Empirical likelihood confidence bands for mean functions of recurrent events with competing risks and a terminal event

Jean-Yves Dauxois (1) , Alexis Flesch (1) , Davit Varron (1)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

In this paper, we study recurrent events with competing risks in the presence of a terminal event and a censorship. We focus our attention on the mean functions which give the mean number of events of a specific type that have occured up to a time $t$. Using empirical likelihood ratio techniques, we are able to build confidence bands for these functions. We have a data set of nosocomial infections in an intensive care unit of a french hospital. For each patient, we know if and when he caught an infection, what infection it was (septicemia, urinary tract infection...), if and when he died and when he left the hospital. Our model fits this context and will be used to build confidence bands for one type of nosocomial infection and even a confidence tube for two types.

Mots clés: confidence bands; empirical likelihood; empirical processes; recurrent events; terminal event; Censoring; competing risks

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Jean-Yves Dauxois, Alexis Flesch, Davit Varron. Empirical likelihood confidence bands for mean functions of recurrent events with competing risks and a terminal event. 2011. ⟨hal-00602699⟩