# Structured Learning in Time-dependent Cox Models

arXiv: https://arxiv.org/abs/2306.12528 · HTML: https://mlsanity.com/paper/2306.12528/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 86 references that are in the map.
- First posted on arXiv 21 Jun 2023.

## Builds on (most cited first, 9 of 9)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Sparse Modeling for Image and Vision Processing](https://mlsanity.com/paper/1411.3230/) (2014)
- [Convex Modeling of Interactions with Strong Heredity](https://mlsanity.com/paper/1410.3517/) (2014)
- [Hierarchical Sparse Modeling: A Choice of Two Group Lasso Formulations](https://mlsanity.com/paper/1512.01631/) (2015)
- [Modeling Treatment Effect Modification in Multidrug-Resistant Tuberculosis in an Individual Patient Data Meta-Analysis](https://mlsanity.com/paper/2101.03997/) (2021)
- [Group Regularized Estimation under Structural Hierarchy](https://mlsanity.com/paper/1411.4691/) (2014)
- [A general framework for formulating structured variable selection](https://mlsanity.com/paper/2110.01031/) (2021)
- [Integrating complex selection rules into the latent overlapping group Lasso for constructing coherent prediction models](https://mlsanity.com/paper/2206.05337/) (2022)
- [Evaluating hybrid controls methodology in early-phase oncology trials: a simulation study based on the MORPHEUS-UC trial](https://mlsanity.com/paper/2209.05354/) (2022)

## Abstract (arXiv)

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.