (continuous), and the interaction term between them.
There is only one hormone, but there are ~10K genes.
I am running independently 10K regressions, one for each gene.
The hypothesis is that interaction between some of the genes and the hormone leads to the clinical outcome. I would like to test if it is so.
The most important statistical assumption one should check in logistic regression (afaik) is linearity. The logit of the probability log(p/1-p) should be in a linear relationship with each of the predictors. This can be checked using a plot.
But, for a large number of genes this is not feasible. Even if I take only the ones that are found to be interesting (as a result of the regression) there are about 100 such genes.
What would be an efficient way to check the assumption?
The same goes for checking for outliers. How does one do it in an efficient way on ~100 regressions?

Probably not a conclusive answer... For each of the ~100 interesting genes passing a first, low pass screening you want to plot the logit of the outcome vs gene expression. That makes ~100 plots. In a 4x5 layout is "only" four or five A4 pages of plots. You can annotate each plot with some metrics of linearity, and plot them in order of such metrics for ease of eyeballing. If you are a bit familiar with R and ggplot this is not a terribly complicated option.
