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It is frequently of interest to jointly analyze two paired sequences ofmultiple tests. This paper studies the problem of detecting whether there aremore pairs of tests that are significant in both sequences than would beexpected by chance. The detection boundary is derived in terms of parameterssuch as the sparsity of the latent significance indicators of the tests in eachsequence, the effect sizes of the non-null tests, and the magnitude of thedependence between the two sequences. A new test for detecting weak dependenceis also proposed, shown to be asymptotically adaptively optimal, studied insimulations, and applied to study of genetic pleiotropy in 10 pediatricautoimmune diseases.

Optimal detection of weak positive latent dependence between two sequences of multiple tests