利用分层抽样数据中完全辅助信息的模型校正方法

In stratified survey sampling, sometimes we have complete auxiliary information. One of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage. In this paper, we extend the model-calibration method to obtain estimators of the finite population mean by using complete auxiliary information from stratified sampling survey data. We show that the resulting estimators effectively use auxiliary information at the estimation stage and possess a number of attractive features such as asymptotically design-unbiased irrespective of the working model and approximately model-unbiased under the model. When a linear working-model is used, the resulting estimators reduce to the usual calibration estimator(or GREG).     

Analysis of a semiparametric mixture model for competing risks

Semiparametric mixture regression models have recently been proposed to model competing risks data in survival analysis. In particular, Ng and McLachlan (Stat Med 22:1097–1111, 2003) and Escarela and Bowater (Commun Stat Theory Methods 37:277–293, 2008) have investigated the computational issues associated with the nonparametric maximum likelihood estimation method in a multinomial logistic/proportional hazards mixture model. In this work, we rigorously establish the existence, consistency, and asymptotic normality of the resulting nonparametric maximum likelihood estimators. We also propose consistent variance estimators for both the finite and infinite dimensional parameters in this model.     

Measurement error in proportional hazards models for survival data with long-term survivors

This work studies a proportional hazards model for survival data with "long-term survivors",in which covariates are subject to linear measurement error.It is well known that the naive estimators from both partial and full likelihood methods are inconsistent under this measurement error model.For measurement error models,methods of unbiased estimating function and corrected likelihood have been proposed in the literature.In this paper,we apply the corrected partial and full likelihood approaches to estimate the model and obtain statistical inference from survival data with long-term survivors.The asymptotic properties of the estimators are established.Simulation results illustrate that the proposed approaches provide useful tools for the models considered.     

Semiparametric additive intensity model with frailty for recurrent events

The seminal Cox’s proportional intensity model with multiplicative frailty is a popular approach to analyzing the frequently encountered recurrent event data in scientific studies. In the case of violating the proportional intensity assumption, the additive intensity model is a useful alternative. Both the additive and proportional intensity models provide two principal frameworks for studying the association between the risk factors and the disease recurrences. However, methodology development on the additive intensity model with frailty is lacking, although would be valuable. In this paper, we propose an additive intensity model with additive frailty to formulate the effects of possibly time-dependent covariates on recurrent events as well as to evaluate the intra-class dependence within recurrent events which is captured by the frailty variable. The asymptotic properties for both the regression parameters and the association parameters in frailty distribution are established. Furthermore, we also investigate the large-sample properties of the estimator for the cumulative baseline intensity function.     

The proportional hazards model for multiple type recurrent gap times

Recurrent events data and gap times between recurrent events are frequently encountered in many clinical and observational studies, and often more than one type of recurrent events is of interest. In this paper, we consider a proportional hazards model for multiple type recurrent gap times data to assess the effect of covariates on the censored event processes of interest. An estimating equation approach is used to obtain the estimators of regression coefficients and baseline cumulative hazard functions. We examine asymptotic properties of the proposed estimators. Finite sample properties of these estimators are demonstrated by simulations.     

Estimating hazard ratios in nested case-control studies by mantel-haenszel method

1. IntroductionConsider a follow-up study which is carried out to investigate the association betweenexposure variables and mortality rate in a cohort. In the case where the cohort is of 1argesise, the complete follow-up ndght be too expensive or difficult, and various nested samplingmethod8 have been suggested by Thomas[l], Prenti..[2] 5 Goldstein and Langholzl'] and otherauthors. Most of the authors employ Coxl4] regression mode1 for estimating the hazard ratio8of exposures.Now a well-reco…     

Conditional likelihood estimation and efficiency comparisons in proportional odds model with missing covariates

In this article, a conditional likelihood approach is developed for dealing with ordinal data with missing covariates in proportional odds model. Based on the validation data set, we propose the Breslow and Cain (Biometrika 75:11–20, 1988) type estimators using different estimates of the selection probabilities, which may be treated as nuisance parameters. Under the assumption that the observed covariates and surrogate variables are categorical, we present large sample theory for the proposed estimators and show that they are more efficient than the estimator using the true selection probabilities. Simulation results support the theoretical analysis. We also illustrate the approaches using data from a survey of cable TV satisfaction.     

