Zero-inflated semi-parametric Cox's regression model for left-censored survival data

Abstract

In this paper, we introduce a semi-parametric regression model for left-censored data in which the response variable has a positive discrete probability at the value zero. To investigate the influence of covariates on the probability on a zero-value, a logistic regression model is used. For the strict positive part of the response variable, a Cox’s regression model is given to model the influence of the covariates. The different parameters in the model are estimated using a likelihood method. Hereby,the baseline hazard function is an infinite dimensional parameter and is estimated by a step-function. As results, we show the consistency of the estimators for the different finite- and infinite-dimensional parameters in the model. We also present a simulation study and apply this model on a practical data example.