  Because of the recent advances of genome sequences, a large number of human
genome sequences are available for the study of human genetics. Genome-wide
association studies typically focus on associations between single-nucleotide
polymorphisms and traits such as major human diseases. However, the statistical
power of classical single-marker association analysis for rare variants is
limited. To address the challenge, rare and low-frequency variants are often
grouped into a gene or pathway level, and the effects of multiple variants
evaluated based on collapsing methods. The sequential kernel association test
(SKAT) is one of the most effective collapsing methods. SKAT utilizes the
kernel matrix. The size of the kernel matrix is O(n^2), where the sample size
is n, so that the calculation of the data using the kernel method requires a
long time. As the sample sizes of human genetic studies increase, the
computational time is getting more and more problematic. In the present paper,
the genotype value decomposition method is proposed for the handling the
sequential kernel in a short period of time. The method can be referred to as
genotype value decomposition. In the present paper, it is shown that the
genetic relationship matrix and Identity by State (IBS) matrix can be obtained
using the genotype value vectors. By using this method, the SKAT can be
conducted with time complexity O(n). The proposed method enables to conduct
SKAT for samples of human genetics.
