Survival analysis is the problem of estimating probability distributions for future event times, which can be seen as a problem in uncertainty quantification. Although there are fundamental theories on strictly proper scoring rules for uncertainty quantification, little is known about those for survival analysis. In this paper, we investigate extensions of four major strictly proper scoring rules for survival analysis and we prove that these extensions are proper under certain conditions, which arise from the discretization of the estimation of probability distributions. We also compare the estimation performances of these extended scoring rules by using real datasets, and the extensions of the logarithmic score and the Brier score performed the best.

翻译：生存分析是估计未来事件时间概率分布的问题，可视为不确定性量化问题。尽管已有关于不确定性量化严格适当评分准则的基础理论，但针对生存分析的此类准则研究尚不充分。本文研究了四种主要严格适当评分准则在生存分析中的扩展形式，并证明这些扩展在特定条件下（源于概率分布估计的离散化）具有适当性。我们通过真实数据集比较了这些扩展评分准则的估计性能，其中对数评分与布莱尔评分的扩展表现最佳。