Over the past decade, statistical methods have been developed to estimate single nucleotide polymorphism (SNP) heritability, which measures the proportion of phenotypic variance explained by all measured SNPs in the data. Estimates of SNP heritability measure the degree to which the available genetic variants influence phenotypes and improve our understanding of the genetic architecture of complex phenotypes. In this article, we review the recently developed and commonly used SNP heritability estimation methods for continuous and binary phenotypes from the perspective of model assumptions and parameter optimization. We primarily focus on their capacity to handle multiple phenotypes and longitudinal measurements, their ability for SNP heritability partition and their use of individual-level data versus summary statistics. State-of-the-art statistical methods that are scalable to the UK Biobank dataset are also elucidated in detail.

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.