I am conducting some statistical tests on a rare event (11 cases out of 171 patient sample). I have two main hypotheses, but in the mean time I also want to conduct some exploratory tests on 6 other variables, in order to explore possible associations.
(1) I am wondering if there are any rules about the number of tests that you can do based on the number of events.
(2) Normally when we do one or several statistical tests, we consider the statistical power (which is related with sample size), and with several tests we also consider the multiple comparisons problem (which is related with the number of tests). In the case of rare events, the statistical power of each of my test would be low, but will rare event also influence (or exaggerate) the multiple comparisons issue, i.e. after conducted several tests, the chance of finding false positives are much higher for rare events?