Principal component based adaptive association test of multiple traits using GWAS summary statistics

Abstract

Genetics hold great promise to precision medicine by tailoring treatment to the individual patient based on their genetic profiles. Toward this goal, many large-scale genome-wide association studies (GWAS) have been performed in the last decade to identify genetic variants associated with various traits and diseases. They have successfully identified tens of thousands of disease-related variants. However they have explained only a small proportion of the overall trait heritability for most traits and are of very limited clinical use. This is partly owing to the small effect sizes of most genetic variants, and the common practice of \"testing association between one trait and one genetic variant at a time\" in most GWAS, even when multiple related traits are often measured for each individual. Increasing evidence suggests that many genetic variants can influence multiple traits simultaneously, and we can gain more power by testing association of multiple traits simultaneously. It is appealing to develop novel multi-trait association test methods that need only GWAS summary data, since it is generally very hard to access the individual-level GWAS phenotype and genotype data.\n\nMost existing GWAS summary data based association test methods have relied on ad hoc approach or crude Monte Carlo approximation. In this paper we develop rigorous statistical methods for efficient and powerful multi-trait association test. We develop robust and efficient methods to accurately estimate the marginal trait correlation matrix using only GWAS summary data. We construct the principal component (PC) based association test from the summary statistics. PC based test has optimal power when the underlying multi-trait signal can be captured by the first PC, and otherwise it will have suboptimal performance. We develop an adaptive test by optimally weighting the PC based test and the omnibus chi-square test to achieve robust performance under various scenarios. We develop efficient numerical algorithms to compute the analytical p-values for all the proposed tests without the need of Monte Carlo sampling. We illustrate the utility of proposed methods through application to the GWAS meta-analysis summary data for multiple lipids and glycemic traits. We identify multiple novel loci that were missed by individual trait based association test.\n\nAll the proposed methods are implemented in an R package available at http://www.github.com/baolinwu/MTAR. The developed R programs are extremely efficient: it takes less than two minutes to compute the list of genome-wide significant SNPs for all proposed multi-trait tests for the lipids GWAS summary data with 2.5 million SNPs on a single Linux desktop.