TripleSurv: Triplet Time-Adaptive Coordinate Learning Approach for Survival Analysis

A core challenge in survival analysis is to model the distribution of 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 loss functions are widely-used learning approaches for survival analysis. However, ranking loss only focus on the ranking of survival time and does not consider potential effect of samples’ exact survival time values. Furthermore, the maximum likelihood estimation 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.