The proportional hazards model for survey data from independent and clustered super-populations

Data from most complex surveys are subject to selection bias and clustering due to the sampling design. Results developed for a random sample from a super-population model may not apply. Ignoring the survey sampling weights may cause biased estimators and erroneous confidence intervals. In this paper, we use the design approach for fitting the proportional hazards (PH) model and prove formally the asymptotic normality of the sample maximum partial likelihood (SMPL) estimators under the PH model for both stochastically independent and clustered failure times. In the first case, we use the central limit theorem for martingales in the joint design-model space, and this enables us to obtain results for a general multistage sampling design under mild and easily verifiable conditions. In the case of clustered failure times, we require asymptotic normality in the sampling design space directly, and this holds for fewer sampling designs than in the first case. We also propose a variance estimator of the SMPL estimator. A key property of this variance estimator is that we do not have to specify the second-stage correlation model.     

带有辅助信息的多元失效时间数据的估计标准部分似然方法

在许多实际研究中, 由于预算限制, 主协变量值只能对某一个有效集进行准确测量, 但同时对应此主协变量的辅助信息则对全部个体均可以观测. 利用这些辅助协变量的信息有助于提高统计研究的效率. 本文在基于共同基准危险率的边际模型框架下, 我们提出了一些统计推断方法来分析多元失效时间数据. 对于回归参数, 我们提出标准的估计部分似然方程来估计它, 同时也给出了累积基准危险率函数的Breslow 型估计. 得到的估计可以证明是相合的和渐近正态的. 利用模拟分析结果来表明了提出的方法在有限样本下的可行性.     

全国科技人员流动情况抽样调查的设计与分析

为了对近年来我国科技人员流动趋势及其效果进行定量分析,由原国家科委科技干部局主持,从1987年6月开始,对全国科学研究开发机构(研究所)、高等院校及大中企业中的科技人员,在1984年1月1日至1987年5月31日期间的流动情况进行了抽样调查.调查内容包括各单位流动人数(分年度及总数)、流向、流动原因及其流动人员的组成结构等基本情况.受主持单位委托,我们承担了此项调查的抽样设计,实施了抽样,并按调查目标量的类型提出了与抽样方案相配套的数据处理公式,包括对各层及总体目标量的估计以及这些估计量的精度.调查结果的报告见[1],其中主要内容已见报(见《光明日报》1987年12月28日第一版).     

Maximum likelihood estimation in the proportional hazards cure model

The proportional hazards cure model generalizes Cox’s proportional hazards model which allows that a proportion of study subjects may never experience the event of interest. Here nonparametric maximum likelihood approach is proposed to estimating the cumulative hazard and the regression parameters. The asymptotic properties of the resulting estimators are established using the modern empirical process theory. And the estimators for the regression parameters are shown to be semiparametric efficient.     

Estimation of some functional of the population distribution based on a stratified random sample

Summary In the preceding papers ([7], [8] and [9]), one of the authors discussed about the estimation of variances, covariances and correlation coefficients of the population based on a stratified random sample. In this paper we consider more general problem; estimating some functional θ(F) of the population distributionF based on a stratified random sample, which include our previous papers as special cases. We propose an unbiased estimator of θ(F) based on a stratified random sample and give an asymptotic expression of the gain in precision due to stratification in the case of proportional allocation. Furthermore, we present the general form of the optimum stratification in the proportional allocation for the estimation of θ(F).     

On Estimation of the Intensity Function of a Point Process

In this paper we review techniques for estimating the intensity function of a spatial point process. We present a unified framework of mass preserving general weight function estimators that encompasses both kernel and tessellation based estimators. We give explicit expressions for the first two moments of these estimators in terms of their product densities, and pay special attention to Poisson processes.     

