Abstract
We consider the scenario where there is an exposure, multiple biologically defined sets of biomarkers, and an outcome. We propose a new two-step procedure that tests if any of the sets of biomarkers mediate the exposure/outcome relationship, while maintaining a prespecified familywise error rate. The first step of the proposed procedure is a screening step that removes all groups that are unlikely to be strongly associated with both the exposure and the outcome. The second step adapts recent advances in postselection inference to test if there are true mediators in each of the remaining candidate sets. We use simulation to show that this simple two-step procedure has higher statistical power to detect true mediating sets when compared with existing procedures. We then use our two-step procedure to identify a set of Lysine-related metabolites that potentially mediate the known relationship between increased body mass index and the increased risk of estrogen-receptor positive breast cancer in postmenopausal women.