rechtecensoring

Right-censoring, referred to in German as rechtecensoring, is a common form of censorship in survival analysis. It occurs when the event of interest has not happened for some subjects before the study ends or before they are lost to follow-up. For each subject, the observed time is Y = min(T, C), where T is the true event time and C is the censoring time. The indicator δ = 1 if the event is observed (T ≤ C) and δ = 0 if the observation is censored (T > C).

Censored observations provide partial information: we know the event time is at least Y, but not the exact value. Right-censoring is most common in medical follow-up and reliability studies. The censoring mechanism is usually assumed non-informative, meaning the probability of being censored depends on observed data but not on the unobserved T, conditional on covariates. If censoring is informative, standard methods may be biased.

Statistical methods for right-censored data include nonparametric and semiparametric approaches. The Kaplan-Meier estimator uses right-censored data to estimate the survival function S(t) = P(T > t). It accounts for individuals at risk up to their censoring time. The log-rank test compares survival curves between groups. In regression settings, the Cox proportional hazards model handles right-censored data via partial likelihood, under the non-informative censoring assumption.

Limitations and practical considerations include the impact of high censoring rates on precision and potential bias if censoring is related to the outcome. When censoring is interval or left-censored, or when censoring is suspected to be informative, specialized methods or sensitivity analyses are used. Right-censoring remains a central concept in timing-related analyses across fields.

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