An Adaptive Association Test for Multiple Phenotypes with GWAS Summary Statistics

Abstract

We study the problem of testing for single marker-multiple phenotype associations based on genome-wide association study (GWAS) summary statistics without access to individual-level genotype and phenotype data. For most published GWASs, because obtaining summary data is substantially easier than accessing individual-level phenotype and genotype data, while often multiple correlated traits have been collected, the problem studied here has become increasingly important. We propose a powerful adaptive test and compare its performance with some existing tests. We illustrate its applications to analyses of a meta-analyzed GWAS dataset with three blood lipid traits and another with sex-stratified anthropometric traits, and further demonstrate its potential power gain over some existing methods through realistic simulation studies. We start from the situation with only one set of (possibly meta-analyzed) genome-wide summary statistics, then extend the method to meta-analysis of multiple sets of genome-wide summary statistics, each from one GWAS. We expect the proposed test to be useful in practice as more powerful than or complementary to existing methods.

Keywords: GEE; adaptive sum of powered score test; meta analysis; multivariate trait; statistical power.

Figure 1

Venn diagrams for the numbers of the significant SNPs (left panel) and loci (right panel) detected by the three tests at the genome-wide significance level of α = 5 × 10⁻⁸.

Figure 2

Simulation I: empirical power of the tests for simulated data with sample size n = 10³ and m₀ = 10⁵ null SNPs. The nominal significance level α = 0.05 for the top panels and α = 0.001 for the bottom panels.

Figure 3

Simulation I: empirical power of the three tests for simulated data with sample size n = 10⁴, m₀ = 10⁴ null SNPs, and nominal significance level α = 10⁻⁶.

Figure 4

The estimated correlation matrix R for the sex-stratified 6 traits.

Figure 5

Venn diagrams for the numbers of the significant SNPs (left panel) and loci (right panel) identified by the three multivariate tests.

Figure 6

A locus identified by the aSPU test, but not by the other two tests.