Model-free time-to-event regression under confounding presents challenges due to biases introduced by causal and censoring sampling mechanisms. This phenomenology poses problems for classical non-parametric estimators like Beran's or the k-nearest neighbours algorithm. In this study, we propose a natural framework that leverages the structure of reproducing kernel Hilbert spaces (RKHS) and, specifically, the concept of kernel mean embedding to address these limitations. Our framework has the potential to enable statistical counterfactual modeling, including counterfactual prediction and hypothesis testing, under right-censoring schemes. Through simulations and an application to the SPRINT trial, we demonstrate the practical effectiveness of our method, yielding coherent results when compared to parallel analyses in existing literature. We also provide a theoretical analysis of our estimator through an RKHS-valued empirical process. Our approach offers a novel tool for performing counterfactual survival estimation in observational studies with incomplete information. It can also be complemented by state-of-the-art algorithms based on semi-parametric and parametric models.

翻译：在混杂因素存在的情况下，无模型时间-事件回归因因果和删失抽样机制引入的偏差而面临挑战。这类现象对经典非参数估计量（如Beran估计或k近邻算法）构成了问题。本研究提出了一个自然框架，利用再生核希尔伯特空间（RKHS）的结构，特别是核均值嵌入的概念来应对这些局限性。该框架有望在右删失机制下实现统计反事实建模，包括反事实预测和假设检验。通过模拟实验及在SPRINT试验中的应用，我们展示了该方法的实际有效性，所得结果与现有文献中的平行分析具有一致性。我们还通过RKHS取值的经验过程对估计量进行了理论分析。该方法为在信息不完整的观察性研究中进行反事实生存估计提供了新工具，并可与基于半参数及参数模型的最新算法相互补充。