具有随机缺失协变量的广义变系数模型

在协变量随机缺失时,文章利用加权拟似然方法给出了广义变系数模型中非参数函数系数的估计。由估计的渐近性质可知,当缺失概率未知时,本文提出的方法与缺失概率已知时的估计的渐近性质类似。通过模拟表明加权拟似然估计要比仅用完整个体的方法要好。     

零膨胀计数数据的联合建模及变量选择

零膨胀计数数据破坏了泊松分布的方差-均值关系，可由取值服从泊松分布的数据和取值为零(退化分布)的数据各占一定比例所构成的混合分布所解释。本文基于自适应弹性网技术， 研究了零膨胀计数数据的联合建模及变量选择问题.对于零膨胀泊松分布，引入潜变量，构造出零膨胀泊松模型的完全似然, 其中由零膨胀部分和泊松部分两项组成.考虑到协变量可能存在共线性和稀疏性，通过对似然函数加自适应弹性网惩罚得到目标函数,然后利用EM算法得到回归系数的稀疏估计量，并用贝叶斯信息准则BIC来确定最优调节参数.本文也给出了估计量的大样本性质的理论证明和模拟研究，最后把所提出的方法应用到实际问题中。     

使用边际似然函数识别变结构模型

 波动率模型中结构化变点的识别一直是计量经济学中一个备受关注但却很困难的问题。本文将贝叶斯方法引入波动率模型中,并使用边际似然函数的方法来识别模型变点,避免了传统计量方法中缺陷。此外,通过在对两种边际似然函数的计算方法的对比,我们发现这两种方法在进行模型比较和模型选择时都非常有效。实证研究中,本文使用了美国股票市场的数据,有效的识别出美国股市中的结构化变化的次数和变点发生的时间,并对美国股市结构化变动的原因进行了初步探讨。     

Cox模型中的自适应Lasso变量选择

文章考虑了Cox模型的变量选择问题,将自适应Lasso引入到Cox模型中,提出了一类基于惩罚偏似然函数的自适应Lasso估计程序.通过对偏似然函数采用二阶泰勒展开式近似逼近,运用循环坐标下降法求解模型,再借助牛顿-拉普森迭代完成整个变量选择和估计过程.随机数据模拟的结果表明该方法具有优良的变量选择效果,并适用于高维数据.     

多类型复发事件数据下一类半参数转移模型

复发事件数据频繁的出现在纵向研究中,基于生物医学中的多类型复发事件数据,提出了一类半参数转移模型,该模型包含了一些重要的半参数模型。同时,模型允许协变量具有加性和乘性的影响,且加性影响随时间而变化。利用广义估计方程的思想,对模型中未知参数和非参数函数进行了估计,并且证明了估计的相合性和渐近正态性。     

不等概率分层抽样条件下Probit模型的参数估计

线性回归分析作为一种传统的统计分析方法,现已得到广泛的应用和完善.但受其对应变量连续性要求的影响,当应变量为分类变量(常见的是二分类变量,即y取0,1两个值)时,线性回归模型不再适用.人们通常采用Probit模型或Lotist模型对二分类因变量进行回归分析,与线性回归不同,Probit回归是一种非线性回归模型,因而在参数估计时,通常采用极大似然估计,并且在随机样本条件下,Probit模型的极大似然估计具有一致性,渐进有效性和渐进正态性.     

含非随机缺失数据的面板数据参数估计方法

抽样调查领域常采用对多个受访者进行跟踪调查得到面板数据,进而对总体特性进行统计推断,在面板数据中常含缺失数据,大多数处理面板缺失数据的软件都是直接删去含缺失值的受访者以得到完全数据集,当数据缺失机制为非随机缺失时会导致总体参数估计结果有偏。本文针对数据缺失机制为非随机缺失情形下,如何对面板数据进行统计分析进行了阐述,主要采用的是基于模型的似然推断法,对目标变量、缺失指示变量和随机效应向量的联合分布建模,在已有选择模型和模式混合模型的基础上,引入随机效应,研究目标变量期望的计算方法,并研究随机效应杂合模型下参数的估计方法,在变量分布相对简单的情形下给出了用极大似然法推断总体参数的估计步骤,最后通过模拟分析比较方法的优劣。     

协变量缺失下非线性分位数回归中参数的经验似然推断

文章考虑协变量缺失下非线性分位数回归中参数部分的经验似然统计推断,提出了加权修正的估计方程,并给出了当缺失机制已知和未知时极大经验似然估计的渐近分布,得到了著名的Horvitz-Thompson现象.     

