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To the Editor—Despite recent work highlighting the advantages of linear mixedmodel (LMM) methods for genome-wide association studies (GWAS) in datasets containing relatedness or population structure1–3, much uncertainty remains about best practices for optimizing GWAS power while controlling confounders. Several recent studies of the interim UK Biobank dataset4 (∼ 150,000 samples) removed> 20% of samples by filtering for relatedness or genetic ancestry and/or used linear regression in preference to mixed-model association. These issues are exacerbated in the full UK Biobank dataset (∼ 500,000 samples), in which suggested sample exclusions decrease sample size by nearly 30% 5. Here we release a much faster version of our BOLT-LMM Bayesian mixed-model association method3 and show that it can be applied with minimal sample exclusions and achieves greatly superior power as …