Confidence intervals for high-dimensional Cox models

Abstract

We provide theoretical justification for post-selection inference in highdimensional Cox models, based on the celebrated debiased Lasso procedure (e.g. Zhang and Zhang, 2014; van de Geer et al., 2014). Our generic model setup allows time-dependent covariates and an unbounded time interval, which is unique among post-selection inference studies on high-dimensional survival analysis. In addition, we adopt a novel proof technique to replace the use of Rebolledo’s central limit theorem as in the seminal work of Andersen and Gill (1982). Our theoretical results, which provide conditions under which our confidence intervals are asymptotically valid, are supported by extensive numerical experiments.