长度偏差右删失数据下比例均值剩余寿命模型的估计方法

本文考虑了长度偏差右删失数据下均值剩余寿命模型的统计推断.当截断变量满足平稳性假设时,长度偏差右删失数据比左截断右删失数据具有更多的信息.为了提高参数估计的效率,我们在估计方程构造中添加了额外信息,通过组合方法获得了新的估计.模拟研究的结果也表明,组合估计方程的方法比仅考虑左截断右删失数据的方法更有效,结果表现更好.     

长度偏差右删失数据下均值剩余寿命的复合估计

长度偏差右删失数据是一类复杂的数据,观察到的数据分布与总体分布有所改变且其删失是有信息删失,通常的统计分析方法并不能直接应用到长度偏差数据中.本文将在长度偏差右删失数据下研究均值剩余寿命函数,提出其非参数估计方法,在估计中通过加入长度偏差右删失数据辅助信息,即截断变量和进入试验后的剩余存活时间同分布的辅助信息来提高估计的效率.虽然极大似然方法是有效估计,但是其构造复杂且计算需要迭代来实现,计算量大.为此,本文考虑通过简单的加入辅助信息的方法来构造估计量,并给出估计量的相合性及渐近正态性.本文提出的加入辅助信息估计方法与以往类似方法相比具有较简单的显式表达式,计算方便.     

长度偏差右删失数据剩余寿命的分位数回归

本文研究长度偏差数据下剩余寿命分位数模型的估计方法,充分考虑有偏抽样机制对模型估计的影响.如果忽略这种有偏性会导致估计产生严重偏差甚至错误的结果.本文首先针对长度偏差右删失数据的剩余寿命分位数提出了对数形式的线性回归模型,对删失变量与协变量独立和不独立的两种情况利用估计方程给出了模型参数的估计.其次,通过经验过程和弱收敛理论给出了参数估计的相合性和渐近正态性.最后,本文对提出的估计方法进行了数值模拟并用该方法对奥斯卡奖数据进行分析.     

一般偏差右删失数据下剩余寿命分位数回归

剩余寿命是刻画个体预期寿命的一个重要度量,对剩余寿命的早期研究主要集中在剩余均值上.然而当总体生存函数偏态或厚尾时剩余均值函数可能不存在,因此统计学者建议用剩余寿命分位数来刻画预期寿命.在完全数据和右删失数据下,剩余寿命分位数的建模和理论已经很完善.但是,在实际的调查研究中经常会遇到偏差抽样数据.例如,临床医学中的左截断数据,流行病学中的病例队列抽样数据,医学大型队列研究中的长度偏差抽样数据等等.忽略抽样偏差会导致参数估计有偏和不合理的推断结果.本文考虑一般偏差右删失数据下剩余寿命分位数回归的统计推断问题.首先,我们提出了一个一般偏差右删失数据下的剩余寿命分位数回归模型,并利用一般估计方程方法对模型中的参数进行了估计.针对已有文献常用的删失变量与协变量独立性假设,本文重点考虑了删失变量依赖于协变量场合.其次,由于估计量的渐近方差中涉及非参密度函数,在估计渐近方差时,本文采用Bootstrap方法.最后,数值模拟显示本文提出的方法有限样本性质表现很好.     

长度偏差右删失数据下分位数回归的估计方程方法

本文首先建立左截断右删失数据下的一般分位数回归方法.当截断变量服从均匀分布时,左截断右删失数据变成长度偏差右删失数据.长度偏差数据因其特殊性,提供了更多的信息.当把适用于左截断右删失数据的一般方法用到长度偏差右删失数据时,得到的估计量并不有效,这是因为它们没有利用该数据的特殊结构.为了提高效率,本文提出复合估计方程方法来解决长度偏差右删失数据下的分位数回归问题,这种方法并不需要估计删失变量的分布.所提出的估计方程可以通过一个求L_1型凸函数最小值的简单算法来求解.本文用经验过程和随机积分的技巧建立了所提出估计量的一致相合性和弱收敛性.随机模拟验证了所提出方法在有限样本时的表现,并且给出了实例分析.     

