Abstract: We provide a theoretical justification for post-selection inference in high-dimensional Cox models, based on the celebrated debiased Lasso procedure. 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. Our theoretical results provide conditions under which our confidence intervals are asymptotically valid, and are supported by extensive numerical experiments.

Key words and phrases: Debiased Lasso, High-dimension statistical inference, survival analysis.