Adaptive Partial Conjunction Hypothesis: Identifying Pleiotropy Across Heterogeneous Effect Units

Genetic effects are increasingly measured across multiple traits, tissues and cell types. Variants can influence several traits through shared pathways and regulate gene expression across several tissues. Resolving these pleiotropic patterns can reveal shared genetic architecture and disease mechanisms. Addressing this calls for the partial conjunction hypothesis (PCH), namely that every feature in a subset is affected. Existing PCH methods, however, rely on simple marginal effect-size models and pool effect sizes within each feature, which is insufficient when effects are heterogeneous. We introduce APCH, an empirical Bayes framework for subset-level inference. APCH models each feature's effect-size distribution with a flexible adaptive shrinkage prior and learns how effect sizes are shared among jointly affected features. We define subset-level posterior quantities, notably a local false sign rate that is more robust and interpretable. In simulations spanning direct pleiotropy, structural-equation effects and genetic correlation, APCH remained calibrated and powerful. Across five type 2 diabetes (T2D)-related traits, APCH identified 12 loci jointly associated with all five traits, whereas only one variant reached genome-wide significance in all five. Across six TWAS of T2D in different tissues, APCH recovered gene--tissue associations missed by single-tissue analyses.