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The Deep Promotion Time Cure Model

Victor Medina-Olivares, Stefan Lessmann, Nadja Klein

TL;DR

A novel method for predicting time-to-event data in the presence of cure fractions based on flexible survival models integrated into a deep neural network (DNN) framework that is suitable for large-scale applications.

Abstract

We propose a novel method for predicting time-to-event in the presence of cure fractions based on flexible survivals models integrated into a deep neural network framework. Our approach allows for non-linear relationships and high-dimensional interactions between covariates and survival and is suitable for large-scale applications. Furthermore, we allow the method to incorporate an identified predictor formed of an additive decomposition of interpretable linear and non-linear effects and add an orthogonalization layer to capture potential higher dimensional interactions. We demonstrate the usefulness and computational efficiency of our method via simulations and apply it to a large portfolio of US mortgage loans. Here, we find not only a better predictive performance of our framework but also a more realistic picture of covariate effects.

The Deep Promotion Time Cure Model

TL;DR

A novel method for predicting time-to-event data in the presence of cure fractions based on flexible survival models integrated into a deep neural network (DNN) framework that is suitable for large-scale applications.

Abstract

We propose a novel method for predicting time-to-event in the presence of cure fractions based on flexible survivals models integrated into a deep neural network framework. Our approach allows for non-linear relationships and high-dimensional interactions between covariates and survival and is suitable for large-scale applications. Furthermore, we allow the method to incorporate an identified predictor formed of an additive decomposition of interpretable linear and non-linear effects and add an orthogonalization layer to capture potential higher dimensional interactions. We demonstrate the usefulness and computational efficiency of our method via simulations and apply it to a large portfolio of US mortgage loans. Here, we find not only a better predictive performance of our framework but also a more realistic picture of covariate effects.
Paper Structure (20 sections, 7 equations, 8 figures, 7 tables)

This paper contains 20 sections, 7 equations, 8 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Related work
  3. Methodology
  4. The Promotion Time Cure Model
  5. The Deep-PTCM
  6. Estimation of the Deep-PTCM
  7. Performance Metrics
  8. AUC for Cure Proportions (AUC)
  9. Integrated Brier Score (IBS)
  10. Simulation study
  11. Application
  12. Data
  13. Network Architecture and Training
  14. Results
  15. Discussion
  16. ...and 5 more sections

Figures (8)

  • Figure 1: Generic representation of the Deep-PTCM architecture.
  • Figure 2: Linear coefficients estimated by Deep-PTCM with orthogonalization (Deep-PTCM-Ort).
  • Figure 3: Single-family loan-level dataset from Freddie Mac. Left: distribution of default events versus duration. Right: ratio between the number of default events and borrowers at risk over calendar time. The solid blue line is the moving average for a six-month window.
  • Figure 4: Left: Kaplan-Meier curve. Right: survival function of the risk factors $S(t)$ (dashed). The blue-shaded curves are those obtained by 500 bootstrap samples with replacement.
  • Figure 5: Comparison of the effect of numerical covariates on the predictor $\eta$ for four cure models.
  • ...and 3 more figures