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

• Published in: Statistics & probability letters Vol. 80; no. 3; pp. 161 - 168
• Main Author: Shen, Pao-sheng
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.02.2010; Elsevier
• Series: Statistics & Probability Letters
• Subjects: Exact sciences and technology; General topics; Mathematics; Nonparametric inference; Parametric inference; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Statistics; Probability theory; Asymptotic behavior; Censored sample; Average; Probability; Statistical estimation; Probability distribution; Semiparametric method; Mean estimation; Statistical method; Function estimation; Survival function; Simulation; Distribution function; Failure time; Mean error; Survival data
• ISSN: 0167-7152; 1879-2103
• DOI: 10.1016/j.spl.2009.10.002

Satten et al. (2001) proposed an estimator of the survival function (denoted by 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 ) , where θ ∈ Θ ⊂ R q , and θ is a q -dimensional vector. We propose two semiparametric estimators of S ( t ) by simultaneously estimating G ( x ; θ ) and S ( t ) . One of the proposed estimators, denoted by S ˆ w ( t ; θ ˆ w ) , is represented as an inverse-probability-weighted average ( Satten and Datta, 2001). The other estimator, denoted by S ˆ ( t ; θ ˆ ) , 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 S ˆ ( t ; θ ˆ ) is smaller than that of S ˆ w ( t ; θ ˆ w ) . However, when truncation is severe and censoring is light, the situation can be reverse.