Non-parametric Tests for Recurrent Events under Competing Risks

Abstract.  We consider a data set on nosocomial infections of patients hospitalized in a French intensive care facility. Patients may suffer from recurrent infections of different types and they also have a high risk of death. To deal with such situations, a model of recurrent events with competing risks and a terminal event is introduced. Our aim was to compare the occurrence rates of two types of events. For this purpose, we propose two tests: one to detect if the occurrence rate of a given type of event increases with time; a second to detect if the instantaneous probability of experiencing an event of a given type is always greater than the one of another type. The asymptotic properties of the test statistics are derived and Monte Carlo methods are used to study the power of the tests. Finally, the procedures developed are applied to the French nosocomial infections data set.