COMPARING CUMULATIVE INCIDENCE FUNCTIONS OF A COMPETING-RISKS MODEL

A competing-risks model refers to a situation where a system (or organ ism) is exposed to two or more causes of failure (or death) but its ev entual failure (or death) can be attributed to exactly one of the caus es 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 statist ically dependent (the latent failure time of an individual failing fro m one cause of failure is statistically correlated with the latent fai lure time of the same individual failing from a different cause of fai lure). This paper provides a simple nonparametric hypothesis test (SNP HT) for comparing the cumulative incidence functions of a competing-ri sks model when two causes of failure are possibly statistically depend ent. The test statistic is the weighted sum of the differences of two cumulative incidence functions at system failure times. The paper, 1) proves that the test statistic has asymptotic normal distributions und er both null & alternative hypotheses, and 2) derives an explicit form ula for the power function of SNPHT. The simulation study for SNPHT, b ased on the absolutely continuous bivariate exponential model, shows t hat the simulated powers and the approximated powers calculated from t he formula are consistent for a moderate sample size. SNPHT is very ea sy to use. The illustrative example involves the failure of small elec trical appliances.