嵌套病例对照研究中的两步估计方法(英文)

本文讨论嵌套病例对照研究中相对危险率的估计问题,引入了相对危险率的两步估计,并在一般嵌套病例对照抽样的假设下讨论了相对危险率的两步估计的相合性问题．最后给出了几个例子．     

嵌套病例对照研究中的两步估计方法（英）

本文讨论嵌套病例对照研究中相对危险率的估计问题，引入了相对危险率的两步估计，并在一般嵌套病例对照抽样的假设下讨论了相对危险率的两步估计的相合性问题，最后给出了几个例子。     

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…     

Additive–multiplicative hazards model with current status data

The additive–multiplicative hazards (AMH) regression model specifies an additive and multiplicative form on the hazard function for the counting process associated with a multidimensional covariate process, which contains the Cox proportional hazards model and the additive hazards model as its special cases. In this paper, we study the AMH model with current status data, where the cumulative hazard hazard function is assumed to be nonparametric and is estimated using B-splines with monotonicity constraint on the functional, while a simultaneous sieve maximum likelihood estimation is proposed to estimate regression parameters. The proposed estimator for the parameter vector is shown to be asymptotically normal and semiparametric efficient. The B-splines estimator of the functional of the cumulative hazard function is shown to achieve the optimal nonparametric rate of convergence. A simulation study is conducted to examine the finite sample performance of the proposed estimators and algorithm, and a real data example is presented for illustration.     

左截断右删失数据下半参数模型风险率函数估计

文章给出了右删失左截断数据半参数模型下的风险率函数估计,讨论了风险率函数估计的渐近性质,获得了这些估计的渐近正态性,对数律和重对数律.由于假定删失机制服从半参数模型下,从而知道模型的更多信息,因此对于给出参数的极大似然估计,可以改进风险率函数估计的渐近性质.也就是说,删失数据模型具有半参数的辅助信息下, 风险率函数估计的渐近方差比通常的完全非参数的估计的渐近方差更小.这说明加入了额外的信息提高了风险率函数估计的效率.     

Hazard Rate Estimation in Nonparametric Regression with Censored Data

Consider a regression model in which the responses are subject to random right censoring. In this model, Beran studied the nonparametric estimation of the conditional cumulative hazard function and the corresponding cumulative distribution function. The main idea is to use smoothing in the covariates. Here we study asymptotic properties of the corresponding hazard function estimator obtained by convolution smoothing of Beran's cumulative hazard estimator. We establish asymptotic expressions for the bias and the variance of the estimator, which together with an asymptotic representation lead to a weak convergence result. Also, the uniform strong consistency of the estimator is obtained.     

Estimating a survival function with doubly censored data in a proportional hazard model

This article presents a non-parametric estimator of a survival function in a proportional hazard model when some of the data are censored on the left and some are censored on the right. The proposed method generalizes the work of Ebrahimi (1985). Uniformly strong consistency and asymptotic normality of the estimator are proved. A computer simulation study is presented to analyse the behaviour of the estimator when model assumptions fit the data and when they do not fit.     

On estimation of survival function under random censoring model

We study an estimator of the survival function under the random censoring model. Bahadur-type representation of the estimator is obtained and asymptotic expression for its mean squared errors is given, which leads to the consistency and asymptotic normality of the estimator. A data-driven local bandwidth selection rule for the estimator is proposed. It is worth noting that the estimator is consistent at left boundary points, which contrasts with the cases of density and hazard rate estimation. A Monte Carlo comparison of different estimators is made and it appears that the proposed data-driven estimators have certain advantages over the common Kaplan-Meier estmator.     

Multivariate Failure Times Regression with a Continuous Auxiliary Covariate

How to take advantage of the available auxiliary covariate information when the primary covariate of interest is not measured is a frequently encountered question in biomedical study. In this paper, we consider the multivariate failure times regression analysis in which the primary covariate is assessed only in a validation set, but a continuous auxiliary covariate for it is available for all subjects in the study cohort. Under the frame of marginal hazard model, we propose to estimate the induced relative risk function in the non-validation set through kernel smoothing method and then obtain an estimated pseudo-partial likelihood function. The proposed estimator which maximizes the estimated pseudo-partial likelihood is shown to be consistent and asymptotically normal. We also give an estimator of the marginal cumulative baseline hazard function. Simulation studies are conducted to evaluate the finite sample performance of our proposed estimator. The proposed method is illustrated by analyzing a heart disease data from the Study of Left Ventricular Dysfunction (SOLVD).     

