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In genome-wide association studies (GWAS) for thousands of phenotypes in large biobanks, most binary traits have substantially fewer cases than controls. Both of the widely used approaches, the linear mixed model and the recently proposed logistic mixed model, perform poorly; they produce large type I error rates when used to analyze unbalanced case-control phenotypes. Here we propose a scalable and accurate generalized mixed model association test that uses the saddlepoint approximation to calibrate the distribution of score test statistics. This method, SAIGE (Scalable and Accurate Implementation of GEneralized mixed model), provides accurate P values even when case-control ratios are extremely unbalanced. SAIGE uses state-of-art optimization strategies to reduce computational costs; hence, it is applicable to GWAS for thousands of phenotypes by large biobanks. Through the analysis of UK …