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Because of the recent advances of genome sequences, a large number of humangenome sequences are available for the study of human genetics. Genome-wideassociation studies typically focus on associations between single-nucleotidepolymorphisms and traits such as major human diseases. However, the statisticalpower of classical single-marker association analysis for rare variants islimited. To address the challenge, rare and low-frequency variants are oftengrouped into a gene or pathway level, and the effects of multiple variantsevaluated based on collapsing methods. The sequential kernel association test(SKAT) is one of the most effective collapsing methods. SKAT utilizes thekernel matrix. The size of the kernel matrix is O(n^2), where the sample sizeis n, so that the calculation of the data using the kernel method requires along time. As the sample sizes of human genetic studies increase, thecomputational time is getting more and more problematic. In the present paper,the genotype value decomposition method is proposed for the handling thesequential kernel in a short period of time. The method can be referred to asgenotype value decomposition. In the present paper, it is shown that thegenetic relationship matrix and Identity by State (IBS) matrix can be obtainedusing the genotype value vectors. By using this method, the SKAT can beconducted with time complexity O(n). The proposed method enables to conductSKAT for samples of human genetics.

Fast computation of kernel statistics using genotype value decomposition