PROJECT SUMMARY Years of genetic research on various complex human traits have implicated several genetic variants as risk factors for two or more diseases/traits, including seemingly unrelated traits. A recent systematic evaluation of >500 traits from >4100 genome-wide association studies (GWAS) has revealed that 90% of the variants associated with these traits influence at least two traits. This phenomenon where a genetic region or locus confers risk to more than one trait is known as pleiotropy. Discovering patterns of pleiotropy is crucial for a comprehensive understanding of biological mechanisms of human diseases and traits (e.g. understand how genetic variation leads to trait variation and inter-trait correlations, and how traits may be causally related to each other), and can have translational impact in the long run (e.g. guide identification of molecular targets or help predict side-effects in drug development). While the scientific significance of studying pleiotropy or genetic overlap is well-understood, statistical methods for identifying common genetic basis between traits are still lacking. This is especially true for traits sampled under a family-based design. To address methodological challenges in investigating pleiotropy, in Aim 1, we propose a novel, innovative statistical method for identifying common genetic variants influencing two possibly correlated traits. In Aim 2, we non-trivially extend our method in Aim 1 to identify rare genetic variants influencing two independent traits. We use only aggregate-level genotype-phenotype association results (or GWAS summary statistics), thus helping protect human subjects data and facilitating global collaborations. The proposed methods, while having the potential to substantially outperform current approaches in the area, will be more general and distinct from existing research efforts in the following ways: applicability to correlated traits (Aim 1; e.g. a disease-related endophenotype and a molecular trait, or two different -omics traits), to traits measured on independent sets of individuals (Aims 1, 2; e.g. separate case-control studies on two diseases), to traits sharing some samples (Aim 1; e.g. case-control studies with shared controls), to study designs where individuals may not be randomly sampled or unrelated (Aims 1, 2; e.g. case-parent trio design), to rare variants (Aim 2), and our open-access tools will allow genomics researchers across the world to readily adopt and apply our methods even in resource- poor environments (Aims 1, 2). Successful implementation of these aims will provide the broader scientific community with novel, powerful and scalable methods, along with well-documented free software, to statistically investigate questions of pleiotropy between complex human diseases/ traits across the entire allele frequency spectrum using GWAS summary statistics only.