Semi-nonparametric inference of lifetime data under competing risks when failure cause is missing completely at random

(joint work with Laurent Bordes et Pierre Joly)

We consider a competing risk model under right censoring when the failure cause is missing completely at random. Two types of models are considered: a semiparametric one with additive hazard rate and a nonparametric one. In each case, preliminary estimators of the unknown parameters are obtained using mainly the lifetimes with known cause of failure. Then we show that the information given by the lifetimes with unknown failure cause can be optimally used to improve our estimates. The large sample behavior of our estimators is obtained and their performance on finite sample sizes illustrated through a simulation study.