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.     

The econometrics of female labor supply and children

This is a survey of applied econometric research on the effects of children on female labor supply. Reasons for interest in the topic, and a basic model and terminology, are reviewed. Concerns are raised about the possible endogeneity of child status variables, and about the instrumental variables approach for dealing with this problem. Alternative ways of conceptualizing and estimating child status effects are considered, together with selected empirical evidence. Relevant developments from the household demand literature are summarized. Basic issues of model choice are also discussed.     

Why do French women have more children than German women? Family policies and attitudes towards child care outside the home

French mothers are still more often economically active than their German counterparts and birth rates in France remain higher than in West Germany. By comparing two countries with many similarities in their family policies, I try to demonstrate that the differences between state policies per se should not be overestimated in explaining the persistent gap in their fertility level. As far as women's attitudes towards child care outside of the home are concerned, there is a strong divide between France and West Germany. In the Old Länder in Germany there is some congruence between attitudes and beliefs towards child care and the shortage of child care provision, especially for toddlers. As a product of the interaction between shortage of child care provision, women's attitudes regarding child care and mothers' low labour force participation rate, German family policy reinforces these attitudes. Conversely, there is slow impetus for policy makers to really develop a comprehensive public child care system. Against this cultural and institutional background, an increasing number of women give priority to their job or to their career. In France, by contrast, norms in respect of education of toddlers and young children have evolved in tandem with the change in attitudes of women towards employment. A majority of French women feel legitimised to be in employment on a full-time basis and to have their children cared for outside the home. Their attitudes are in tune with the premises of family policy which has integrated the model of 'the employed mother'. Les Francaises continuent àavoir plus d'enfants que les Allemandes de l'Ouest alors que les différences entre les taux d'activité des mères se sont progressivement atténuées. La proportion de femmes qui n'ont pas d'enfants, en particulier, est beaucoup plus importante en Allemagne de l'Ouest. En comparant deux pays dont les politiques sociales et familiales présentent des similarités, on se propose d'aller au delà des explications les plus couramment admises. En France, contrairement à l'Allemagne de l'Ouest, les normes régissant l'éducation des jeunes enfants ont évolué en phase avec les changements qui ont affectéles comportements des femmes sur le marché du travail. Il est devenu légitime socialement pour les Francaises de travailler à plein temps tout en faisant garder son enfant à l'extérieur du domicile. Les Allemandes de l'Ouest, par contre, intériorisent toujours fortement la norme selon laquelle l'éducation d'un jeune enfant nécessite la présence permanente de sa mère. Mais de plus en plus éduquées, elles sont amenées à accorder la priorité à leur maintien dans l'emploi et à renoncer à la maternité. Pour mieux comprendre les différences de fácondité entre les deux pays, il semble donc fructueux de se focaliser sur les interactions à l'aeuvre entre leurs politiques familiales, les valeurs auxquelles adhèrent la majorité des couples concernant l'éducation des jeunes enfants et les attitudes des femmes face au travail rémunéré.     

The transition to parenthood in Puerto Rico: Occupational status and the timing of first births

This study examines the relationship between occupational status and fertility timing during a period of rapid development in Puerto Rico. Our fundamental hypothesis is that women with higher status occupations face greater opportunity costs than those with less valued jobs and therefore will be more likely to postpone parenthood until later ages than women without such high costs. We test this hypothesis using event history techniques with data from the 1982 Puerto Rico Fertility and Family Planning Assessment, an island-wide survey of women between the ages of 15 and 49. The analysis examines the effects of occupational status on the timing of first births, and finds strong support for the basic hypothesis, especially regarding the post-ponement of teen births. After the teen years, the effects are less pronounced. Overall, it appears that employment opportunities have played an important role in childbearing decisions in Puerto Rico.An earlier version of this paper was presented at the annual meeting of the Population Association of America, Denver, Colorado, 30 April–2 May 1992.     

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.     

国有股和法人股对公司业绩的影响--公用事业型上市公司的实证研究

公司的股份集中于少数几个大股东手中是中国公司股权结构的一个普遍特征,研究这些大股东如何凭借其持股地位影响公司业绩是中国公司股权结构研究的一个非常重要的问题.本文选取了在上交所上市的公用事业型公司1998年至2002年的平行数据进行实证研究,结果表明,法人股对公司业绩有积极影响,国有股对公司业绩的影响视具体情况而定.     

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.     

社会服务供给集约化发展思路探索

针对我国目前社会服务供给主体发展现状和社会服务供给特性,结合市场集中度和集约化管理理论,分析我国社会服务供给主体存在的主要问题,论述社会服务供给市场集中度与社会服务供给集约化的关系,提出通过降低准入门槛、鼓励主体竞合、强化规模运营、培育大型主体、理顺主体关系、完善竞争机制及优化市场结构等策略与措施,来推动社会服务供给集约化管理。