A Berry-Esséen Bound for the Product-Limit Estimator under Left-Truncation and Right-Censoring

For left-truncated and right-censored data, the product-limit estimator F?_xis a well-known nonparametric estimator for the distribution function F_x of the target variable X such as the survival time. Since F?_xas a very complicated product form we establish first the Berry-Esseen bound for the cumulative hazard estimator of F_x The cumulative hazard estimator can be represented as a U-statistic. By using the result in Helmers and van Zwet [6], we derive the Berry-esséen bound for this U-statistic. Then Berry-Esseen bounds for the distribution of the cumulative hazard estimator and the normal distribution and the distribution of the product-limit estimator and the normal distribution are obtained.     

The maximum full and partial likelihood estimators in the proportional hazard model

Summary The maximum full likelihood estimator in the proportional hazard model is explored in relation to the maximum partial likelihood estimator. In the scalar parameter case both the estimators have a common sign, and the absolute value of the former is strictly greater than that of the latter except for trivial cases. We point out also that the maximum full likelihood estimator after a simple modification of the likelihood equation provides a good approximation to the maximum partial likelihood estimator. Similar results are valid for the likelihood ratio tests. The Institute of Statistical Mathematics     

Hazard function estimation with cause-of-death data missing at random

Hazard function estimation is an important part of survival analysis. Interest often centers on estimating the hazard function associated with a particular cause of death. We propose three nonparametric kernel estimators for the hazard function, all of which are appropriate when death times are subject to random censorship and censoring indicators can be missing at random. Specifically, we present a regression surrogate estimator, an imputation estimator, and an inverse probability weighted estimator. All three estimators are uniformly strongly consistent and asymptotically normal. We derive asymptotic representations of the mean squared error and the mean integrated squared error for these estimators and we discuss a data-driven bandwidth selection method. A simulation study, conducted to assess finite sample behavior, demonstrates that the proposed hazard estimators perform relatively well. We illustrate our methods with an analysis of some vascular disease data.     

一种估计Clayton模型中关联参数的方法

在右删失情形下,基于二元风险函数的核估计,我们对Clayton模型中的关联参数给出了一种新的估计方法.新的估计量具有相合性和渐近分布,随机模拟也显示这种估计方法是非常有效的.     

An additive stochastic model of mortality rates: An application to longevity risk in reserve evaluation

The paper proposes an additive continuous-time stochastic mortality model which revises that (B&H model) of Ballotta and Haberman (2006). The structure of the B&H model implies that the future hazard rate is proportional to the stochastic component, thus inducing two questionable features. First, in the B&H model, the uncertainty of the future hazard rate will be enlarged as the base hazard rate increases. However, an increase in the base hazard rate may not cause a dramatic increase suggested by the exponential component of B&H (2006). Second, in the B&H model, the uncertainty of the future hazard rate will be larger in the group which is older and will be greatly augmented by the interaction of age and time. But the uncertainty of the future hazard rate may not increase with an increase in age. The problems can be resolved by our additive structure which is the sum of a deterministic estimator and a stochastic component. Since using the additive structure will contribute to the fact that the stochastic component is independent of age and the base hazard rate, in our model the uncertainty of the future hazard rate will not be affected by an increase in age or in the base hazard rate. We further demonstrate an application of our model by calculating reserves of longevity risks for pure endowments and various common annuity products in the UK. We also compare our results with those of the B&H model.     

