Bias by censoring for competing events in survival analysis

In time-to-event or survival modelling, an important aim is to estimate the cumulative incidence (ie, the absolute risk by time t) of an event of interest. In medical applications, such events include death due to cancer, infection or cardiovascular causes, time to remission after treatment, and time to graft failure after transplantation. The occurrence of these events is often precluded by another earlier event (a competing risk) that, when censored for, leads to biased cumulative incidence estimators. Examples of such competing events are death due to other causes when the interest is in death due to cancer, death before remission when analysing time to oncological remission, and death with a functioning graft when interested in graft failure after transplantation. Non-fatal competing events also exist—for instance, receiving a second transplant organ when analysing the time to graft failure, receiving a vaccine when analysing the time to infection, or receiving a competing…
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