Comparing cumulative incidence functions of a competing-risks model

A competing-risks model refers to a situation where a system (or organism) is exposed to two or more causes of failure (or death) but its eventual failure (or death) can be attributed to exactly one of the causes of failure. The basic information available in the competing-risks situation is the time to failure of the system, and the corresponding cause of failure. In practice, the causes of failure are often statistically dependent (the latent failure time of an individual failing from one cause of failure is statistically correlated with the latent failure time of the same individual failing from a different cause of failure). This paper provides a simple nonparametric hypothesis test (SNPHT) for comparing the cumulative incidence functions of a competing-risks model when two causes of failure are possibly statistically dependent. The test statistic is the weighted sum of the differences of two cumulative incidence functions at system failure times. This paper: (1) proves that the test statistic has asymptotic normal distributions under both null and alternative hypotheses; and (2) derives an explicit formula for the power function of SNPHT. The simulation study for SNPHT, based on the absolutely continuous bivariate exponential model, shows that the simulated powers and the approximated powers calculated from the formula are consistent for a moderate sample size. SNPHT is very easy to use. The illustrative example involves the failure of small electrical appliances.