A provable two-stage algorithm for penalized hazards regression

TL;DR

This paper introduces a two-stage convex optimization algorithm for penalized Cox's proportional hazards regression, leveraging local strong convexity to achieve provable statistical and computational guarantees.

Contribution

It proposes a novel two-stage convex programming approach tailored for nonconvex penalized hazards regression, with theoretical guarantees and empirical validation.

Findings

Establishes the strong oracle property of the estimators.

Demonstrates the algorithm's effectiveness through numerical studies.

Provides theoretical analysis of statistical and computational tradeoffs.

Abstract

From an optimizer's perspective, achieving the global optimum for a general nonconvex problem is often provably NP-hard using the classical worst-case analysis. In the case of Cox's proportional hazards model, by taking its statistical model structures into account, we identify local strong convexity near the global optimum, motivated by which we propose to use two convex programs to optimize the folded-concave penalized Cox's proportional hazards regression. Theoretically, we investigate the statistical and computational tradeoffs of the proposed algorithm and establish the strong oracle property of the resulting estimators. Numerical studies and real data analysis lend further support to our algorithm and theory.