In the analysis of survival data, one may encounter the problem of competing risks where each subject may fail due to one of Kcauses, referred to as competing risks. In the competing risk problem, an experimental unit is observed until a particular event occurs in the presence of several events. The occurrence of any one event sometimes precludes us from observing the other events of interest. The cumulative incidence function, C i(t), gives the probability of experiencing the i thcompeting cause of failure prior to time tand before any of the other competing causes of failure. Estimating the cumulative incidence function is of primary interest in most clinical studies. Therefore, we compare several methods of estimating the cumulative incidence function using nonparametric and semi-parametric methods described in the literature, as well as those implemented in popular software packages.
Often we are also interested in comparing the risk of failure from a particular cause over two or more treatment groups. Some authors have recently pointed out that under certain circumstances, when testing for a treatment effect in the presence of competing risks, the popular cumulative incidence based approach may be problematic. Four methods commonly used when testing for a treatment effect in the presence of competing risks are: (1) the test based on Cox’s proportional hazards model, (2) the log-rank test, (3) Gray’s test, and (4) a test due to Fine and Gray. We investigate the level of significance and power associated with these four methods of testing for failure specific treatment effects in the presence of competing risks via a simulation study.