Title: Beyond summary statistics
Description: Over the past 20 years, Genome-Wide Association Studies (GWAS) have identified thousands of variants in the genome linked to genetic diseases. However, these associations often reveal little about underlying genetic etiology, which for many phenotypes is thought to be highly heterogeneous. This work investigates statistical methods to move beyond conventional GWAS methods to both improve estimation of associations and to extract additional etiological insights from known associations, with a focus on schizophrenia. This thesis addresses the above aim through three primary topics: First, we describe DNA.Land, a web platform to crowdsource the collection of genomic data with user consent and active participation, thereby rapidly increasing sample sizes and power required for GWAS. Second, we describe methods to characterize the latent genomic contributors to heterogeneity in GWAS phenotypes. We develop a Z-score test to detect heterogeneity using correlations between variants among affected individuals, and we develop a contrastive tensor decomposition to explicitly characterize subtype-specific SNP effects independently of confounding heterogeneity such as ancestry.

Using these methods we provide evidence of significant heterogeneity in GWAS cohorts for schizophrenia. Lastly, a major avenue of investigation beyond GWAS is identifying the genes through which associated SNPs mechanistically affect the presentation of phenotypes. We develop a method to improve estimation of expression quantitative trait loci by joint inference over gene expression reference data and GWAS data, incorporating insights from the liability threshold model. These methods will advance ongoing efforts to explain the complex etiology of genetic diseases as well as improve the accuracy of disease prediction models based on these insights.