Graph-structured Sparse Mixed Models for Genetic Association with Confounding Factors Correction

Genome-Wide Association Study (GWAS) plays an essential role in understanding human genetics. While various methods have been introduced to increase the signals of GWAS with consideration of population stratification, polygenicity, or pleiotropy. There seems no existing methods that can consdier these three different aspects of genetic association studies together. In this paper, we introduce a new set of models that can utilize the relatedness of available phenotypes to help improve the signals regarding pleiotropy, calculate multivariate coefficients corresponds to polygenicity, and correct population stratification through modelling random effects. We first propose the sparse graph-structured linear mixed model (sGLMM). Then the tree-guided sparse linear mixed model (TgSLMM) has further put forward to explore how specifically clusters are. Our method turns out to outperform other existing approaches after simulation experiments and be capable of exploring the correct genetic association and scales to the large dataset like human genome. Further, we validate, compare and use the effectiveness of both sGLMM and TgSLMM in the real-world genomic dataset on Human Alzheimer's Disease discovered by our model, and justify a few of the most important genetic loci. Overlapping SNPs implies that association between each pair of traits follows only one path and is acyclic, which more corresponds to tree structure.