A Fast and Accurate Method for Genome-Wide Time-to-Event Data Analysis and Its Application to UK Biobank

With increasing biobanking efforts connecting electronic health records and national registries to germline genetics, the time-to-event data analysis has attracted increasing attention in the genetics studies of human diseases. In time-to-event data analysis, the Cox proportional hazards (PH) regression model is one of the most used approaches. However, existing methods and tools are not scalable when analyzing a large biobank with hundreds of thousands of samples and endpoints, and they are not accurate when testing low-frequency and rare variants. Here, we propose a scalable and accurate method, SPACox (a saddlepoint approximation implementation based on the Cox PH regression model), that is applicable for genome-wide scale time-to-event data analysis. SPACox requires fitting a Cox PH regression model only once across the genome-wide analysis and then uses a saddlepoint approximation (SPA) to calibrate the test statistics. Simulation studies show that SPACox is 76-252 times faster than other existing alternatives, such as gwasurvivr, 185-511 times faster than the standard Wald test, and more than 6,000 times faster than the Firth correction and can control type I error rates at the genome-wide significance level regardless of minor allele frequencies. Through the analysis of UK Biobank inpatient data of 282,871 white British European ancestry samples, we show that SPACox can efficiently analyze large sample sizes and accurately control type I error rates. We identified 611 loci associated with time-to-event phenotypes of 12 common diseases, of which 38 loci would be missed within a logistic regression framework with a binary phenotype defined as event occurrence status during the follow-up period.