Fast heritability estimation based on MINQUE and batch training

Heritability, the proportion of phenotypic variance explained by genome-wide single nucleotide polymorphisms (SNPs) in unrelated individuals, is an important measure of the genetic contribution to human diseases and plays a critical role in studying the genetic architecture of human diseases. Linear mixed model (LMM) has been widely used for SNP heritability estimation, where variance component parameters are commonly estimated by using a restricted maximum likelihood (REML) method. REML is an iterative optimization algorithm, which is computationally intensive when applied to large-scale datasets (e.g. UK Biobank). To facilitate the heritability analysis of large-scale genetic datasets, we develop a fast approach, minimum norm quadratic unbiased estimator (MINQUE) with batch training, to estimate variance components from LMM (LMM.MNQ.BCH). In LMM.MNQ.BCH, the parameters are estimated by MINQUE, which has a closed-form solution for fast computation and has no convergence issue. Batch training has also been adopted in LMM.MNQ.BCH to accelerate the computation for large-scale genetic datasets. Through simulations and real data analysis, we demonstrate that LMM.MNQ.BCH is much faster than two existing approaches, GCTA and BOLT-REML.