Cross-GWAS coherence test at the gene and pathway level
Authors: Krefl Daniel , Bergmann Sven 
Published: May 2021

Proximal genetic variants are frequently correlated, implying that the corresponding effect sizes detected by genome-wide association studies (GWAS) are also not independent. Methods already exist to account for this when aggregating effects from a single GWAS across genes or pathways. Here we present a rigorous yet fast method for detecting genes with coherent association signals for two traits, facilitating cross-GWAS analyses. To this end, we devised a new significance test for the covariance of datapoints not drawn independently but with a known inter-sample covariance structure. We show that the distribution of its test statistic is a linear combination of χ2 distributions with positive and negative coefficients. The corresponding cumulative distribution function can be efficiently calculated with Davies’ algorithm at high precision. We apply this general framework to test for dependence between SNP-wise effect sizes of two GWAS at the gene level. We extend this test to detect also gene-wise causal links. We demonstrate the utility of our method by uncovering potential shared genetic links between the severity of COVID-19 and (1) being prescribed class M05B medication (drugs affecting bone structure and mineralization), (2) rheumatoid arthritis, (3) vitamin D (25OHD), and (4) serum calcium concentrations. Our method detects a potential role played by chemokine receptor genes linked to TH 1 versus TH 2 immune response, a gene related to integrin beta-1 cell surface expression, and other genes potentially impacting the severity of COVID-19. Our approach will be useful for similar analyses involving datapoints with known auto-correlation structures.

Author summary

Genome-wide association studies (GWAS) deliver effect size estimates of a given trait for millions of Single Nucleotide Polymorphisms (SNPs). Powerful tools already exist using these summary statistics to elucidate the global joint genetic contribution to a pair of traits, such as cross-trait LD-score regression, but these methods cannot reveal the joint contributions at the level of genes and pathways. Here we present a novel methodology to co-analyze the association data from a pair of GWAS to identify genes and pathways that may be relevant to both individual traits. Our test novelty is that a gene is considered co-relevant if the SNP-wise effects from both GWAS tend to have the same sign and magnitude in the gene window. This is different from the commonly used approach asking only for the aggregate signals from two GWAS to be jointly significant. Our method is feasible due to novel insight into the product-normal distribution. We apply our new method to test for co-significant genes for severe COVID-19 and conditions leading to the prescription of common medications. Of the 23 medication classes we tested for coherent co-significant genes, only one, M05B (drugs affecting bone structure and mineralization), yielded Bonferroni significant hits. We then searched for available GWAS data for related conditions and found that also rheumatoid arthritis, calcium concentration, and vitamin D are traits pointing to several co-relevant genes in our new coherence analysis. Furthermore, testing for anti-coherence showed that the medication classes H03A (thyroid preparations), R03A, and R03BA (drugs for obstructive airway diseases) feature Bonferroni co-significant genes. Our joint analysis provides new insights into potential COVID-19 disease mechanisms.