Estimation in a model for a semi-Markov process with covariates under right-censoring

Abstract

A semi-Markov model with covariates is proposed for a multi-state process with a finite number of states such that the transition probabilities between the states and the distribution functions of the duration times between the occurrence of two states depend on a discrete covariate. The hazard rates for the time elapsed between two successive states depend on the covariate through a proportional hazards model involving a set of regression parameters, while the transition probabilities depend on the covariate in an unspecified way. We propose estimators for these parameters and for the cumulative hazard functions of the sojourn times. A difficulty comes from the fact that when a sojourn time in a state is right-censored, the next state is unknown. We prove that our estimators are consistent and asymptotically Gaussian under the model constraints.