Choice and interpretation of statistical tests used when competing risks are present

Abstract

In clinical cancer research, competing risks are frequently encountered. For example, individuals undergoing treatment for surgically resectable disease may experience recurrence near the removed tumor, metastatic recurrence at other sites, occurrence of second primary cancer, or death resulting from noncancer causes before any of these events. Two quantities, the cause-specific hazard function and the cumulative incidence function, are commonly used to summarize outcomes by event type. Tests for event-specific differences between treatment groups may thus be based on comparison of (a) cause-specific hazards via a log-rank or related test, or (b) the cumulative incidence functions via one of several available tests. Inferential results for tests based on these different metrics can differ considerably for the same cause-specific end point. Depending on the questions of principal interest, one or both metrics may be appropriate to consider. We present simulation study results and discuss examples from cancer clinical trials to illustrate these points and provide guidance for analysis when competing risks are present.

Fig 1.

(A) Cumulative cause-specific hazard and (B) cumulative incidence of events comprising disease-free survival in a clinical trial for lymph node–negative, estrogen-receptor–positive breast cancer., Vertically from top, graph pairs represent breast cancer recurrence, contralateral breast tumors, endometrial cancer, and other events.

Fig 2.

Cumulative incidence and cumulative hazard plots from the simulated data examples. The estimated curves are based on large samples from distributions having the parameters specified in Table 2. (A, B) Scenario 1; (C, D) scenario 2.