# Variable Selection for Multivariate Failure Time Data via Regularized Sparse-Input Neural Network

## TL;DR

This paper introduces a new method for analyzing survival data with multiple outcomes by combining variable selection and model estimation using a neural network approach.

## Contribution

The novel contribution is a unified framework using regularized sparse-input neural networks for multivariate failure time data.

## Key findings

- The proposed methods outperform traditional approaches in variable selection and prediction.
- The framework identifies both known clinical factors and new genetic markers in prostate cancer data.
- The method remains robust even when the assumption of common predictors is violated.

## Abstract

This study addresses the problem of simultaneous variable selection and model estimation in multivariate failure time data, a common challenge in clinical trials with multiple correlated time-to-event endpoints. We propose a unified framework that identifies predictors shared across outcomes, applicable to both low- and high-dimensional settings. For linear marginal hazard models, we develop a penalized pseudo-partial likelihood approach with a group LASSO-type penalty applied to the ℓ2 norms of coefficients corresponding to the same covariates across marginal hazard functions. To capture potential nonlinear effects, we further extend the approach to a sparse-input neural network model with structured group penalties on input-layer weights. Both methods are optimized using a composite gradient descent algorithm combining standard gradient steps with proximal updates. Simulation studies demonstrate that the proposed methods yield superior variable selection and predictive performance compared to traditional and outcome-specific approaches, while remaining robust to violations of the common predictor assumption. In an application to advanced prostate cancer data, the framework identifies both established clinical factors and potentially novel prognostic single-nucleotide polymorphisms for overall and progression-free survival. This work provides a flexible and robust tool for analyzing complex multivariate survival data, with potential utility in prognostic modeling and personalized medicine.