# On the assumption of independent right censoring

## TL;DR

This paper examines various assumptions on right-censoring mechanisms in survival analysis, distinguishing between minimal identifiability and stronger independence assumptions, and characterizes their implications for estimator consistency.

## Contribution

It provides a comprehensive classification of eight assumptions on right censoring, clarifying their relationships and implications for survival analysis estimators.

## Key findings

- Eight assumptions categorized into two groups.
- Characterization of pointwise and full independence.
- Examples illustrating assumption differences.

## Abstract

Various assumptions on a right-censoring mechanism to ensure consistency of the Kaplan--Meier and Aalen--Johansen estimators in a competing risks setting are studied. Specifically, eight different assumptions are seen to fall in two categories: a weaker identifiability assumption, which is the weakest possible assumption in a precise sense, and a stronger representativity assumption which ensures the existence of an independent censoring time. When a given censoring time is considered, similar assumptions can be made on the censoring time. This allows for a characterization of so-called pointwise independence as well as full independence of censoring time and event time and type. Examples illustrate how the various assumptions differ.