发表机构
Department of Radiation Oncology, University of Colorado School of Medicine; Department of Radiation Oncology, University of Texas Southwestern Medical Center（科罗拉多大学医学院放射肿瘤学系; 德克萨斯大学西南医学中心放射肿瘤学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究在深度生存模型中，针对小且严重删失的肿瘤学队列端到端训练时频繁计算C-index成本高的问题，提出价值单调一致性损失SCL，它与架构无关，训练时损失值与C-index强相关，能可靠替代C-index用于模型选择等。
AI 中文摘要
深度生存模型几乎完全通过一致性指数（C-index）进行评估，但通常使用似然目标（如Cox偏似然、离散时间负对数似然和DeepHit似然）进行训练。这种不匹配通常被认为是可以接受的，因为在训练期间可以在验证数据上重新计算C-index。然而，对于在小的、严重删失的肿瘤学队列上对高容量编码器进行端到端训练，频繁的C-index评估计算成本很高，使得损失值本身成为监测、早期停止和模型选择的重要信号。我们表明似然损失在此目的上不可靠，并提出了一种价值单调一致性损失。我们证明每个严格适当的生存似然都存在损失下降而C-index不变的方向，导致损失值与排序性能解耦。然后我们研究了一种Sigmoid一致性损失（SCL），其值在一个温度项的范围内近似于1减去C-index，确保在优化过程中较低的损失对应较高的C-index。该损失与架构无关，对于线性模型可简化为凸生存排序支持向量机。在来自四种模态的18个数据集上使用统一的五折交叉验证协议，SCL实现了与标准似然损失相当的判别能力，并且是最佳的或在最佳C-index的一个标准差范围内。与似然损失不同，SCL在训练期间保持损失值与C-index之间的强相关性，秩相关为0.96至0.99，而似然损失为-0.03至0.53。通过综合Brier分数测量的校准效果相当。SCL提供了一个价值单调的优化目标，其值可以在昂贵的端到端训练期间作为C-index的可靠替代。
英文摘要
Deep survival models are evaluated almost exclusively by the concordance index (C-index), yet they are commonly trained using likelihood objectives such as the Cox partial likelihood, discrete-time negative log-likelihood, and DeepHit likelihood. This mismatch is usually considered acceptable because the C-index can be recomputed on validation data during training. However, for end-to-end training of high-capacity encoders on small, heavily censored oncology cohorts, frequent C-index evaluation is computationally expensive, making the loss value itself an important signal for monitoring, early stopping, and model selection. We show that likelihood losses are unreliable for this purpose and propose a value-monotone concordance loss. We prove that every strictly proper survival likelihood admits directions where the loss decreases while the C-index remains unchanged, causing the loss value to decouple from ranking performance. We then study a sigmoid concordance loss (SCL), whose value approximates one minus the C-index up to a temperature term, ensuring that lower loss corresponds to higher C-index during optimization. The loss is architecture agnostic and reduces to a convex survival ranking support vector machine for linear models. Across eighteen datasets from four modalities using a unified five-fold cross-validation protocol, SCL achieves discrimination comparable to standard likelihood losses and is the best or within one standard deviation of the best C-index. Unlike likelihood losses, SCL maintains a strong correlation between loss value and C-index during training, with rank correlations of 0.96 to 0.99 compared with -0.03 to 0.53 for likelihood losses. Calibration measured by the integrated Brier score is comparable. SCL provides a value-monotone optimization objective whose value can serve as a reliable surrogate for the C-index during expensive end-to-end training.
