Statistical models are considered for (partial) observation of independent, identically distributed failure times, subjected to censoring from the right. A minimal class of censoring patterns is determined under the assumption that the failure intensities are as they would have been without censoring. This class is then used to discuss the statistical models for right censored survival data, where, e.g., the Kaplan-Meier estimator exploits all available information about the failure time distribution. The counting process description of survival data is used throughout.
"Right Censoring and Martingale Methods for Failure Time Data." Ann. Statist. 17 (3) 1133 - 1156, September, 1989. https://doi.org/10.1214/aos/1176347260