LAUSR

Abstract This article develops two orthogonal contributions to scalable sparse regression for competing risks time-to-event data. First, we study and accelerate the broken adaptive ridge method (BAR), a surrogate -based iteratively reweighted -penalization algorithm that achieves sparsity in its limit, in the context of the Fine-Gray (1999) proportional subdistributional hazards (PSH) model. In particular, we derive a new algorithm for BAR regression, named cycBAR, that performs cyclic updates of each coordinate using an explicit thresholding formula. The new cycBAR algorithm effectively avoids fitting multiple reweighted -penalizations and thus yields impressive speedups over the original BAR algorithm. Second, we address a pivotal computational issue related to fitting the PSH model. Specifically, the cost of computing the log-pseudo likelihood and its derivatives grows at the rate of with the sample size n in current implementations. We propose a novel forward-backward scan algorithm that reduces the computation costs to O(n). The proposed method applies to both unpenalized and penalized estimation for the PSH model and has exhibited drastic speedups over current implementations. Finally, combining the two algorithms can yield > 1000 fold speedups over the original BAR algorithm. Illustrations of the impressive scalability of our proposed algorithm for large competing risks data are given using both simulations and data from the United States Renal Data System. Supplementary materials for this article are available online.