Reducing sample size needed for cox-proportional hazards model analysis using more efficient sampling method

Abstract

In general, survival data are time-to-event data, such as time to death, time to appearance of a tumor, or time to recurrence of a disease. Models for survival data have frequently been based on the proportional hazards model, proposed by Cox. The Cox model has intensive application in the field of social, medical, behavioral and public health sciences. In this paper we propose a more efficient sampling method of recruiting subjects for survival analysis. We propose using a Moving Extreme Ranked Set Sampling (MERSS) scheme with ranking based on an easy-to-evaluate baseline auxiliary variable known to be associated with survival time. This paper demonstrates that this approach provides a more powerful testing procedure as well as a more efficient estimate of hazard ratio than that based on simple random sampling (SRS). Theoretical derivation and simulation studies are provided. The Iowa 65+ Rural study data are used to illustrate the methods developed in this paper.     

A simple estimator for a shared frailty regression model

Summary. We propose a simple estimation procedure for a proportional hazards frailty regression model for clustered survival data in which the dependence is generated by a positive stable distribution. Inferences for the frailty parameter can be obtained by using output from Cox regression analyses. The computational burden is substantially less than that of the other approaches to estimation. The large sample behaviour of the estimator is studied and simulations show that the approximations are appropriate for use with realistic sample sizes. The methods are motivated by studies of familial associations in the natural history of diseases. Their practical utility is illustrated with sib pair data from Beaver Dam, Wisconsin.     

Sampling design proportional to order statistic of auxiliary variable

The sampling designs dependent on sample moments of auxiliary variables are well known. Lahiri (Bull Int Stat Inst 33:133–140, 1951) considered a sampling design proportionate to a sample mean of an auxiliary variable. Sing and Srivastava (Biometrika 67(1):205–209, 1980) proposed the sampling design proportionate to a sample variance while Wywiał (J Indian Stat Assoc 37:73–87, 1999) a sampling design proportionate to a sample generalized variance of auxiliary variables. Some other sampling designs dependent on moments of an auxiliary variable were considered e.g. in Wywiał (Some contributions to multivariate methods in, survey sampling. Katowice University of Economics, Katowice, 2003a); Stat Transit 4(5):779–798, 2000) where accuracy of some sampling strategies were compared, too.These sampling designs cannot be useful in the case when there are some censored observations of the auxiliary variable. Moreover, they can be much too sensitive to outliers observations. In these cases the sampling design proportionate to the order statistic of an auxiliary variable can be more useful. That is why such an unequal probability sampling design is proposed here. Its particular cases as well as its conditional version are considered, too. The sampling scheme implementing this sampling design is proposed. The inclusion probabilities of the first and second orders were evaluated. The well known Horvitz–Thompson estimator is taken into account. A ratio estimator dependent on an order statistic is constructed. It is similar to the well known ratio estimator based on the population and sample means. Moreover, it is an unbiased estimator of the population mean when the sample is drawn according to the proposed sampling design dependent on the appropriate order statistic.     

Testing the Equality of Two Exponential Distributions

This paper proposes an overlapping-based test statistic for testing the equality of two exponential distributions with different scale and location parameters. The test statistic is defined as the maximum likelihood estimate of the Weitzman's overlapping coefficient, which estimates the agreement of two densities. The proposed test statistic is derived in closed form. Simulated critical points are generated for the proposed test statistic for various sample sizes and significance levels via Monte Carlo Simulations. Statistical powers of the proposed test are computed via simulation studies and compared to those of the existing Log likelihood ratio test.     

