Time to Event Models

In many health sciences applications, binary outcomes are incompletely observed. For example, if we are studying whether cancer patients experience a relapse after an initial remission, we may not be able to follow patients to the end of their lives; instead, we may only know whether each patient has relapsed before the end of the study. If a patient has not relapsed by that point, we might not know if they will relapse at some other date or if they will stay cancer-free for the rest of their lives. ¹ Their recurrence status at end-of-life is missing data. If some study participants withdraw from a study before the scheduled end date, additional missing data arise. Standard logistic regression cannot handle such right-censored data directly without introducing bias.

However, these outcome observations are not entirely missing. We know that those patients stayed relapse-free at least until the time point when they were last observed. If we also know the time-to-event for participants who experienced events while under study, we can analyze the time-to-event-or-study-exit alongside an event indicator using survival analysis. The survival analysis framework provides the foundation for the topics covered in this module.

Footnotes

1. Binary outcomes are typically defined for a specific time-point. It is important to clearly define whether we are interested in outcome status at end of study, at end of life, or at some other time.