论文标题
适当的一致性指数，以适应时变风险
A Proper Concordance Index for Time-Varying Risk
论文作者
论文摘要
Harrel的一致性指数是生存模型的常用歧视度量，尤其是对于个人的相对订购个人风险是时间无关的模型，例如比例危害模型。关于如何将相对风险随时间变化的模型扩展到模型，例如，在越过危险率的情况下，相对风险会有所不同。我们表明，从真实的数据生成模型将它们最大化的意义上说，这些协和索引不合适。此外，我们表明，仅当使用的风险分数与第一个事件时的危险率一致时，对于每个可比较的事件，一致性指数是正确的。因此，我们建议在计算一致性时使用危险率作为时间变化的风险评分。通过模拟，我们证明了其他一致性指数可能导致通过真实模型选择错误的模型，从而证明我们建议的风险预测在模型选择和损失功能中的使用是合理的，例如深度学习模型。
Harrel's concordance index is a commonly used discrimination metric for survival models, particularly for models where the relative ordering of the risk of individuals is time-independent, such as the proportional hazards model. There are several suggestions, but no consensus, on how it could be extended to models where relative risk can vary over time, e.g.\ in case of crossing hazard rates. We show that these concordance indices are not proper, in the sense that they are maximised in the limit by the true data generating model. Furthermore, we show that a concordance index is proper if and only if the risk score used is concordant with the hazard rate at the first event time for each comparable pair of events. Thus, we suggest using the hazard rate as the time-varying risk score when calculating concordance. Through simulations, we demonstrate situations in which other concordance indices can lead to incorrect models being selected over a true model, justifying the use of our suggested risk prediction in both model selection and in loss functions in, e.g., deep learning models.
