Nonparametric estimation of average effects of a continuous treatment for survival data with a cured fraction

Estimating the causal effect of a continuous treatment on survival data, particularly in cases where there is a cured fraction from observational studies, is a significant issue. However, this topic is not well addressed in the existing literature. Current methods either rely on strong parametric assumptions or struggle to effectively control for confounding variables. In this study, we propose a novel nonparametric estimation method that utilizes a weighted generalized Kaplan-Meier survival estimator. This method aims to estimate the average effects of a continuous treatment on both the probability of being cured and the restricted mean survival time. Notably, our approach does not require any parametric assumptions about the effects, and it can efficiently control for multiple confounding variables. A simulation study demonstrates that our proposed method outperforms existing approaches, particularly when the average effects are complex or when confounding is strong. We apply this method to data from a study of chlamydia patients to evaluate the average effects of years of schooling on the probability of being immune to reinfection, as well as on the restricted mean survival time.