Regression Trees for Cumulative Incidence Functions

A subject being followed over time may experience several types of events related, for example, to disease morbidity and mortality. For example, in a Phase III trial of concomitant versus sequential chemotherapy and thoracic radiotherapy for patients with inoperable non-small cell lung cancer (NSCLC) conducted by the Radiation Therapy Oncology Group (RTOG), patients were followed up to 5 years, the occurrence of either disease progression or death being of particular interest. Such "competing risks" data are commonly encountered in cancer and other biomedical followup studies, in addition to the potential complication of right-censoring on the event time(s) of interest. Two quantities are often used when analyzing competing risks data: the cause-specific hazard function (CSH) and the cumulative incidence function (CIF). For a given event, the former describes the instantaneous risk of this event at time t, given that no events have yet occurred; the latter describes the probability of occurrence, or absolute risk, of that event across time and can be derived directly from the subdistribution hazard function (Fine and Gray, 1999).