病例-队列设计下长度偏差数据的比例均值剩余寿命模型的统计推断

在大型队列研究中,病例-队列设计是一种可以有效节约成本的试验设计方法.本文研究了在病例-队列设计下,基于长度偏差数据的比例均值剩余寿命模型的统计推断问题,提出了一种带有时间相依权重的加权混合估计方程方法来估计模型中的回归系数,并证明了在适当条件下,所得到的估计量具有相合性与渐近正态性.模拟结果表明本文所提出的方法在有限样本下的表现不错.最后,我们将所提出的方法应用到了一组实际数据中.     

信息右删失数据下比例风险模型的估计问题（英文）

在生存分析中,对右删失数据问题的研究常假设删失时间与失效时间相互独立.然而研究者经常要面对非独立删失的问题,即删失时间与失效时间可能相互关联并彼此影响,尤其表现在临床试验中.如果不考虑这种相关性,便无法得到生存函数的有效估计.针对这种相依结构已有很多处理方法,其中连接函数因结构简单而尤为受到关注.本文主要对信息右删失数据下比例风险模型的相关估计问题进行了研究.利用阿基米德连接函数对删失时间和失效时间的联合分布函数进行假定,在连接函数参数的可识别条件下,得到了连接函数的参数、比例风险模型参数以及基准累积风险函数的极大似然估计,并通过模拟计算的方法验证了估计方法的可行性以及估计量的有效性.     

右删失长度偏差数据分位数差的非参数估计

利用长度偏差数据所特有的辅助信息,对带右删失的长度偏差数据的分位数差提出了一种新的非参数估计.该方法提高了估计的有效性,所得的估计量形式简洁,便于计算.同时,本文用经验过程理论建立了该分位数差估计的相合性及渐近正态性,并给出方差估计的重抽样方法.本文还通过数值模拟考察了该估计量在有限样本下的表现,并将其应用到一个关于老年痴呆的实际数据中.     

左截断右删失数据下百分剩余寿命函数的非参数估计

在左截断右删失数据的模型中，文章讨论３了可靠性中一类重要的α－百分剩余寿命函数的非参数估计，证明了该估计的强一致相合性并获得了该仗垢弱收敛性结果。     

广义指数比例风险模型下区间删失数据的贝叶斯估计

本文研究了失效时间服从广义指数分布,且风险率函数为比例风险模型时,II型区间删失数据的贝叶斯估计。假定参数的先验分布为无信息先验,建立贝叶斯层次模型从而得到后验密度函数。通过MH算法得到参数估计值,数值模拟结果验证了所提方法的有效性。最后将所提方法应用到乳腺癌患者和血友病患者这两个实际数据中进行分析。     

基于长偏置数据的一个光滑剩余生命函数估计量(英文)

受希勒引理的启发,针对长偏置数据给出一个带泊松权重的平均剩余生命函数的光滑估计量.同时研究了该光滑估计量的渐进性质,例如强相合性及渐进正态性等性质.     

Proportional Mean Residual Life Model with Varying Coefficients for Length-Biased and Right-Censored Data

Length-biased data are encountered in many fields,including economics,engineering and epidemiological cohort studies.There are two main challenges in the analysis of such data:the assumption of independent censoring is violated and the assumed model for the underlying population is no longer satisfied for the observed data.In this paper,a proportional mean residual life varyingcoefficient model for length-biased data is considered and a local pseudo likelihood method is proposed for estimating the coefficient functions in the model.Asymptotic properties are investigated for the proposed estimators.The finite sample performance of the proposed methodology is demonstrated by simulation studies.Finally,the method is applied to a real data set concerning the Academy Awards.     

Estimating the Finite Population Versions of Mean Residual Life-Time Function and Hazard Function Using Bayes Method

In this paper we introduce a finite population version of the mean residual life-time (MRL) function and the hazard function, and study Bayesian estimation of these functions. The unknown parameter is the complete set (y1,...;,yN) of lifetimes of the N units which constitute the complete population. A hierarchical type prior is used, where the yi's are assumed conditionally independent given a random parameter . The data consists of a random sample of n values of yi. The Bayes estimators of MRL and hazard functions, respectively, are then obtained as the posterior expectations of the unknown functions.     

