Left Truncation

A survival analysis situation in which individuals are only included once they reach a certain point, such as registry entry, rather than a true start.

Source: Kalbfleisch & Prentice 2002

Left truncation arises when people enter a study only on reaching some later point, such as registering with a disease registry, so anyone who had the event before that point never appears in the data at all. This differs from censoring, where the individual is known but their exact time is not, since truncated individuals are missing entirely. The analysis must account for it by counting each person as at risk only from their entry, or survival at early times will be overstated. The unseen early events would otherwise bias the estimate. Klein and Moeschberger (2003) describe this.

Source: Klein & Moeschberger 2003

Left truncation arises when inclusion in a study requires individuals to survive event-free to a certain point, so that those who experienced the event earlier are excluded and never observed. For example, a registry that enrols patients some time after diagnosis includes only those who survived to enrolment, missing those who died before. Similarly, studies conditioning on reaching a particular age or milestone truncate those who did not. This selective inclusion of survivors, determined by a point later than the true origin, produces left truncation.

Source: Kalbfleisch & Prentice 2002

Left truncation is handled by including individuals in the risk set only from the time they enter observation, rather than from the time origin, so that they contribute to the analysis only over the period they are actually observed and at risk. Methods that account for left truncation adjust the risk set at each event time to include only those already under observation, using their delayed entry times. Handling left truncation this way avoids the bias that would arise from ignoring that included individuals had to survive to enter the study.

Source: Collett 2015

Left truncation must be accounted for because the individuals included had to survive event-free to the point of entry, so they are a selected group of survivors, and treating them as if observed from the time origin would overestimate survival by ignoring those who experienced the event earlier and were excluded. Failing to adjust the risk set for the delayed entry biases the estimates. Because left truncation systematically selects survivors, accounting for it by including individuals only from their entry time is necessary for valid survival estimates.

Source: Kalbfleisch & Prentice 2002

Left truncation differs from left censoring in what is known: in left truncation, individuals who experienced the event before the entry point are excluded entirely and never observed, so the sample is a selected group of survivors, whereas in left censoring, an individual is included but the event is known only to have occurred before a certain time, not exactly when. So left truncation concerns selective inclusion and requires adjusting the risk set, while left censoring concerns incomplete knowledge of an event time for included individuals. The two are distinct and handled differently in survival analysis.

Source: Kalbfleisch & Prentice 2002