Structured Learning in Time-dependent Cox Models

TL;DR

This paper introduces a flexible variable selection framework for time-dependent Cox models that can handle complex covariate structures, improving estimation accuracy and computational efficiency in survival analysis.

Contribution

It proposes a novel adaptable method for variable selection in time-dependent Cox models, capable of enforcing arbitrary sparsity patterns and structures.

Findings

Accurate estimation with low false alarm rates.

Efficient solution via network flow algorithm.

Successful application to medical survival data.

Abstract

Cox models with time-dependent coefficients and covariates are widely used in survival analysis. In high-dimensional settings, sparse regularization techniques are employed for variable selection, but existing methods for time-dependent Cox models lack flexibility in enforcing specific sparsity patterns (i.e., covariate structures). We propose a flexible framework for variable selection in time-dependent Cox models, accommodating complex selection rules. Our method can adapt to arbitrary grouping structures, including interaction selection, temporal, spatial, tree, and directed acyclic graph structures. It achieves accurate estimation with low false alarm rates. We develop the sox package, implementing a network flow algorithm for efficiently solving models with complex covariate structures. sox offers a user-friendly interface for specifying grouping structures and delivers fast computation. Through examples, including a case study on identifying predictors of time to all-cause death in atrial fibrillation patients, we demonstrate the practical application of our method with specific selection rules.