Multiplex confounding factor correction for genomic association mapping with squared sparse linear mixed model

Genome-wide Association Study has presented a promising way to understand the association between human genomes and complex traits. Many simple polymorphic loci have been shown to explain a significant fraction of phenotypic variability. However, challenges remain in the non-triviality of explaining complex traits associated with multifactorial genetic loci, especially considering the confounding factors caused by population structure, family structure, and cryptic relatedness. In this paper, we propose a Squared-LMM (LMM²) model, aiming to jointly correct population and genetic confounding factors. We offer two strategies of utilizing LMM² for association mapping: 1) It serves as an extension of univariate LMM, which could effectively correct population structure, but consider each SNP in isolation. 2) It is integrated with the multivariate regression model to discover association relationship between complex traits and multifactorial genetic loci. We refer to this second model as sparse Squared-LMM (sLMM²). Further, we extend LMM²/sLMM² by raising the power of our squared model to the LMMⁿ/sLMMⁿ model. We demonstrate the practical use of our model with synthetic phenotypic variants generated from genetic loci of Arabidopsis Thaliana. The experiment shows that our method achieves a more accurate and significant prediction on the association relationship between traits and loci. We also evaluate our models on collected phenotypes and genotypes with the number of candidate genes that the models could discover. The results suggest the potential and promising usage of our method in genome-wide association studies.