[Paper Review] Deep Kernel Survival Analysis and Subject-Specific Survival Time Prediction Intervals

George H. Chen|arXiv (Cornell University)|Jul 25, 2020

Domain Adaptation and Few-Shot Learning6 citations

TL;DR

This paper introduces a deep neural network framework that learns kernel functions for kernel survival analysis, enabling subject-specific survival predictions with statistically valid prediction intervals. It demonstrates that these intervals can quantify uncertainty across methods and serve as a new performance metric, while achieving competitive accuracy with existing models.

ABSTRACT

Kernel survival analysis methods predict subject-specific survival curves and times using information about which training subjects are most similar to a test subject. These most similar training subjects could serve as forecast evidence. How similar any two subjects are is given by the kernel function. In this paper, we present the first neural network framework that learns which kernel functions to use in kernel survival analysis. We also show how to use kernel functions to construct prediction intervals of survival time estimates that are statistically valid for individuals similar to a test subject. These prediction intervals can use any kernel function, such as ones learned using our neural kernel learning framework or using random survival forests. Our experiments show that our neural kernel survival estimators are competitive with a variety of existing survival analysis methods, and that our prediction intervals can help compare different methods' uncertainties, even for estimators that do not use kernels. In particular, these prediction interval widths can be used as a new performance metric for survival analysis methods.

Motivation & Objective

• To develop a neural network framework that learns optimal kernel functions for kernel survival analysis, improving subject-specific survival predictions.
• To construct prediction intervals for survival times that are statistically valid at the individual level using split conformal prediction.
• To enable uncertainty quantification across diverse survival analysis methods, even those not based on kernels.
• To evaluate the performance of deep kernel survival estimators and their prediction intervals on real healthcare datasets.
• To provide a new metric—prediction interval width—for comparing uncertainty in survival models.

Proposed method

• Adapts neural kernel learning from classification to survival analysis, using a base neural network to map subjects into an embedding space where kernel similarity is computed via Euclidean distance.
• Employs Beran’s conditional Kaplan-Meier estimator with learned kernel functions to predict subject-specific survival curves and times.
• Applies split conformal prediction and its weighted variant to generate marginal and locally valid prediction intervals for survival time estimates.
• Uses a user-specified target coverage level α to calibrate prediction intervals, ensuring empirical coverage matches nominal levels.
• Supports both marginal and local validity: local intervals are averaged over subjects similar to the test subject via the kernel function.
• Enables warm-start training using random survival forests or other neural survival models to improve convergence and performance.

Experimental results

Research questions

• RQ1 Can a deep neural network framework effectively learn kernel functions for kernel survival analysis, improving prediction accuracy?
• RQ2 Can prediction intervals constructed using kernel-based conformal prediction be statistically valid for individual subjects?
• RQ3 How do the widths of prediction intervals compare across different survival analysis methods, and can they serve as a performance metric?
• RQ4 Does the use of locally valid prediction intervals improve clinical interpretability compared to marginally valid ones?
• RQ5 Can the proposed method be applied to non-kernel-based survival estimators by separately learning a kernel for interval construction?

Key findings

• The proposed deep kernel survival estimators, such as nks-res-diag and nks-mlp with random survival forest initialization, achieve competitive C-index values compared to existing methods.
• Prediction intervals constructed using split conformal prediction exhibit empirical coverage probabilities that closely match the user-specified target coverage levels (e.g., 90% for α = 0.1).
• The width of prediction intervals can be used to compare uncertainty across different survival models, even when those models do not use kernel functions.
• Locally valid prediction intervals are more informative for individual clinical decisions, as they reflect uncertainty relative to similar patients.
• The method enables identification of subjects with higher prediction uncertainty by analyzing interval widths in the context of similar training subjects.
• Despite statistical validity, prediction interval widths remain relatively wide, suggesting room for improvement in uncertainty calibration.