An Efficient Estimation of the Mean Residual Life Function with Length-Biased Right-Censored Data

Hongping Wu,Yihui Luan

doi:10.1155/2014/937397

Abstract

The mean residual life (MRL) function for a lifetime random variableT0is one of the basic parameters of interest in survival analysis. In this paper, we propose a new estimator of the MRL function with length-biased right-censored data and evaluate its performance through a small Monte Carlo simulation study. The results of the simulations show that the proposed estimator outperforms the existing one referred to in Data and Model Setup Section in terms of Monte Carlo bias and mean square error, especially when the censoring rate is heavy. We also show that the proposed estimator converges in distribution under some conditions.

Highlights

The mean residual life (MRL) function at time t is defined to be the expected remaining lifetime of a system given survival up to time t
We propose a new estimator of the MRL function with length-biased right-censored data and evaluate its performance through a small Monte Carlo simulation study
For right-censored data, consistent estimator of the MRL function with its asymptotic normal distribution has been given by Yang [3] and Kumazawa [4]

Summary

Introduction

The MRL function at time t is defined to be the expected remaining lifetime of a system given survival up to time t. A more recent work on estimation of the MRL with left-truncated and right-censored data has been constructed by Zhao et al [7], and they showed that the proposed estimator converges weakly to a Gaussian process. To estimate the survival distribution, Luo and Tsai [12] proposed a pseudopartial likelihood approach, and Huang and Qin [8] proposed a new nonparametric estimator based on the product-limit estimator. Their estimators were proved to be uniformly consistent and converge weakly to Gaussian processes. In this paper we propose a new estimator of the MRL function with length-biased and right-censored data.

Notations and Estimators

The Asymptotic Properties

Simulations