Modelling proposals in competing risk studiesempirical likelihood approaches to compare different risks

Resumen

In standard competing risks studies, every unit or subject is exposed to different risks at the same time, but its actual failure or death is attributed to exactly one of them which is then called the cause of failure. In general, the goal of these studies is to distinguish between the following three alternatives: (1) the risks are equal, (2) the risks are not equal, and (3) the risks are linearly ordered. We concentrate on modelling proposals in competing risk studies and develop empirical likelihood (EL) based tests for testing the hypothesis that the cumulative incidence functions (CIF) corresponding to k-competing risks are equal against the alternative that they are not equal or that they are linearly ordered. The proposed test statistics are functionals of localized empirical likelihood statistics. Their asymptotic null distributions are distribution-free and have a simple representation in terms of a standard Brownian motion or a standard Brownian bridge. The tests we propose here are extended to the case of rightcensored survival data via multiple imputation. In order to assess the usefulness of the proposed tests, and to illustrate the theoretical results for their asymptotic distributions, we include a simulation study and also discuss an example involving survival times of mice exposed to radiation.