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Deep Survival Analysis for Competing Risk Modeling with Functional Covariates and Missing Data Imputation

Penglei Gao, Yan Zou, Abhijit Duggal, Shuaiqi Huang, Faming Liang, Xiaofeng Wang

TL;DR

The paper tackles time-to-event prediction with competing risks in ICU settings that include functional covariates and missing data. It introduces FCRN, a deep learning framework that encodes time-varying covariates via a learnable Basis Layer and imputes missing values with a gradient-based Imputation-regularized Optimization module, jointly estimating both cause-specific and sub-distribution hazards in discrete time. Across synthetic data and two large ICU cohorts (MIMIC-IV and Cleveland Clinic), FCRN outperforms Random Survival Forests and traditional competing-risks models, showing improved calibration and robustness to missing data and functional inputs, with strong cross-cohort generalization. These results suggest practical value for ICU discharge planning and post-discharge care by enabling precise risk stratification for readmission and mortality. The work provides a cohesive end-to-end approach for integrating heterogeneous clinical data in prognostic modeling for critical care.

Abstract

We introduce the Functional Competing Risk Net (FCRN), a unified deep-learning framework for discrete-time survival analysis under competing risks, which seamlessly integrates functional covariates and handles missing data within an end-to-end model. By combining a micro-network Basis Layer for functional data representation with a gradient-based imputation module, FCRN simultaneously learns to impute missing values and predict event-specific hazards. Evaluated on multiple simulated datasets and a real-world ICU case study using the MIMIC-IV and Cleveland Clinic datasets, FCRN demonstrates substantial improvements in prediction accuracy over random survival forests and traditional competing risks models. This approach advances prognostic modeling in critical care by more effectively capturing dynamic risk factors and static predictors while accommodating irregular and incomplete data.

Deep Survival Analysis for Competing Risk Modeling with Functional Covariates and Missing Data Imputation

TL;DR

The paper tackles time-to-event prediction with competing risks in ICU settings that include functional covariates and missing data. It introduces FCRN, a deep learning framework that encodes time-varying covariates via a learnable Basis Layer and imputes missing values with a gradient-based Imputation-regularized Optimization module, jointly estimating both cause-specific and sub-distribution hazards in discrete time. Across synthetic data and two large ICU cohorts (MIMIC-IV and Cleveland Clinic), FCRN outperforms Random Survival Forests and traditional competing-risks models, showing improved calibration and robustness to missing data and functional inputs, with strong cross-cohort generalization. These results suggest practical value for ICU discharge planning and post-discharge care by enabling precise risk stratification for readmission and mortality. The work provides a cohesive end-to-end approach for integrating heterogeneous clinical data in prognostic modeling for critical care.

Abstract

We introduce the Functional Competing Risk Net (FCRN), a unified deep-learning framework for discrete-time survival analysis under competing risks, which seamlessly integrates functional covariates and handles missing data within an end-to-end model. By combining a micro-network Basis Layer for functional data representation with a gradient-based imputation module, FCRN simultaneously learns to impute missing values and predict event-specific hazards. Evaluated on multiple simulated datasets and a real-world ICU case study using the MIMIC-IV and Cleveland Clinic datasets, FCRN demonstrates substantial improvements in prediction accuracy over random survival forests and traditional competing risks models. This approach advances prognostic modeling in critical care by more effectively capturing dynamic risk factors and static predictors while accommodating irregular and incomplete data.

Paper Structure

This paper contains 14 sections, 33 equations, 4 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Method
  4. Problem Statements
  5. Discrete-time Cause-specific Model
  6. Discrete-time Sub-distribution Model
  7. Deep-learning Framework with Functional Covariates and Missing Data
  8. Experimental Results
  9. Dataset
  10. Evaluation Metrics
  11. Implementation Details
  12. Results of Synthetic Data
  13. Results of Real-world Data Analysis
  14. Discussion and conclusions

Figures (4)

  • Figure 1: ICU data overview and the prediction flow.
  • Figure 2: The overall deep-learning framework of our method. (a) The main network architecture consists of three components for the Cause-specific and the sub-distribution model. (b) Basis layer utilizes the micro neural network with functional input. (c) Algorithm of missing value imputation based on the observed data and the network outcome $y$.
  • Figure 3: Detailed structure of the Basis Layer.
  • Figure 4: Sampled functional curves for the two real-world datasets.