• Department of Biostatistics, Brown University, 121 S Main St, Providence, RI 02912, USA.
• Department of Statistics and Data Science, Carnegie Mellon University, 132 J Baker Hall, Pittsburgh, PA 15213, USA.
• Department of Biostatistics and Epidemiology, University Pennsylvania, 423 Guardian Drive, Philadelphia, PA 19104, USA.

Instrumental variable (IV) methods allow us the opportunity to address unmeasured confounding in causal inference. However, most IV methods are only applicable to discrete or continuous outcomes with very few IV methods for censored survival outcomes. In this article, we propose nonparametric estimators for the local average treatment effect on survival probabilities under both covariate-dependent and outcome-dependent censoring. We provide an efficient influence function-based estimator and a simple estimation procedure when the IV is either binary or continuous. The proposed estimators possess double-robustness properties and can easily incorporate nonparametric estimation using machine learning tools. In simulation studies, we demonstrate the flexibility and double robustness of our proposed estimators under various plausible scenarios. We apply our method to the Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial for estimating the causal effect of screening on survival probabilities and investigate the causal contrasts between the two interventions under different censoring assumptions.