含无误差协变量的重复测量误差模型及其应用

文章讨论响应变量和部分协变量含测量误差的重复测量数据的建模和估计问题,获得参数极大似然估计的EM迭代算法以及估计量的渐近协方差矩阵,并利用Monte-Carlo模拟说明估计的有效性和模型的价值.最后,将研究理论用于处理气象数据的测量误差校正问题.     

中国粮食市场的动态均衡模型及粮食安全调控

由于价格变量同时出现在需求函数和供给函数中,又由于使用数据建模时需求和供给的均衡量是同一数据,通常估计得到的两个函数中价格的符号经常与经济学理论相悖。文章通过对模型的精心设计,使用完全信息极大似然估计,建立了与微观经济理论相符的中国粮食市场动态均衡模型。在此基础上,从数量上分析了决定市场出清的主要变量的作用。最后,从中国粮食安全的角度出发,讨论了政府调控粮食市场的基本原则和策略。     

Bayesian regression model for recurrent event data with event-varying covariate effects and event effect

In the course of hypertension, cardiovascular disease events (e.g. stroke, heart failure) occur frequently and recurrently. The scientific interest in such study may lie in the estimation of treatment effect while accounting for the correlation among event times. The correlation among recurrent event times comes from two sources: subject-specific heterogeneity (e.g. varied lifestyles, genetic variations, and other unmeasurable effects) and event dependence (i.e. event incidences may change the risk of future recurrent events). Moreover, event incidences may change the disease progression so that there may exist event-varying covariate effects (the covariate effects may change after each event) and event effect (the effect of prior events on the future events). In this article, we propose a Bayesian regression model that not only accommodates correlation among recurrent events from both sources, but also explicitly characterizes the event-varying covariate effects and event effect. This model is especially useful in quantifying how the incidences of events change the effects of covariates and risk of future events. We compare the proposed model with several commonly used recurrent event models and apply our model to the motivating lipid-lowering trial (LLT) component of the Antihypertensive and Lipid-Lowering Treatment to Prevent Heart Attack Trial (ALLHAT) (ALLHAT-LLT).     

Semiparametric Estimation of a Change-point for Recurrent Events Data

One particular recurrent events data scenario involves patients experiencing events according to a common intensity rate, and then a treatment may be applied. The treatment might be effective for a limited amount of time, so that the intensity rate would be expected to change abruptly when the effect of the treatment wears out. In particular, we allow models for the intensity rate, post-treatment, to be at first decreasing and then change to increasing (and vice versa). Two estimators of the location of this change are proposed.     

Nonparametric inference for the joint distribution of recurrent marked variables and recurrent survival time

Time between recurrent medical events may be correlated with the cost incurred at each event. As a result, it may be of interest to describe the relationship between recurrent events and recurrent medical costs by estimating a joint distribution. In this paper, we propose a nonparametric estimator for the joint distribution of recurrent events and recurrent medical costs in right-censored data. We also derive the asymptotic variance of our estimator, a test for equality of recurrent marker distributions, and present simulation studies to demonstrate the performance of our point and variance estimators. Our estimator is shown to perform well for a wide range of levels of correlation, demonstrating that our estimators can be employed in a variety of situations when the correlation structure may be unknown in advance. We apply our methods to hospitalization events and their corresponding costs in the second Multicenter Automatic Defibrillator Implantation Trial (MADIT-II), which was a randomized clinical trial studying the effect of implantable cardioverter-defibrillators in preventing ventricular arrhythmia.     

Joint model for bivariate zero-inflated recurrent event data with terminal events

Bivariate recurrent event data are observed when subjects are at risk of experiencing two different type of recurrent events. In this paper, our interest is to suggest statistical model when there is a substantial portion of subjects not experiencing recurrent events but having a terminal event. In a context of recurrent event data, zero events can be related with either the risk free group or a terminal event. For simultaneously reflecting both a zero inflation and a terminal event in a context of bivariate recurrent event data, a joint model is implemented with bivariate frailty effects. Simulation studies are performed to evaluate the suggested models. Infection data from AML (acute myeloid leukemia) patients are analyzed as an application.     

