A key ingredient in survival analysis is observational time (or time at risk), i.e. the period during which an individual (or any other type of observation) is actually observed. The observational period (also called follow-up period) starts when the individual enters the study and ends at: a) the occurrence of the event, b) by the end of follow-up, c) at loss to follow-up/dropout, or d) in the case of death. In relation to these points, we need to discuss the concept of censoring.

Censoring

Left-censoring: The term left-censoring applies to situations when we know that the event occurred prior to the start of the observation period, but we cannot be sure about the exact time the event occurred.

Right-censoring: In cases b-d, as specified above this table, the term right-censoring would apply. It means that we are only able to know anything about the development of the individual up until that specific point (we do not know if or when the event will happen afterwards). Put differently, right-censoring refers to a situation where an individual can no longer be observed and the event has not occurred during the observational/follow-up period.

Interval-censoring: Interval-censoring refers to instances when we know an event occurred between two time points, but we cannot be sure when the event occurred within that interval.

Example Below is an illustration of what (right-)censoring might look like. Lines that end with a circle denote that the event has taken place (individuals A, G, and I), whereas the lines that end with a diamond denote that the individual has been censored. In the case of individuals C, D, E, H, and J, they are censored at the end of follow-up. Individuals B and F have been censored earlier than that, perhaps because of death or emigration.

One assumption that we need to make is that the censoring is non-informative. In other words, we assume that those that are censored are not being censored because they have a lower or higher risk of the event itself. Such violations are difficult to formally test but are probably quite common. For example, it is likely that individuals that are censored because of death would be more likely to have experienced the event at some point if they had not died (at least if the event is related to health in some way).

Summary It is necessary to have precise information about when the follow-up starts, when it ends, and when the event occurred. There must also be an unambiguous definition of the time scale. Moreover, we need to consider censoring (most survival analyses have right-censoring), since our results might be biased otherwise.

Note There is also a second concept in survival analysis, often confused with censoring, called truncation. Truncation refers to situations when the observation period for certain individuals is smaller or larger than your study’s observation period. As you cannot observe these individuals (and researchers are therefore not aware of their existence) they are not included. This may also introduce bias into your results. Left and right truncation is quite common in health sciences, and special methods are required to deal with it, but these will not be covered in this guide.