Estimation of the survival function with redistribution algorithm under semi-competing risks data

Abstract

This paper focuses on the estimation of the survival function of the non-terminal event time for semi-competing risks data. Without extra assumptions, we cannot make inference on the non-terminal event time because the non-terminal event time is dependently censored by the terminal event time. Thus, we utilize the Archimedean copula model to specify the dependency between the non-terminal event time and the terminal event time. Under the Archimedean copula assumption, we apply the redistribution method to estimate the survival function of the non-terminal event time and compare it with the copula-graphic estimator introduced by Lakhal et al. (2008). We also apply our suggested approach to analyze the Bone Marrow Transplant data.