Censoring Mechanisms

The most common form of censoring, occurring when a subject's event time is only known to exceed a certain value. This happens when the study ends before the event occurs, the subject is lost to follow-up, or withdraws from the study. Key assumption: censoring must be non-informative—the censoring mechanism is independent of the event risk. Violations require methods like Inverse Probability Censoring Weighting (IPCW).

• Type I: Study ends at a fixed calendar date
• Type II: Study ends after a predetermined number of events
• Random: Subject drops out for reasons unrelated to the outcome

Occurs when the event of interest has already happened before the observation period begins, but the exact timing is unknown. For example, a seroconversion study where a subject tests positive at their first visit—the infection occurred at some unknown point before enrollment. Left-censored data requires specialized likelihood constructions that integrate over the unknown early time interval.

• Common in environmental exposure studies where contamination predates monitoring
• Handled via interval-censored methods with a lower bound of zero

Arises when the event time is known only to lie within a specific interval, not at an exact moment. This is the natural outcome of periodic inspections—you know failure occurred between two clinic visits, but not precisely when. Turnbull's non-parametric estimator generalizes the Kaplan-Meier for interval-censored data.

• Case I: Current status data (single inspection per subject)
• Case II: Multiple inspection times per subject
• Parametric models like Weibull or log-normal AFT are often preferred for efficiency

Distinct from left-censoring, left-truncation occurs when subjects are only observable if they have survived past a certain entry threshold. Individuals who experienced the event before that threshold are entirely absent from the sample. Delayed entry in the Kaplan-Meier estimator adjusts the risk set to account for this late arrival.

• Classic example: pension fund mortality studies where only employees surviving to retirement age enter the dataset
• Requires conditioning on survival to the truncation time in the likelihood function

A violation of the standard independence assumption where the censoring mechanism is correlated with the event risk. For instance, patients who drop out of a cancer trial because their condition worsens—their censoring is directly related to prognosis. Standard Cox models yield biased estimates under informative censoring.

• IPCW: Weight uncensored observations by the inverse probability of remaining uncensored
• Joint models: Simultaneously model the longitudinal dropout process and survival
• Sensitivity analyses: Test robustness under varying degrees of dependence

The most benign form of right-censoring, occurring purely because the study follow-up period ends before all subjects experience the event. This is under the control of the investigator and is generally considered non-informative by design. The censoring time is fixed by the study calendar, not by subject behavior.

• Produces staggered entry patterns in Kaplan-Meier curves
• The proportion of administrative censoring directly impacts statistical power
• Distinguished from loss-to-follow-up, which may carry informative risk