Quantile residual lifetime for left-truncated and right-censored data

Abstract

This article proposes a simple nonparametric estimator of quantile residual lifetime function under left-truncated and right-censored data. The asymptotic consistency and normality of this estimator are proved and the variance expression is calculated. Two bootstrap procedures are employed in the simulation study, where the latter bootstrap from Zeng & Lin (2008) is 4000 times faster than the former naive one, and the numerical results in both methods show that our estimating approach works well. A real data example is used to illustrate its application. Keywordsleft-truncated, right-censored, quantile residual lifetime, empirical process MSC(2010) 62N01, 90B25Citation: Wang Y X, Liu P, Zhou Y. Quantile residual lifetime for left-truncated and right-censored data.

Composite estimator of mean residual lifetime with length-biased and right-censored data

“…最后得到的估计方法与基于极大似然估计Ŝ mle (t)、文献 [13] 给出的估计Ŝ HQ n (t) 进行 比较, 很明显, 我们的估计方法比基于 HQ 估计方法更有效, 同时与极大似然估计相比效率损失也不 大, 且我们提出估计有较简单的显式表达式, 容易计算并方便推出所提出估计的大样本性. 进一步还 可以研究半参数下的剩余寿命均值模型、剩余寿命分位数半参数模型等, 虽然有一些工作研究过这两 个模型 [7,10] , 但是在复杂的长度偏差右删失数据下仍然有许多待解决的问题.…”

“…剩余寿命越来越受到人们的关注, 目前主要有两种测量的方式: 均值剩余寿命函数和剩余寿命中 位数函数, 分别由文献 [4,5] 提出. 这两种函数都已有很多方法研究过, 涉及参数、非参数和半参数方 法, 以及包不包含自变量等 [6,7] . 在删失数据下, 文献 [8] 提出了一类灵活的回归模型来估计均值剩余 寿命, 包括文献 [6] 等研究的模型.…”

Estimating equation estimators of quantile differences for one sample with length-biased and right-censored data

“…As a special case of quantile differences, quantile residual lifetime has been studied widely, see for instance, Chapter 3 in [6]. Actually, quantile differences are receiving increasing attention in the recent literature, including [26,34,19,7,33,11,27,31,30] among others.…”

Nonparametric and semiparametric estimation of quantile residual lifetime for length‐biased and right‐censored data

“…But the main problem is that biased samples will be obtained under this sampling strategy, as only those who developed the disease but do not experience a failure event can be recruited into the study. Wang, Liu, & Zhou () studied quantile residual lifetime with left‐truncated and right‐censored data and showed residual lifetime can be overestimated if omitting the left truncation.…”

“…Recently Liu, Wang, & Zhou () studied the quantile residual lifetime with length‐biased and right‐censored data based on the nonparametric maximum likelihood estimation approach (Asgharian, M'Lan, & Wolfson, ; Asgharian & Wolfson, ), but the estimated distribution of the biased survival time does not have a closed‐form expression, which complicates the computation and asymptotic properties derivation of the quantile residual lifetime estimator. Besides Wang, Liu, & Zhou () proposed an estimator of the quantile residual lifetime under left‐truncated and right‐censored data. Their approach may be extended to censored length‐biased data; however, their method does not employ the auxiliary information of the truncation variable.…”