Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Deep Neural Networks for Survival Analysis Based on a Multi-Task Framework

Stephane Fotso

TL;DR

The paper tackles survival analysis when nonlinear relationships exist between features and time-to-event outcomes. It introduces Neural Multi-Task Logistic Regression (N-MTLR), a deep learning extension of the MTLR framework that maps features through a nonlinear psi(x) to predict interval-specific event probabilities. Through extensive experiments on simulated and real datasets, N-MTLR outperforms linear MTLR and matches or surpasses CoxPH, especially in nonlinear settings, and is implemented in Python with TensorFlow/Keras. This approach offers a practical, flexible alternative for accurate survival predictions under censoring without relying on CoxPH assumptions.

Abstract

Survival analysis/time-to-event models are extremely useful as they can help companies predict when a customer will buy a product, churn or default on a loan, and therefore help them improve their ROI. In this paper, we introduce a new method to calculate survival functions using the Multi-Task Logistic Regression (MTLR) model as its base and a deep learning architecture as its core. Based on the Concordance index (C-index) and Brier score, this method outperforms the MTLR in all the experiments disclosed in this paper as well as the Cox Proportional Hazard (CoxPH) model when nonlinear dependencies are found.

Deep Neural Networks for Survival Analysis Based on a Multi-Task Framework

TL;DR

The paper tackles survival analysis when nonlinear relationships exist between features and time-to-event outcomes. It introduces Neural Multi-Task Logistic Regression (N-MTLR), a deep learning extension of the MTLR framework that maps features through a nonlinear psi(x) to predict interval-specific event probabilities. Through extensive experiments on simulated and real datasets, N-MTLR outperforms linear MTLR and matches or surpasses CoxPH, especially in nonlinear settings, and is implemented in Python with TensorFlow/Keras. This approach offers a practical, flexible alternative for accurate survival predictions under censoring without relying on CoxPH assumptions.

Abstract

Survival analysis/time-to-event models are extremely useful as they can help companies predict when a customer will buy a product, churn or default on a loan, and therefore help them improve their ROI. In this paper, we introduce a new method to calculate survival functions using the Multi-Task Logistic Regression (MTLR) model as its base and a deep learning architecture as its core. Based on the Concordance index (C-index) and Brier score, this method outperforms the MTLR in all the experiments disclosed in this paper as well as the Cox Proportional Hazard (CoxPH) model when nonlinear dependencies are found.

Paper Structure

This paper contains 24 sections, 4 equations, 6 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Survival Analysis, an Overview
  3. Notations
  4. Classical Models
  5. Kaplan-Meier Model
  6. Cox Proportional Hazard Model
  7. Multi-Task Logistic Regression (MTLR)
  8. Neural Multi-Task Logistic Regression (N-MTLR)
  9. Added value
  10. Proposed Model
  11. Example
  12. Experiments
  13. Performance metrics
  14. Concordance Index
  15. Brier Score
  16. ...and 9 more sections

Figures (6)

  • Figure 2: Representation of a 2-hidden layer transformation
  • Figure 3: C-index and Brier score --- Weibull survival times with linear risk function
  • Figure 4: C-index and Brier score --- Weibull survival times with a square risk function
  • Figure 5: C-index and Brier score --- Weibull survival times with a gaussian risk function
  • Figure 6: C-index and Brier score --- WHAS
  • ...and 1 more figures