Time-to-event prediction has been an important practical task for longitudinal studies in many fields such as manufacturing, medicine, and healthcare. While most of the conventional survival analysis approaches suffer from the presence of censored failures and statistically circumscribed assumptions, few attempts have been made to develop survival learning machines that explore the underlying relationship between repeated measures of covariates and failure-free survival probability. This requires a purely dynamic-data-driven prediction approach, free of survival models or statistical assumptions. To this end, we propose two real-time survival networks: a time-dependent survival neural network (TSNN) with a feed-forward architecture and a recurrent survival neural network (RSNN) incorporating long short-term memory units. The TSNN additively estimates a latent failure risk arising from the repeated measures and performs multiple binary classifications to generate prognostics of survival probability, while the RSNN with time-dependent input covariates implicitly estimates the relation between these covariates and the survival probability. We propose a novel survival learning criterion to train the neural networks by minimizing the censoring Kullback–Leibler divergence, which guarantees monotonicity of the resulting probability. Besides the failure-event AUC, C-index, and censoring Brier score, we redefine a survival time estimate to evaluate the performance of the competing models. Experiments on four datasets demonstrate the great promise of our approach in real applications.

中文翻译：

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生存神经网络用于纵向研究中的事件预测时间

事件预测时间已成为许多领域（例如制造业，医学和医疗保健）中纵向研究的重要实际任务。尽管大多数传统的生存分析方法都存在被审查的故障和统计上受限制的假设，但很少有人尝试开发生存学习机，以探索协变量重复测量与无故障生存概率之间的潜在关系。这需要纯粹的动态数据驱动的预测方法，而没有生存模型或统计假设。为此，我们提出了两个实时生存网络：具有前馈架构的时间相关生存神经网络（TSNN）和包含长短期记忆单元的递归生存神经网络（RSNN）。TSNN可累加估算重复测量产生的潜在故障风险，并执行多种二元分类以生成生存概率的预测，而带有时变输入协变量的RSNN隐式估算这些协变量与生存概率之间的关系。我们提出了一种新颖的生存学习准则，通过最小化审查Kullback-Leibler散度来训练神经网络，从而保证了所得概率的单调性。除了故障事件AUC，C指数和审查Brier分数，我们还重新定义了生存时间估算值，以评估竞争模型的性能。在四个数据集上进行的实验证明了我们的方法在实际应用中的巨大前景。