右删失情形下平均生存时间的加权Bootstrap推断

在右删失情形下,基于一类合成数据,采用加权Bootstrap方法获得了平均生存时间的加权Bootstrap估计及其加权Bootstrap分布,并就权重是否独立两种情形,证明了此估计的相合性及此分布近似的有效性.基于此,构造了平均生存时间的置信区间.在数值模拟中,取权为Dirichlet(n;1,…,1),并从覆盖概率和区间长度角度,比较了加权Bootstrap和渐近正态逼近产生的置信区间.     

The Histogram and Boxplot for the Display of Lifetime Data

Abstract

The importance of histograms and boxplots as exploratory data analysis (EDA) tools has been well established. Yet, adopting them for lifetime data is not straightforward. The first problem, particularly in histograms, is how to deal with censored observations. The second problem is that the underlying distribution of lifetime data is often highly positively skewed. Therefore, in the classical boxplot, large observations can be wrongly diagnosed as outliers. This article extends the definition of the histogram to accommodate for right-censored observations. We apply the “redistribution to the right” method so that the weight of each uncensored observation is actually the jump of the Kaplan—Meier estimation at this point. We also propose modified boxplots to resolve both problems of right censoring and skewness. In our procedure, the fences differ from those of the classical boxplot. Simulation results are presented for an evaluation of our procedure and an example is presented for illustration.     

Weighted Empirical Likelihood Ratio Confidence Intervals for the Mean with Censored Data

We propose a procedure to construct the empirical likelihood ratio confidence interval for the mean using a resampling method. This approach leads to the definition of a likelihood function for censored data, called weighted empirical likelihood function. With the second order expansion of the log likelihood ratio, a weighted empirical likelihood ratio confidence interval for the mean is proposed and shown by simulation studies to have comparable coverage accuracy to alternative methods, including the nonparametric bootstrap-t. The procedures proposed here apply in a unified way to different types of censored data, such as right censored data, doubly censored data and interval censored data, and computationally more efficient than the bootstrap-t method. An example of a set of doubly censored breast cancer data is presented with the application of our methods.     

Empirical Likelihood Estimation for the Two-Sample Mean under Density Ratio Models Using Auxiliary Information

Auxiliary population information is often available in finite population inference problems, and the empirical likelihood (EL) approach has been demonstrated to be flexible and useful for such problems. The present paper concerns EL when interest centers on inference for the mean of the baseline distribution under two-sample density ratio models. Although dual EL is a convenient technical tool since it has the same maximum point and maximum likelihood as DRM-based EL, it can not combine such auxiliary information into the likelihood conveniently and may have loss of efficiency. By contrast, the classical EL approach of Qin and Lawless\ucite{21} does not have this problem and incorporate seamlessly auxiliary information. Based on the EL using auxiliary information and the dual EL methods, we construct both point and interval estimations and make a careful comparison. Though the point estimation efficiency gain obtained by the former is not noticeable, we find that they may have different performances in interval estimation. In terms of coverage accuracy, the two intervals are comparable for not or moderate skewed populations, and the EL interval using auxiliary information can be much superior for severely skewed populations.     

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??Auxiliary population information is often available in finite population inference problems, and the empirical likelihood (EL) approach has been demonstrated to be flexible and useful for such problems. The present paper concerns EL when interest centers on inference for the mean of the baseline distribution under two-sample density ratio models. Although dual EL is a convenient technical tool since it has the same maximum point and maximum likelihood as DRM-based EL, it can not combine such auxiliary information into the likelihood conveniently and may have loss of efficiency. By contrast, the classical EL approach of Qin and Lawless\ucite{21} does not have this problem and incorporate seamlessly auxiliary information. Based on the EL using auxiliary information and the dual EL methods, we construct both point and interval estimations and make a careful comparison. Though the point estimation efficiency gain obtained by the former is not noticeable, we find that they may have different performances in interval estimation. In terms of coverage accuracy, the two intervals are comparable for not or moderate skewed populations, and the EL interval using auxiliary information can be much superior for severely skewed populations.