  Motivated by multi-center biomedical studies that cannot share individual
data due to privacy and ownership concerns, we develop communication-efficient
iterative distributed algorithms for estimation and inference in the
high-dimensional sparse Cox proportional hazards model. We demonstrate that our
estimator, even with a relatively small number of iterations, achieves the same
convergence rate as the ideal full-sample estimator under very mild conditions.
To construct confidence intervals for linear combinations of high-dimensional
hazard regression coefficients, we introduce a novel debiased method, establish
central limit theorems, and provide consistent variance estimators that yield
asymptotically valid distributed confidence intervals. In addition, we provide
valid and powerful distributed hypothesis tests for any coordinate element
based on a decorrelated score test. We allow time-dependent covariates as well
as censored survival times. Extensive numerical experiments on both simulated
and real data lend further support to our theory and demonstrate that our
communication-efficient distributed estimators, confidence intervals, and
hypothesis tests improve upon alternative methods.