Bayesian Estimation and Model Choice in Item Response Models

Item response models are essential tools for analyzing results from many educational and psychological tests. Such models are used to quantify the probability of correct response as a function of unobserved examinee ability and other parameters explaining the difficulty and the discriminatory power of the questions in the test. Some of these models also incorporate a threshold parameter for the probability of the correct response to account for the effect of guessing the correct answer in multiple choice type tests. In this article we consider fitting of such models using the Gibbs sampler. A data augmentation method to analyze a normal-ogive model incorporating a threshold guessing parameter is introduced and compared with a Metropolis-Hastings sampling method. The proposed method is an order of magnitude more efficient than the existing method. Another objective of this paper is to develop Bayesian model choice techniques for model discrimination. A predictive approach based on a variant of the Bayes factor is used and compared with another decision theoretic method which minimizes an expected loss function on the predictive space. A classical model choice technique based on a modified likelihood ratio test statistic is shown as one component of the second criterion. As a consequence the Bayesian methods proposed in this paper are contrasted with the classical approach based on the likelihood ratio test. Several examples are given to illustrate the methods.     

The numerical evaluation of the distribution function of a bilinear from to a quadratic from with econometric examples

This paper considers a general and computationally convenient method of evaluating the distribution function of statistics that are the ratio of a bilinear form to a quadratic form. Numerous Economemc applications of the method are given.     

中国省际人口流动与 人力资本流动差异性分析

人力资本流动与人口流动相关却不相同,本文采用2010-2016年全国流动人口动态监测数据,从流动方向和流动强度两方面对我国省际人口流动引致的人力资本流动现象加以研究。结果表明从流动方向分析,各省人口净流动方向基本呈现时间一致性并且流入流出区域具有稳定性。在调查期间人口净流出省份为16个,人口净流入省份为15个,没有明显变化。人力资本净流向与人口净流向完全一致,但省际人口净流向与高级人力资本净流向并不完全一致,山西、广西、重庆等省市的高级人力资本净流向始终与总人力资本净流向相反。本文采用流出流入比率和迁移选择中心两种指标测算人力资本流动强度,结果基本一致。人力资本流动中心与人口流动中心分布均较为固定。2010年人力资本流动强度最大的省份在2016年的流动强度也更强,流动强度在省际呈现惯性和马太效应。人力资本流入最强地区包括北京、天津、上海三个直辖市,人力资本流出最强省份始终包括安徽、四川、河南等省份。以人力资本流出弹性衡量人力资本流出强度与人口流出强度的相对强弱,东部地区、东北地区省份人力资本的流出强度始终大于人口流出强度,西部地区省份差异较大。考虑各省近五年经济增长状况,人口流动或者人力资本流动对经济增长的影响是非线性的。     

Generalized estimator of population mean by using conventional and non-conventional measures in the presence of measurement errors

In survey research, it is assumed that reported response by the individual is correct. However, given the issues of prestige bias, self-respect, respondent's reported data often produces estimated values which are highly deviated from the true values. This causes measurement error (ME) to be present in the sample estimates. In this article, the estimation of population mean in the presence of measurement error using information on a single auxiliary variable is studied. A generalized estimator of population mean is proposed. The class of estimators is obtained by using some conventional and non-conventional measures. Simulation and numerical study is also conducted to assess the performance of estimators in the presence and absence of measurement error.     

治理出生性别比失衡问题的再思考

针对我国20世纪80年代以来出生人口性别比持续升高现象分析认为,在我国,造成出生人口性别比升高的直接原因是非法胎儿性别鉴定的存在,深层次原因则是源于农村较低的经济发展水平和由此引起的社会保障制度不完善,以及国家在倡导男女平等的基本国策方面缺乏切实有效的政策措施。由此提出,建设社会主义新型生育文化、制定提高女性社会地位的相关政策、加强相关法规建设、完善社会保障制度以及借鉴他国成功经验等应是综合治理出生人口性别比升高的具体对策。     

中国大陆婚姻状况变迁及婚姻挤压问题分析

本文以2005年全国1％人口抽样调查数据为基础,通过城乡之间的比较,借助对婚姻挤压以及中国大龄未婚人口现象的系统描述来揭示其存在的特征和后果。婚姻挤压和大龄未婚现象既与个人因素有关,同样受到社会结构变迁的影响,不仅在性别上有所差异,城乡之间也存在较大差别,农村未婚女青年的比例较低,最多的大龄未婚女青年集中在城市。而婚姻迁移和社会对于男女两性的期望不同将会对新的婚姻挤压问题造成进一步的冲击。