  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.
