Covariance of Interdependent Samples with Application to GWAS

Krefl, D.; Bergmann, S.

We devise a significance test for covariance of samples not drawn independently, but with known inter-sample covariance structure. The test distribution we propose is a linear combination of {chi}2 distributions, with positive and negative coefficients. The corresponding cumulative distribution function can be efficiently calculated with Davies algorithm at high precision. As an application, we propose a test for dependence between SNP-wise effect sizes of two genome-wide association studies at the level of genes. The test can be extended to detect gene-wise causal links. We illustrate this method by uncovering potential shared genetic links between severity of Covid-19, taking of class M05B medication (drugs affecting bone structure and mineralization), Vitamin D (25OHD) and Calcium concentrations. In particular, 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.