Truncation in survival analysis refers to the exclusion of individuals or events from the dataset based on specific criteria related to the time of the event. This exclusion can happen in two primary forms: left truncation and right truncation.

Left truncation occurs when individuals who experienced the event of interest before a certain time are not included in the study. This is often due to a "delayed entry" into the study where only those who survive until a certain entry point are observed. For instance, in an occupational study, workers who retired or died before the study's initiation would not be part of the dataset, leading to a bias that only includes those still at risk after the entry point.

Right truncation is less common and occurs when only individuals who have experienced the event by a certain time are included. This can happen in studies where the event has already occurred, and only those with observed outcomes are considered. An example would be a mortality study where only deaths within a specific timeframe are recorded, excluding those who lived beyond the observation period.

The difference between truncation and censoring lies in data availability. Censoring occurs when there is incomplete information about the event time; the exact time might not be known, but there is some information available, such as the fact that an event has not occurred up to a certain point (right censoring) or had already occurred before observation began (left censoring). In contrast, truncation involves no data at all for certain subjects who do not meet the entry criteria; they are completely excluded from the analysis.

Other examples of truncation include studies on diseases where only individuals diagnosed after a specific date are included, excluding those diagnosed earlier (left truncation). Similarly, in astronomical studies, only observable stars within a certain distance are considered, while those too far away to be detected are excluded (right truncation).