  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.
