Subsampling Technique to Estimate Variance Component for UK-Biobank Traits

The estimation of heritability has been an important question in statistical genetics. Due to the clear mathematical properties, the modified Haseman-Elston regression has been found a bridge that connects and develops various parallel heritability estimation methods. With the increasing sample size, estimating heritability for biobank-scale data poses a challenge for statistical computation, in particular that the calculation of the genetic relationship matrix is a huge challenge in statistical computation. Using Haseman-Elston framework, in this study we explicitly analysed the mathematical structure of the key term tr(K^T K), the trace of high order term of the genetic relationship matrix, a component involved in the estimation procedure. In this study, we proposed two estimators, which can estimate tr(K^T K) with greatly reduced sampling variance compared to the existing method under the same computational complexity. We applied this method to 81 traits in UK Biobank data, and compared the chromosome-wise partition heritability with the whole-genome heritability, also as an approach for testing polygenicity.