Semiparametric estimation of survival function when data are subject to dependent censoring and left truncation

Satten et al. (2001) proposed an estimator of the survival function (denoted by S(t)S(t)) of failure times that is in the class of survival function estimators proposed by Robins (1993). The estimator is appropriate when data are subject to dependent censoring. In this article, we consider the case when data are subject to dependent censoring and left truncation, where the distribution function of the truncation variables is parameterized as G(x;θ)G(x;θ), where θ∈Θ⊂Rqθ∈Θ⊂Rq, and θθ is a qq-dimensional vector. We propose two semiparametric estimators of S(t)S(t) by simultaneously estimating G(x;θ)G(x;θ) and S(t)S(t). One of the proposed estimators, denoted by Sˆw(t;θˆw), is represented as an inverse-probability-weighted average (Satten and Datta, 2001). The other estimator, denoted by Sˆ(t;θˆ), is an extension of the estimator proposed by Satten et al.. The asymptotic properties of both estimators are established. Simulation results show that when truncation is not severe the mean squared error of Sˆ(t;θˆ) is smaller than that of Sˆw(t;θˆw). However, when truncation is severe and censoring is light, the situation can be reverse.