Candès Emmanuel J, Lei Lihua, Ren Zhimei
ArXiv. 2023 Apr 23:arXiv:2103.09763v3.
Existing survival analysis techniques heavily rely on strong modelling assumptions and are, therefore, prone to model misspecification errors. In this paper, we develop an inferential method based on ideas from conformal prediction, which can wrap around any survival prediction algorithm to produce calibrated, covariate-dependent lower predictive bounds on survival times. In the Type I right-censoring setting, when the censoring times are completely exogenous, the lower predictive bounds have guaranteed coverage in finite samples without any assumptions other than that of operating on independent and identically distributed data points. Under a more general conditionally independent censoring assumption, the bounds satisfy a doubly robust property which states the following: marginal coverage is approximately guaranteed if either the censoring mechanism or the conditional survival function is estimated well. Further, we demonstrate that the lower predictive bounds remain valid and informative for other types of censoring. The validity and efficiency of our procedure are demonstrated on synthetic data and real COVID-19 data from the UK Biobank.
现有的生存分析技术严重依赖于强大的建模假设，因此容易出现模型设定错误。在本文中，我们基于共形预测的思想开发了一种推理方法，该方法可以围绕任何生存预测算法，以生成关于生存时间的校准的、依赖协变量的较低预测界限。在I型右删失设置中，当删失时间完全是外生的时候，在有限样本中，除了对独立同分布的数据点进行操作这一假设外，无需任何其他假设，较低预测界限就能保证覆盖率。在更一般的条件独立删失假设下，这些界限满足双重稳健性，表述如下：如果删失机制或条件生存函数估计良好，则大致保证边际覆盖率。此外，我们证明了较低预测界限对于其他类型的删失仍然有效且具有信息性。我们的方法的有效性和效率在合成数据以及来自英国生物银行的真实新冠疫情数据上得到了验证。
