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.     

Estimation of location extremes within general families of scale mixtures

In this paper, we study the estimation of the minimum and maximum location parameters, respectively, representing the minimum guaranteed lifetime of series and parallel systems of components, within a general class of scale mixtures. The conditional or underlying distribution has only the primary restriction of being a location-scale family with positive support. The mixing distribution is also quite general in that we only assume that it has positive support and finite second moment. For demonstrative purposes several special cases are highlighted such as the gamma, inverse-Gaussian, and discrete mixture. Various estimators, including bootstrap bias corrected estimators, are compared with respect to both mean-squared-error and Pitman's measure of closeness.     

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.     

Managing dependency in China outsourcing relationships

Abstract

This paper examines manufacturing firms’ use of guanxi and formal control to address dependence on suppliers and achieve desired outsourcing performance in China. Using survey data collected from manufacturing firms operating in China, a structural equation model is used to test the research model. The results suggest that manufacturing firms with high dependence on suppliers build Chinese guanxi with those suppliers to overcome the dependence and enhance outsourcing performance. In addition, Chinese guanxi also appears to facilitate the use of formal control, which was also found to have a positive relationship with outsourcing performance. This paper contributes to the literature by illustrating the importance of guanxi in achieving desired outsourcing performance in the China context, particularly in the case where a manufacturer perceives high dependency on its major supplier.     

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.     

锚定比率可以衡量股价高估吗？——基于崩盘风险视角的经验证据

股价高估指的是公司市场价值超出其内在价值的现象,但如何衡量内在价值一直存在争议。借鉴行为金融文献中锚定效应的概念,结合中国资本市场的特殊性,本文提出了锚定比率(简称"RPR")这一新的股价高估指标。为了证实该指标的有效性,本文利用事后的股价崩盘风险进行了相关检验。结果表明:第一,锚定比率与股价崩盘风险正相关;第二,更少的分析师跟踪、更多的散户持股以及更高的股票流动性均会强化锚定比率对股价崩盘风险的影响;第三,在控制常用的股价高估指标、两类代理问题和管理层"捂盘"行为后,本文的结果依然成立;第四,利用崩盘事件,本文证实了锚定比率会加剧股价下跌的程度,且长期来看股价会保持"惯性"而非"反转"。本文的研究表明投资者做决策时对股价高点存在明显的锚定效应,丰富了锚定效应在中国资本市场中的运用。更重要的是,本文提出了一个可能更适合于中国资本市场的股价高估指标,该指标意味着资本市场定价机制的不完善是导致股价高估和频繁崩盘的重要原因,这对于改善资本市场定价效率、降低股价崩盘风险有一定的启示作用。     

中国城市居民最低生活保障水平分析

以2005年的统计数据为主要依据,通过测算及横向与纵向的比较,对我国城市居民最低生活保障水平进行了分析,目的在于廓清人们对中国目前最低生活保障水平的认识.综合分析表明,尽管在制度设计和具体实施中仍存在缺陷和问题,但保障水平过高肯定不是当前低保制度面临的问题,对低保"养懒汉"的抨击也是一种片面的夸大.