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.     

乔伊斯的文学实验精神在小说整体布局中的体现

爱尔兰著名作家詹姆斯·乔伊斯在其文学作品创作过程中始终追求艺术形式的创新.作为20世纪初现代主义文学倾向的代表人物,乔伊斯在小说<一个青年艺术家的肖像>中大胆突破传统,以强烈的文学实验精神将其创作理论应用到实际创作中.以时间、意识和技巧为创作中心,生动展示了主人公斯蒂芬·迪达勒斯的现代精神气质.本文以其代表作小说<一个青年艺术家的肖像>为实例,旨在从两个方面展示乔伊斯的文学实验精神,即乔伊斯美学理论在实际创作中的应用以及其现代主义创作技巧在体现小说整体布局中的作用.     

计算中国男性人体环节体积的二元回归方程的研究

采用CT—图像分析法,在尸体研究的基础上,对50例中国男性样本(18～23岁)进行了全身CT横断层扫描、影像分析和测算,获得了样本各环节的长度和体积等惯性数据。进而确定了中国男性青年人体体积的分布,并据此建立了以身高、体重为自变量的直接计算中国青年人体各环节体积的二元回归方程。     

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.     

Leaving Home Early: Passing from Girlhood to Womanhood

This paper presents a case study of a young woman’s narrative of leaving home and her transition to adulthood. The case study is part of a larger research project about young women with an experience of an early break-up from home, through running away or being thrown out. Empirical material underlying this paper consists of a qualitative study of 12 young women that have been interviewed. The aim of the study is to understand how events like running away/being thrown out of home influences their transition to adulthood. The particular narrative demonstrates how a young woman presents and accounts for such a dramatic event as running away or being thrown out from home, and how that is understood in relation to her adulthood. A further aim is to illustrate how social services efforts are reflected in her narrative.     

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.     

Analysis of dependently truncated data in Cox framework

Truncation is a known feature of bone marrow transplant (BMT) registry data, for which the survival time of a leukemia patient is left truncated by the waiting time to transplant. It was recently noted that a longer waiting time was linked to poorer survival. A straightforward solution is a Cox model on the survival time with the waiting time as both truncation variable and covariate. The Cox model should also include other recognized risk factors as covariates. In this article, we focus on estimating the distribution function of waiting time and the probability of selection under the aforementioned Cox model.     

Deterred by debt? Young people,schools and the escalating cost of UK higher education

Popular commentaries lament that reforms to the financing of Higher Education (HE) in the UK will operate as a significant deterrent to HE participation amongst students from less advantaged backgrounds. This view of debt as a deterrent is powerful and exists not only at a societal level, but also, as we show, is present in schools. Our data reveal, however, that these ‘debt commentaries’ play out very differently across schools according to the nature of their catchment and the sorts of views staff hold about pupils in relation to their fear of debt. Furthermore, students’ views on debt largely contradict these popular ‘debt-as-deterrent’ narratives and instead are often characterised by acceptance, ambivalence and at times positive orientations towards the prospect of debt. These findings vividly illuminate both the regional and institutional specificity of staff and student decision making in relation to ‘debt’, hence they have substantial implications for HE funding policy specifically and debates about widening participation in HE more generally, where ensuring greater equity in the scope of choices young people have when it comes to choosing a university is a pressing concern.