Fast Lasso method for Large-scale and Ultrahigh-dimensional Cox Model with applications to UK Biobank

We develop a scalable and highly efficient algorithm to fit a Cox proportional hazard model by maximizing the L 1 -regularized (Lasso) partial likelihood function, based on the Batch Screening Iterative Lasso (BASIL) method developed in (Qian et al. 2019). The output of our algorithm is the full Lasso path, the parameter estimates at all predefined regularization parameters, as well as their validation accuracy measured using the concordance index (C-index) or the validation deviance. To demonstrate the effectiveness of our algorithm, we analyze a large genotype-survival time dataset across 306 disease outcomes from the UK Biobank (Sudlow et al. 2015). Our approach, which we refer to as snpnet-Cox, is implemented in a publicly available package.