Doubly valid and doubly sharp sensitivity analysis to unobserved confounding for survival outcomes

Abstract

Time-to-event outcomes are central in oncology and rare diseases, where treatment effects are often summarized by differences in survival curves or Restricted Mean Survival Time (RMST). In real-world data, estimating these causal effects relies on the absence of unobserved confounding, an assumption that is rarely satisfied. We develop a sensitivity analysis framework for causal treatment effects with survival outcomes under the Marginal Sensitivity Model (MSM). We introduce doubly valid and doubly sharp (DVDS) bounds for differences in survival functions and RMST, extending recent DVDS results to the time-to-event setting while accounting for informative censoring. In practice, our method yields tighter bounds and improved computational efficiency compared to a previous approach from the literature, on simulated and real data. For tractability, we assume independence between censoring and unobserved confounding, a limit that should be addressed in future works.