TripleSurv: Triplet Time-adaptive Coordinate Loss for Survival Analysis

TL;DR

TripleSurv tackles censored time-to-event prediction by introducing a time-adaptive TAPR-loss that folds time differences into pairwise ranking, and by coordinating this with likelihood and calibration losses in a unified objective. By modeling discrete-time survival with Cat or MTLR distributions, TripleSurv achieves strong discrimination (C-index), robust calibration (IBS), and reliable time-dependent performance (TDAUC) across four diverse datasets, including high-censor-rate and semi-synthetic tasks. The method demonstrates superior or competitive performance against state-of-the-art baselines and provides a flexible, robust framework for real-world survival analysis. These results suggest meaningful practical impact for prognosis and decision-making in domains with censored data, and the approach is extensible to multi-modal data in future work.

Abstract

A core challenge in survival analysis is to model the distribution of censored time-to-event data, where the event of interest may be a death, failure, or occurrence of a specific event. Previous studies have showed that ranking and maximum likelihood estimation (MLE)loss functions are widely-used for survival analysis. However, ranking loss only focus on the ranking of survival time and does not consider potential effect of samples for exact survival time values. Furthermore, the MLE is unbounded and easily subject to outliers (e.g., censored data), which may cause poor performance of modeling. To handle the complexities of learning process and exploit valuable survival time values, we propose a time-adaptive coordinate loss function, TripleSurv, to achieve adaptive adjustments by introducing the differences in the survival time between sample pairs into the ranking, which can encourage the model to quantitatively rank relative risk of pairs, ultimately enhancing the accuracy of predictions. Most importantly, the TripleSurv is proficient in quantifying the relative risk between samples by ranking ordering of pairs, and consider the time interval as a trade-off to calibrate the robustness of model over sample distribution. Our TripleSurv is evaluated on three real-world survival datasets and a public synthetic dataset. The results show that our method outperforms the state-of-the-art methods and exhibits good model performance and robustness on modeling various sophisticated data distributions with different censor rates. Our code will be available upon acceptance.

Figures (6)

• Figure 1: Diagram of the interval partition of study time.
• Figure 2: The fully-connected neural network for one-dimensional data.
• Figure 3: Performance comparison using the TDAUC in SUPPORT.
• Figure 4: Performance comparison using the TDAUC in BIDDING.
• Figure 5: Performance comparison using the TDAUC in METABRIC.