Reconstruction of a Matrix of Genotypic Correlations between Variants within a Gene for Joint Analysis of Imputed and Sequenced Data

Abstract

Abstract— When combining imputed and sequenced data in a single gene-based association analysis, the problem of reconstructing genetic correlation matrices arises. It is related to the fact that the correlations between genotypes of all imputed variants and the correlations between genotypes of all sequenced variants are known for a gene but we do not know the correlations between genotypes of variants, one of which is imputed, and the other is sequenced. To recover these correlations, we propose an efficient method based on maximising the determinant of the matrix. This method has a number of useful properties and an analytical solution for our task. Approbation of the proposed method was performed by comparing reconstructed and real correlation matrices constructed on individual genotypes from the UK Biobank. Comparison of the results of gene-based association analysis performed by the SKAT, BT, and PCA methods on reconstructed and real matrices using modelled summary statistics and calculated summary statistics on real phenotypes showed high quality of reconstruction and robustness of the method to different gene structures.