What is censoring in survival data, and why can you not just drop censored subjects?

Why

In a study of time to relapse, some patients are still relapse-free when the study closes and others move away. Clark and colleagues describe this as right censoring: the true event time is unknown but lies beyond the last observation. Those patients still carry information.

A patient followed for 22 months without relapse tells you that at least someone survived 22 months event-free. Dropping censored patients keeps mostly those who had events, so survival looks worse than it is. Treating censoring as an event is worse still.

The Kaplan-Meier estimator handles it by computing, at each event time, the proportion of patients still at risk who have the event, and multiplying the survival fractions together. A censored patient counts in the risk set until they leave and then simply drops out of the denominator. The log-rank test compares groups in the same way.

All of this rests on an assumption: censoring must be non-informative, meaning those censored have the same future risk as those still followed. If patients drop out because they are getting sicker, or because a toxic drug made them withdraw, standard methods give biased answers, and a sensitivity analysis is needed. The same ideas apply outside medicine, for example to time to cell death in an imaging assay that ends at 72 hours.