Semiparametric proportional means model for marker data contingent on recurrent event

In many biomedical studies with recurrent events, some markers can only be measured when events happen. For example, medical cost attributed to hospitalization can only incur when patients are hospitalized. Such marker data are contingent on recurrent events. In this paper, we present a proportional means model for modelling the markers using the observed covariates contingent on the recurrent event. We also model the recurrent event via a marginal rate model. Estimating equations are constructed to derive the point estimators for the parameters in the proposed models. The estimators are shown to be asymptotically normal. Simulation studies are conducted to examine the finite-sample properties of the proposed estimators and the proposed method is applied to a data set from the Vitamin A Community Trial.     

Recurrent events analysis in the presence of time-dependent covariates and dependent censoring

Summary.  Recurrent events models have had considerable attention recently. The majority of approaches show the consistency of parameter estimates under the assumption that censoring is independent of the recurrent events process of interest conditional on the covariates that are included in the model. We provide an overview of available recurrent events analysis methods and present an inverse probability of censoring weighted estimator for the regression parameters in the Andersen–Gill model that is commonly used for recurrent event analysis. This estimator remains consistent under informative censoring if the censoring mechanism is estimated consistently, and it generally improves on the naïve estimator for the Andersen–Gill model in the case of independent censoring. We illustrate the bias of ad hoc estimators in the presence of informative censoring with a simulation study and provide a data analysis of recurrent lung exacerbations in cystic fibrosis patients when some patients are lost to follow-up.     

A joint modelling approach for clustered recurrent events and death events

In dental implant research studies, events such as implant complications including pain or infection may be observed recurrently before failure events, i.e. the death of implants. It is natural to assume that recurrent events and failure events are correlated to each other, since they happen on the same implant (subject) and complication times have strong effects on the implant survival time. On the other hand, each patient may have more than one implant. Therefore these recurrent events or failure events are clustered since implant complication times or failure times within the same patient (cluster) are likely to be correlated. The overall implant survival times and recurrent complication times are both interesting to us. In this paper, a joint modelling approach is proposed for modelling complication events and dental implant survival times simultaneously. The proposed method uses a frailty process to model the correlation within cluster and the correlation within subjects. We use Bayesian methods to obtain estimates of the parameters. Performance of the joint models are shown via simulation studies and data analysis.     

Modeling marginal features in studies of recurrent events in the presence of a terminal event

We study models for recurrent events with special emphasis on the situation where a terminal event acts as a competing risk for the recurrent events process and where there may be gaps between periods during which subjects are at risk for the recurrent event. We focus on marginal analysis of the expected number of events and show that an Aalen–Johansen type estimator proposed by Cook and Lawless is applicable in this situation. A motivating example deals with psychiatric hospital admissions where we supplement with analyses of the marginal distribution of time to the competing event and the marginal distribution of the time spent in hospital. Pseudo-observations are used for the latter purpose.

     

Regression analysis of multivariate recurrent event data with a dependent terminal event

Recurrent event data occur in many clinical and observational studies (Cook and Lawless, Analysis of recurrent event data, 2007) and in these situations, there may exist a terminal event such as death that is related to the recurrent event of interest (Ghosh and Lin, Biometrics 56:554–562, 2000; Wang et al., J Am Stat Assoc 96:1057–1065, 2001; Huang and Wang, J Am Stat Assoc 99:1153–1165, 2004; Ye et al., Biometrics 63:78–87, 2007). In addition, sometimes there may exist more than one type of recurrent events, that is, one faces multivariate recurrent event data with some dependent terminal event (Chen and Cook, Biostatistics 5:129–143, 2004). It is apparent that for the analysis of such data, one has to take into account the dependence both among different types of recurrent events and between the recurrent and terminal events. In this paper, we propose a joint modeling approach for regression analysis of the data and both finite and asymptotic properties of the resulting estimates of unknown parameters are established. The methodology is applied to a set of bivariate recurrent event data arising from a study of leukemia patients.     

Time-varying coefficients in a multivariate frailty model: Application to breast cancer recurrences of several types and death

During their follow-up, patients with cancer can experience several types of recurrent events and can also die. Over the last decades, several joint models have been proposed to deal with recurrent events with dependent terminal event. Most of them require the proportional hazard assumption. In the case of long follow-up, this assumption could be violated. We propose a joint frailty model for two types of recurrent events and a dependent terminal event to account for potential dependencies between events with potentially time-varying coefficients. For that, regression splines are used to model the time-varying coefficients. Baseline hazard functions (BHF) are estimated with piecewise constant functions or with cubic M-Splines functions. The maximum likelihood estimation method provides parameter estimates. Likelihood ratio tests are performed to test the time dependency and the statistical association of the covariates. This model was driven by breast cancer data where the maximum follow-up was close to 20 years.