The partial Koziol-Green model with covariates

Abstract

Two important models in survival analysis are that of general random censorship and the proportional hazards submodel of Koziol and Green. The difference between the two models is the way in which the lifetime variable is censored (informative versus non-informative censoring). In this paper the two viewpoints are combined into a new model which allows the lifetimes to be censored by two types of variables, one of which censors in an informative way and the other one in a non-informative way. The lifetimes and the censoring times are also allowed to depend on covariates in a very general way. The estimator for the conditional distribution of the lifetimes generalizes that of Gather and Pawlitschko (1998. Metrika 48, 189–209), who recently studied the situation without covariate information. Results obtained are the uniform strong consistency (with rate), an almost sure asymptotic representation and the weak convergence of the process.