Differences in set-based tests for sparse alternatives when testing sets of outcomes compared to sets of explanatory factors in genetic association studies

Set-based association tests are widely popular in genetic association settings for their ability to aggregate weak signals and reduce multiple testing burdens. In particular, a class of set-based tests including the Higher Criticism, Berk-Jones, and other statistics have recently been popularized for reaching a so-called detection boundary when signals are rare and weak. Such tests have been applied in two subtly different settings: (a) associating a genetic variant set with a single phenotype and (b) associating a single genetic variant with a phenotype set. A significant issue in practice is the choice of test, especially when deciding between innovated and generalized type methods for detection boundary tests. Conflicting guidance is present in the literature. This work describes how correlation structures generate marked differences in relative operating characteristics for settings (a) and (b). The implications for study design are significant. We also develop novel power bounds that facilitate the aforementioned calculations and allow for analysis of individual testing settings. In more concrete terms, our investigation is motivated by translational expression quantitative trait loci (eQTL) studies in lung cancer. These studies involve both testing for groups of variants associated with a single gene expression (multiple explanatory factors) and testing whether a single variant is associated with a group of gene expressions (multiple outcomes). Results are supported by a collection of simulation studies and illustrated through lung cancer eQTL examples.