Bayesian Inference in Marshall–Olkin Bivariate Exponential Shared Gamma Frailty Regression Model under Random Censoring

Many analyses in the epidemiological and the prognostic studies and in the studies of event history data require methods that allow for unobserved covariates or “frailties”. We consider the shared frailty model in the framework of parametric proportional hazard model. There are certain assumptions about the distribution of frailty and baseline distribution. The exponential distribution is the commonly used distribution for analyzing lifetime data. In this paper, we consider shared gamma frailty model with bivariate exponential of Marshall and Olkin (1967 Marshall, A.W., Olkin, I. (1967). A multivariate exponential distribution. J. Am. Stat. Assoc. 62:30–44.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) distribution as baseline hazard for bivariate survival times. We solve the inferential problem in a Bayesian framework with the help of a comprehensive simulation study and real data example. We fit the model to the real-life bivariate survival data set of diabetic retinopathy data. We introduce Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in the proposed model and then compare the true values of the parameters with the estimated values for different sample sizes.     

Bias Adjustment Minimizing the Asymptotic Mean Square Error

A method of bias adjustment which minimizes the asymptotic mean square error is presented for an estimator typically given by maximum likelihood. Generally, this adjustment includes unknown population values. However, in some examples, the adjustment can be done without population values. In the case of a logit, a reasonable fixed value for the adjustment is found, which gives the asymptotic mean square error smaller than those of the asymptotically unbiased estimator and the maximum likelihood estimator. The weighted-score method, which yields directly the estimator with the minimized asymptotic mean square error, is also given.     

Maximum entropy in the mean methods in propensity score matching for interval and noisy data

Abstract

In this paper, we propose maximum entropy in the mean methods for propensity score matching classification problems. We provide a new methodological approach and estimation algorithms to handle explicitly cases when data is available: (i) in interval form; (ii) with bounded measurement or observational errors; or (iii) both as intervals and with bounded errors. We show that entropy in the mean methods for these three cases generally outperform benchmark error-free approaches.     

Asymptotic cumulants of the estimator of the canonical parameter in the exponential family

Asymptotic cumulants of the maximum likelihood estimator of the canonical parameter in the exponential family are obtained up to the fourth order with the added higher-order asymptotic variance. In the case of a scalar parameter, the corresponding results with and without studentization are given. These results are also obtained for the estimators by the weighted score, especially for those using the Jeffreys prior. The asymptotic cumulants are used for reducing bias and mean square error to improve a point estimator and for interval estimation to have higher-order accuracy. It is shown that the kurtosis to squared skewness ratio of the sufficient statistic plays a fundamental role.     

Point and Interval Estimation for Bivariate Normal Distribution Based on Progressively Type-II Censored Data

ABSTRACT

The maximum likelihood estimates (MLEs) of parameters of a bivariate normal distribution are derived based on progressively Type-II censored data. The asymptotic variances and covariances of the MLEs are derived from the Fisher information matrix. Using the asymptotic normality of MLEs and the asymptotic variances and covariances derived from the Fisher information matrix, interval estimation of the parameters is discussed and the probability coverages of the 90% and 95% confidence intervals for all the parameters are then evaluated by means of Monte Carlo simulations. To improve the probability coverages of the confidence intervals, especially for the correlation coefficient, sample-based Monte Carlo percentage points are determined and the probability coverages of the 90% and 95% confidence intervals obtained using these percentage points are evaluated and shown to be quite satisfactory. Finally, an illustrative example is presented.     

Projecting From Advance Data Using Propensity Modeling: An Application to Income and Tax Statistics

This article proposes and evaluates two new methods of reweighting preliminary data to obtain estimates more closely approximating those derived from the final data set. In our motivating example, the preliminary data are an early sample of tax returns, and the final data set is the sample after all tax returns have been processed. The new methods estimate a predicted propensity for late filing for each return in the advance sample and then poststratify based on these propensity scores. Using advance and complete sample data for 1982, we demonstrate that the new methods produce advance estimates generally much closer to the final estimates than those derived from the current advance estimation techniques. The results demonstrate the value of propensity modeling, a general-purpose methodology that can be applied to a wide range of problems, including adjustment for unit nonresponse and frame undercoverage as well as statistical matching.     

基于EM算法的改进MLM模型及参数估计

传统的分层模型假设组与组之间独立,没有考虑组之间的相关性。而以地理单元分组的数据往往具有空间依赖性,个体不仅受本地区的影响,也可能受相邻地区的影响。此时,传统分层模型层-2残差分布的假设不再成立。为了处理空间分层数据,将空间统计和空间计量经济模型的思想引入到分层模型中,既纳入分层的思想,又顾及空间相关性,提出了空间分层线性模型,并给出了其固定效应、方差协方差成分和空间回归参数的最大似然估计,在运用EM算法时,结合运用了Fisher得分算法。     

Testing for the Presence of a Cure Fraction in Clustered Interval‐Censored Survival Data

Clustered interval‐censored survival data are often encountered in clinical and epidemiological studies due to geographic exposures and periodic visits of patients. When a nonnegligible cured proportion exists in the population, several authors in recent years have proposed to use mixture cure models incorporating random effects or frailties to analyze such complex data. However, the implementation of the mixture cure modeling approaches may be cumbersome. Interest then lies in determining whether or not it is necessary to adjust the cured proportion prior to the mixture cure analysis. This paper mainly focuses on the development of a score for testing the presence of cured subjects in clustered and interval‐censored survival data. Through simulation, we evaluate the sampling distribution and power behaviour of the score test. A bootstrap approach is further developed, leading to more accurate significance levels and greater power in small sample situations. We illustrate applications of the test using data sets from a smoking cessation study and a retrospective study of early breast cancer patients.     

浅议中高层管理者绩效评估指标的设计

从中高层管理者绩效评估指标设计中存在的问题出发 ,强调了绩效评估理念在绩效评估指标设计中的重要性 ,阐明了绩效评估的理念 ,并以适用于中高层管理者绩效评估的平衡计分卡为例 ,介绍了如何将绩效评估理念全面地贯彻到绩效评估指标的具体设计过程之中 ,最后针对我国的绩效评估现状提出相应建议。     

大学生职业选择匹配度量表的编制与估计

运用深度访谈和文献法初步编制条目,经过419份有效数据的预测和1680份有效数据的正式检测,构建出信度与效度均为合理的大学生职业选择匹配度量表。运用回归分析方法,建构职业选择影响因素权重等值和不等值条件下的匹配度估计模型,作为量化大学生职业选择与社会生活满意匹配度,服务提高大学生就业质量的操作分析工具。