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.

翻译：生存分析的核心挑战在于对含有删失的时间-事件数据进行建模，其中感兴趣的事件可能是死亡、故障或特定事件的发生。已有研究表明，排序损失和最大似然估计（MLE）损失函数在生存分析中被广泛使用。然而，排序损失仅关注生存时间的排序，未考虑样本对精确生存时间值的潜在影响。此外，MLE损失函数无界且易受异常值（如删失数据）影响，可能导致建模性能不佳。为应对学习过程的复杂性并充分利用有价值的生存时间值，我们提出一种时间自适应坐标损失函数TripleSurv，通过将样本对之间的生存时间差异引入排序过程来实现自适应调整，从而激励模型对样本对的相对风险进行定量排序，最终提升预测精度。最重要的是，TripleSurv能够通过样本对的排序顺序量化相对风险，并考虑时间间隔作为权衡因素，以校准模型在样本分布上的鲁棒性。我们在三个真实生存数据集和一个公开合成数据集上评估了TripleSurv。结果表明，该方法优于现有最先进方法，并在对具有不同删失率的多种复杂数据分布进行建模时，展现出良好的模型性能和鲁棒性。我们的代码将在论文被接收后公开。