STRONG REPRESENTATIONS OF THE SURVIVAL FUNCTION ESTIMATOR ON INCREASING SETS FOR TRUNCATED AND CENSORED DATA

1991MRSubjectClassification62G05,62E201IntroductionandtheMainResultsInthisarticlewestudysllrvivaldatawhicharesubjecttobothlefttrull(:ationandrightcensoring(LTRC).Morespecifically,let(X,T,Y)denoterandomvariableswhereXisthevariableofinterest,calledthelifetimevariable,withunknowndistributionfullctioll(d.f.)F;Tistherandomlefttruncatiolltiliiewitharbitraryd.f.G,andYistherandorl.1rightcensoringtirliewitharbitraryd.f.H.ItisassumedthatX,T,Yarerxlutuallyindependent.Intheran相似文献   

Case-cohort analysis with general additive-multiplicative hazard models

The case-cohort design is widely used in large epidemiological studies and prevention trials for cost reduction. In such a design, covariates are assembled only for a subcohort which is a random subset of the entire cohort and any additional cases outside the subcohort. In this paper, we discuss the case-cohort analysis with a class of general additive-multiplicative hazard models which includes the commonly used Cox model and additive hazard model as special cases. Two sampling schemes for the subcohort, Bernoulli sampling with arbitrary selection probabilities and stratified simple random sampling with fixed subcohort sizes, are discussed. In each setting, an estimating function is constructed to estimate the regression parameters. The resulting estimator is shown to be consistent and asymptotically normally distributed. The limiting variance-covariance matrix can be consistently estimated by the case-cohort data. A simulation study is conducted to assess the finite sample performances of the proposed method and a real example is provided.     

Mixed proportional hazard models with continuous finite mixture unobserved heterogeneity: an application to Canadian firm survival

This paper proposes a methodology that accounts for the selection effect due to non‐random entry in duration models using latent‐class models. A mixed proportional hazard model with continuous finite mixture unobserved heterogeneity (MPH‐CFM) is introduced to correct for the potential bias induced by the selection effect. Conditions for identification, consistency, and asymptotic normality of the MPH‐CFM are provided. The estimator is used to investigate the duration of new entrant Canadian manufacturing firms. For the current application, the MPH‐CFM is compared with alternative duration models and found to be superior. Empirically, the results indicate that there are two classes of firms. Class I starts with high hazard and decreases non‐monotonically while Class II has a negligible hazard. These empirical results can be used to understand alternative models of firm dynamics. Copyright © 2017 John Wiley & Sons, Ltd.     

Properties of estimators of baseline hazard functions in a semiparametric cure model

We consider a semiparametric cure model combining the Cox model with the logistic model. There are the two distinct methods for estimating the nonparametric baseline hazard function of the model; one is based on a pseudo partial likelihood and the other is to use an EM algorithm. In this paper, we discuss the consistency and the asymptotic normality of the estimators from the two methods. Then, we show that the estimator from the pseudo partial likelihood can be characterized by the (forward) Volterra integral equation, and the estimator from the EM algorithm by the Fredholm integral equation. These characterizations reveal differences in the properties between the estimators from the two methods. In addition, a simulation study is performed to numerically confirm the results in several finite samples.     

The shape of the hazard function for cancer incidence

A population-based cohort consisting of 126,141 men and 122,208 women born between 1874 and 1931 and at risk for breast or colorectal cancer after 1965 was identified by linking the Utah Population Data Base and the Utah Cancer Registry. The hazard function for cancer incidence is estimated from left truncated and right censored data based on the conditional likelihood. Four estimation procedures based on the conditional likelihood are used to estimate the age-specific hazard function from the data; these were the life-table method, a kernel method based on the Nelson Aalen estimator, a spline estimate, and a proportional hazards estimate based on splines with birth year as sole covariate.The results are consistent with an increasing hazard for both breast and colorectal cancer through age 85 or 90. After age 85 or 90, the hazard function for female breast and colorectal cancer may reach a plateua or decrease, although the hazard function for male colorectal cancer appears to continue to rise through age 105. The hazard function for both breast and colorectal cancer appears to be higher for more recent birth cohorts, with a more pronounced birth-cohort effect for breast cancer than for colorectal cancer. The age specific for colorectal cancer appears to be higher for men than for women. The shape of the hazard function for both breast and colorectal cancer appear to be consistent with a two-stage model for spontaneous carcinogenesis in which the initiation rate is constant or increasing. Inheritance of initiated cells appears to play a minor role.     

带辅助协变量的分组相关失效时间数据的边际模型

本文研究了带有辅助协变量的分组相关失效时间数据的边际风险模型,获得了未知参数的伪偏似然估计,证明了所得估计的相合性和渐进正态性.