Lu Chengyuan, Putter Hein, Girondo Mar Rodríguez, Goeman Jelle J
Biomedical Data Sciences, Leiden University Medical Center, Leiden, the Netherlands.
Stat Med. 2025 Jul;44(15-17):e70193. doi: 10.1002/sim.70193.
Assessing the predictive performance is a crucial aspect in survival modeling, essential for model selection, tuning parameter determination, and evaluating additional predictive ability. The predictive log-likelihood has been recommended as a suitable evaluation measure, particularly for survival models, which generally return entire survival curves rather than point predictions. However, applying predictive likelihood in semiparametric and nonparametric survival models is problematic since the survival curves are step-functions, which result in zero predictive likelihood when events occur at previously unobserved time points. The most well-known existing solution, Verweij's predictive partial likelihood, is limited to Cox models. In this article, we propose a novel approach based on nearest-neighbor kernel smoothing that is usable in general semi- and nonparametric survival models. We show that our new method performs competitively with existing methods in the Cox setting while offering broader applicability, including testing for the presence of a frailty term and determining the optimal level of smoothness in penalized additive hazards models.
评估预测性能是生存建模中的一个关键方面，对于模型选择、调优参数确定以及评估额外的预测能力至关重要。预测对数似然已被推荐为一种合适的评估指标，特别是对于生存模型，生存模型通常返回整个生存曲线而非点预测。然而，在半参数和非参数生存模型中应用预测似然存在问题，因为生存曲线是阶梯函数，当事件发生在先前未观察到的时间点时会导致预测似然为零。现有的最著名解决方案，即Verweij的预测偏似然，仅限于Cox模型。在本文中，我们提出了一种基于最近邻核平滑的新方法，该方法可用于一般的半参数和非参数生存模型。我们表明，我们的新方法在Cox设置中与现有方法相比具有竞争力，同时具有更广泛的适用性，包括检验脆弱项的存在以及确定惩罚加法风险模型中的最佳平滑水平。
