Censored Data

Suppose that in an experiment or study, a group of individuals (objects, patients, or devices) is followed over time with the goal of observing an event such as failure or death. Individuals who do not experience the event of interest in the observation period are said to be censored, and the data obtained from such individuals are known as censored data.

In most cases, experiments or studies have a finite observation period, so for some individuals, the observation period may not be long enough to observe the event of interest. Also, individuals may cease to be at risk before the observation period. For example, in a clinical trial setting, patients might drop out of the study, or in the case of testing the reliability of a device, the device may fail for reasons other than the one the experimenter is interested in. Such individuals known not to experience the event within or before the observation period are said to be right censored.

Censored data may demonstrate left censoring and interval censoring, as well. In the former, the event of interest occurs before the observation period. For example, suppose a group of women is selected to be followed for the development of breast cancer. If some of these women had already developed breast cancer, then the time to the development of breast cancer is left censored for them. In the case of interval censoring, one observes an interval within which the event of interest occurred, but the actual time of [Page 126] occurrence remains unknown. Interval censoring occurs when devices are tested only at specific times, say t1, t2, … tk, and failures occur between two consecutive times. Right and left censoring are special cases of interval censoring with the intervals (T, ∞) and (0, S), respectively, where S is the starting time and T is the ending time of the study.

When data contain censored observations, special care has to be taken in the analysis. Common statistical methods used to analyze censored data include the Kaplan-Meier estimator, the log-rank test, the Cox proportional hazard model, and the accelerated failure time model.