Covariance of Interdependent Samples with Application to GWAS

Abstract

AbstractProximal genetic variants are frequently correlated, implying that also the corresponding effect sizes detected by genome-wide association studies (GWAS) are not independent. There are already methods taking this into account 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 covariance of datapoints not drawn independently, but with 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 level of genes. 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 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 TH1 versus TH2 immune reaction, a gene related to integrin beta-1 cell surface expression, and other genes potentially impacting severity of COVID-19. Our approach will be useful for similar analyses involving data-points with known auto-correlation structures.Author summaryGenome wide association studies (GWAS) deliver effect size estimates of a given trait for millions of Single Nucleotide Polymorphisms (SNPs). There are already powerful tools to use 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-analyse the association data from a pair of GWAS in order to identify genes and pathways that may be of relevance to both of the respective traits. The novelty in our test is that a gene is considered to be 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 made feasible due to a 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 prescription of common medications. Out of the 23 medication classes we tested for coherent cosignificant 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 a number of 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.