Censoring

The most common form of censoring in clinical studies. It occurs when a subject's event time is known only to be greater than a certain value. This happens when a patient is lost to follow-up, withdraws from the study, or the study ends before the event occurs. Standard survival methods like the Kaplan-Meier estimator and Cox proportional hazards model are designed to handle independent right censoring by incorporating partial information up to the censoring time.

Occurs when the event of interest has already happened before the observation period begins, meaning the true event time is known only to be less than a specific value. For example, in a study of HIV seroconversion, a subject may test positive at their first visit, indicating infection occurred before enrollment. Left censoring requires specialized analytical approaches distinct from right censoring, often involving interval-censored methods or assumptions about the event time distribution.

Arises when the event is known to have occurred within a finite time interval, but the exact moment is unknown. This is typical in longitudinal studies with periodic follow-up visits. For instance, if a patient is tumor-free at a 6-month scan but shows recurrence at a 12-month scan, the recurrence time is interval-censored between months 6 and 12. Turnbull's algorithm is a non-parametric method commonly used to estimate the survival function under interval censoring.

A fixed-duration study design where all subjects begin observation at the same time, and the study terminates at a pre-specified calendar date. Any subject who has not experienced the event by that end date is censored. The number of events is a random variable, but the censoring time is fixed. This is common in animal carcinogenicity studies and engineering life-testing experiments where the test duration is predetermined.

A study design where observation continues until a pre-specified number of events has occurred, rather than a fixed time. For example, an experiment may run until exactly 50% of subjects have failed. The study duration is a random variable, but the number of observed events is fixed. This approach is frequently used in industrial reliability testing to control experimental cost and duration while ensuring a minimum number of failures for analysis.

A critical assumption underlying most survival analysis methods. Censoring is non-informative if the probability of being censored is unrelated to the probability of experiencing the event. For example, a patient moving out of state is typically non-informative. Violation of this assumption—informative censoring—occurs when censoring is related to prognosis, such as sicker patients dropping out, and leads to biased survival estimates requiring sensitivity analyses or joint modeling approaches.