With the first test I have no population issues, since the two groups I'm comparing are normally distributed and differ only on one variable (disease vs. no disease). I plotted my data on a ROC and obtained my optimal cutoff (I'm working with MedCalc and no previous gold standard for this test).

Then, I had to sample a cohort from each group based on their positivity in the first test in order to perform two serial tests only on positive samples (there was no biological interest in testing negative samples). I selected two populations with the same frequency distribution, skewed on the right for positivity. I tested these samples separately for two additional variables, and I obtained my results.

The questions are:

- can I ROC the data I obtained from the two serial tests non-parametrically and calculate a secondary cut-off (which I would apply only on these data, obviously)?

- classical comparison of ROCs of the two serial data is a correct way to interpret the predictive value of the two serial tests?

- if I want to calculate the correlation of the two variables, do I assume that the data are non-parametric, even if they have the same freq dist but are biased because chosen under an arbitrary parameter in the first test? put simply: spearman or pearson?

Thank you for any help, and I apologize for any bastardization of the statistical language.