Adaptive estimation of the intensity of inhomogeneous Poisson processes via concentration inequalities

 In this paper, we establish oracle inequalities for penalized projection estimators of the intensity of an inhomogeneous Poisson process. We study consequently the adaptive properties of penalized projection estimators. At first we provide lower bounds for the minimax risk over various sets of smoothness for the intensity and then we prove that our estimators achieve these lower bounds up to some constants. The crucial tools to obtain the oracle inequalities are new concentration inequalities for suprema of integral functionals of Poisson processes which are analogous to Talagrand's inequalities for empirical processes. Received: 24 April 2001 / Revised version: 9 October 2002 / Published online: 15 April 2003 Mathematics Subject Classification (2000): 60E15, 62G05, 62G07 Key words or phrases: Inhomogeneous Poisson process – Concentration inequalities – Model selection – Penalized projection estimator – Adaptive estimation     

多元失效时间数据的一般边际半参数危险率模型研究

在生物医学研究中,多元失效时间数据非常常见.该文提出用一般边际半参数危险率回归模型来分析多元失效时间数据.此模型包括了三种常用边际模型:边际比例风险模型、边际加速失效时间模型和边际加速危险模型作为子模型.对于模型中的回归系数,可以通过估计方程的方法来估计它,同时也给出了基准累积危险率函数的估计.得到的估计可以证明是相合的和渐近正态的.     

Statistical analysis of the generalized linear proportional hazards model

We analyze finite sample properties of modified partial likelihood estimators of parameters for the generalized proportional hazards model by simulation. A goodness-of-fit test for the proportional hazards model against the GPH model is proposed. Lung cancer data are analyzed. Bibliography: 7 titles.Published in Zapiski Nauchnykh Seminarov POMI, Vol. 294, 2002, pp. 5–18     

On estimation and inference in a partially linear hazard model with varying coefficients

We study estimation and inference in a marginal proportional hazards model that can handle (1) linear effects, (2) non-linear effects and (3) interactions between covariates. The model under consideration is an amalgamation of three existing marginal proportional hazards models studied in the literature. Developing an estimation and inference procedure with desirable properties for the amalgamated model is rather challenging due to the co-existence of all three effects listed above. Much of the existing literature has avoided the problem by considering narrow versions of the model. The object of this paper is to show that an estimation and inference procedure that accommodates all three effects is within reach. We present a profile partial-likelihood approach for estimating the unknowns in the amalgamated model with the resultant estimators of the unknown parameters being root- \(n\) consistent and the estimated functions achieving optimal convergence rates. Asymptotic normality is also established for the estimators.     

Estimating parameters of a log-linear intensity for a repairable system

The log-linear intensity is often used in survival analysis of technical products with rapid deterioration. It is an extremely important intensity to characterize the probabilistic behavior of a large number of real phenomena. In this paper we develop statistical methods for an alternating repair model using a log-linear intensity. The maximum likelihood estimator is considered for determining the estimations of the model parameters. The distribution of the life times after perfect repairs and imperfect repairs are obtained. The estimation of the Fisher information matrix is given. Simultaneous confidence regions based on the likelihood ratio statistics are developed for the estimators of the parameters. The proposed model is demonstrated using the well known data on airplane air-conditioning failures from Plane 7.     

Additive hazards models for gap time data with multiple causes

Recurrent event data with multiple causes are often observed in biomedical studies. The additive hazards model describes a different aspect of the association between covariates and the failure time than does the proportional hazards model. In this paper, we introduce additive hazards models for the analysis of gap time data of recurrent events with multiple causes. We estimate the regression parameter vector and cumulative baseline cause specific hazard rate function using counting process approach. Asymptotic properties of the estimators are studied. The proposed model is applied to the kidney dialysis data given in Lawless (2003). A simulation study is carried out to assess the performance of the estimates.     

The Additive Hazards Model for Multiple Type Recurrent Gap Times

In many biomedical and engineering studies, recurrent event data and gap times between successive events are common and often more than one type of recurrent events is of interest. It is well known that the proportional hazards model may not be appropriate for fitting survival times in some settings. In the paper, we consider an additive hazards model for multiple type recurrent gap times data to assess the effect of covariates. For inferences about regression coefficients and baseline cumulative hazard functions, an estimating equation approach is developed. Furthermore, we establish asymptotic properties of the proposed estimators.