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领域的一项课题。尽管针对不确定性量化已有关于严格恰当评分规则的基础理论，但关于生存分析中此类规则的研究仍较为有限。本文探究了四种主要严格恰当评分规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）具有恰当性。我们进一步利用实际数据集比较了这些扩展评分规则的估计性能，其中对数评分与布里尔评分的扩展表现最优。