Fast variance component analysis using large-scale ancestral recombination graphs

Recent algorithmic advancements have enabled the inference of genome-wide ancestral recombination graphs (ARGs) from genomic data in large cohorts. These inferred ARGs provide a detailed representation of genealogical relatedness along the genome and have been shown to complement genotype imputation in complex trait analyses by capturing the effects of unobserved genomic variants. An inferred ARG can be used to construct a genetic relatedness matrix, which can be leveraged within a linear mixed model for the analysis of complex traits. However, these analyses are computationally infeasible for large datasets. We introduce a computationally efficient approach, called ARG-RHE, to estimate narrow-sense heritability and perform region-based association testing using an ARG. ARG-RHE leverages a method for computing genotype-matrix products from genealogical data in sublinear time, along with scalable randomized algorithms. This enables fast estimation of variance components and their statistical significance, supports parallel analysis of multiple quantitative traits, and facilitates other linear mixed-model analyses. We conduct extensive simulations to verify the computational efficiency, statistical power, and robustness of this approach. We then apply it to detect associations between 21,159 genes and 52 blood-related traits, using an ARG inferred from genotype data of 337,464 individuals from the UK Biobank. In these analyses, combining ARG-based and imputation-based testing yields 8% more gene-trait associations than using imputation alone, suggesting that inferred genome-wide genealogies may effectively complement genotype imputation in the analysis of complex traits.