Whole genome sequencing (WGS) studies in large biobanks provide an unprecedented opportunity to study the rare-variant (RV) effects on the natural history of human diseases by analyzing censored time-to-event (TTE) phenotypes, such as age at disease diagnosis, disease progression, and lifespan. Unlike existing methods developed for continuous and categorical phenotypes, rare-variant association tests (RVATs) for TTE phenotypes in large biobanks face several major challenges, including heavy censoring, cryptic relatedness, and population structure. We introduce GATE-STAAR (Genetic Analysis of Time-to-Event phenotypes via the variant-Set Test for Association using Annotation infoRmation), a powerful and computationally efficient frailty model framework for RVATs of TTE phenotypes in large biobanks. GATE-STAAR accounts for high censoring rates, cryptic relatedness, and population structure in large biobanks, while incorporating multifaceted variant functional annotations to improve power and result interpretability. We propose a rare-variant saddlepoint approximation method to effectively address heavy censoring in WGS TTE analysis. We demonstrate through extensive simulations that GATE-STAAR is powerful while maintaining proper control of type I error rates. We apply GATE-STAAR to analyze the WGS data of approximately 400,000 UK Biobank participants of white British ancestry across a variety of TTE phenotypes, and validate the findings using participants of European ancestry from the All of Us Research Program. These analyses uncover RV associations with age at diagnosis of a range of diseases.
Keywords: rare variants; saddlepoint approximation; time-to-event analysis; whole genome sequencing.