Efficient estimation of SNP heritability using Gaussian predictive process in large scale cohort studies

With the advent of high throughput genetic data, there have been attempts to estimate heritability from genome-wide SNP data on a cohort of distantly related individuals using linear mixed model (LMM). Fitting such an LMM in a large scale cohort study, however, is tremendously challenging due to its high dimensional linear algebraic operations. In this paper, we propose a new method named PredLMM approximating the aforementioned LMM motivated by the concepts of genetic coalescence and Gaussian predictive process. PredLMM has substantially better computational complexity than most of the existing LMM based methods and thus, provides a fast alternative for estimating heritability in large scale cohort studies. Theoretically, we show that under a model of genetic coalescence, the limiting form of our approximation is the celebrated predictive process approximation of large Gaussian process likelihoods that has well-established accuracy standards. We illustrate our approach with extensive simulation studies and use it to estimate the heritability of multiple quantitative traits from the UK Biobank cohort.Author summary: In recent years, there is an increased interest of estimating heritability from genome-wide SNP data in large scale cohort studies. Here, we propose the PredLMM, a computationally rapid and memory-efficient linear mixed model for heritability estimation. The proposed approach can estimate SNP heritability on Biobank-scale datasets in a fraction of time compared to the existing mixed model based approaches. Along with the extensive simulations illustrating the precision and robustness of the PredLMM, we have also estimated heritability of several anthropometric traits from the UK Biobank cohort.