p vs p_cross with disease replicates?

[zweiss22]

I am trying to use C-SIDE to analyze a Visium study with 6 donors (3 with Type 2 Diabetes, 3 Healthy) with multiple replicates per donor. I ran ‘run.CSIDE.replicates’ and am looking at the output but am confused about the difference between p and p_cross.

I want to identify genes that are DE between T2D and healthy samples. Which p value should I use for this?

Thanks!