With decades of electronic health records linked to genetic data, large biobanks provide unprecedented opportunities for systematically understanding the genetics of the natural history of complex diseases. Genome-wide survival association analysis can identify genetic variants associated with ages of onset, disease progression and lifespan. We developed an efficient and accurate frailty (random effects) model approach for genome-wide survival association analysis of censored time-to-event (TTE) phenotypes in large biobanks by accounting for both population structure and relatedness. Our method utilizes state-of-the-art optimization strategies to reduce the computational cost. The saddlepoint approximation is used to allow for analysis of heavily censored phenotypes (>90%) and low frequency variants (down to minor allele count 20). We demonstrated the performance of our method through extensive simulation studies and analysis of five TTE phenotypes, including lifespan, with heavy censoring rates (90.9% to 99.8%) on ~400,000 UK Biobank participants with white British ancestry and ~180,000 samples in FinnGen, respectively. We further performed genome-wide association analysis for 871 TTE phenotypes in UK Biobank and presented the genome-wide scale phenome-wide association (PheWAS) results with the PheWeb browser. ### Competing Interest Statement B.M.N. is on the scientific advisory board of Deep Genomics, and is a consultant for CAMP4 Therapeutics, Takeda and Biogen. X.L. is a consultant to AbbVie Pharmaceuticals and Verily Life Sciences. M.J.D. is a founder of Maze Therapeutics and on the scientific advisory board of BC Platforms.

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