Potential application of elastic nets for shared polygenicity detection with adapted threshold selection

Current research suggests that hundreds to thousands of single nucleotide polymorphisms (SNPs) with small to modest effect sizes contribute to the genetic basis of many disorders, a phenomenon labeled as polygenicity. Additionally, many such disorders demonstrate polygenic overlap, in which risk alleles are shared at associated genetic loci. A simple strategy to detect polygenic overlap between two phenotypes is based on rank-ordering the univariate p-values from two genome-wide association studies (GWASs). Although high-dimensional variable selection strategies such as Lasso and elastic nets have been utilized in other GWAS analysis settings, they are yet to be utilized for detecting shared polygenicity. In this paper, we illustrate how elastic nets, with polygenic scores as the dependent variable and with appropriate adaptation in selecting the penalty parameter, may be utilized for detecting a subset of SNPs involved in shared polygenicity. We provide theory to better understand our approaches, and illustrate their utility using synthetic datasets. Results from extensive simulations are presented comparing the elastic net approaches with the rank ordering approach, in various scenarios. Results from simulations studies exhibit one of the elastic net approaches to be superior when the correlations among the SNPs are high. Finally, we apply the methods on two real datasets to illustrate further the capabilities, limitations and differences among the methods.