Steady-state Gibbs sampler estimation for lung cancer data

This paper is based on the application of a Bayesian model to a clinical trial study to determine a more effective treatment to lower mortality rates and consequently to increase survival times among patients with lung cancer. In this study, Qian et al. [13 J. Qian, D.K. Stangl, and S. George, A Weibull model for survival data: Using prediction to decide when to stop a clinical trial, in Bayesian Biostatistics, D. Berry and D. Stangl, eds., Marcel Dekker, New York, 1996, pp. 187–205. [Google Scholar]] strived to determine if a Weibull survival model can be used to decide whether to stop a clinical trial. The traditional Gibbs sampler was used to estimate the model parameters. This paper proposes to use the independent steady-state Gibbs sampling (ISSGS) approach, introduced by Dunbar et al. [3 M. Dunbar, H.M. Samawi, R. Vogel, and L. Yu, A more efficient Gibbs sampler estimation using steady state simulation: Application to public health studies, J. Stat. Simul. Comput. 10.1080/00949655.2013.770857.[Taylor &; Francis Online] , [Google Scholar]], to improve the original Gibbs sampler in multidimensional problems. It is demonstrated that ISSGS provides accuracy with unbiased estimation and improves the performance and convergence of the Gibbs sampler in this application.     

Economic design of quick switching sampling system for assuring Weibull distributed mean life

In this paper, we propose the quick switching sampling system for assuring mean life of a product under time truncated life test where the lifetime of the product follows the Weibull distribution and the mean life is considered as the quality of the product. The optimal parameters of the proposed system are determined using two points on the operating characteristic curve approach for various combinations of consumer's risk and ratio of true mean life time and specified life time. Tables are constructed to determine the optimal parameters for specified acceptable quality level and limiting quality level along with the corresponding probabilities of acceptance. The proposed system is compared with other existing sampling plans under Weibull lifetime model. In addition, an economical design of the proposed system is also discussed.     

Estimation of the marginal survival time in the presence of dependent competing risks using inverse probability of censoring weighted (IPCW) methods

In medical studies, there is interest in inferring the marginal distribution of a survival time subject to competing risks. The Kyushu Lipid Intervention Study (KLIS) was a clinical study for hypercholesterolemia, where pravastatin treatment was compared with conventional treatment. The primary endpoint was time to events of coronary heart disease (CHD). In this study, however, some subjects died from causes other than CHD or were censored due to loss to follow-up. Because the treatments were targeted to reduce CHD events, the investigators were interested in the effect of the treatment on CHD events in the absence of causes of death or events other than CHD. In this paper, we present a method for estimating treatment group-specific marginal survival curves of time-to-event data in the presence of dependent competing risks. The proposed method is a straightforward extension of the Inverse Probability of Censoring Weighted (IPCW) method to settings with more than one reason for censoring. The results of our analysis showed that the IPCW marginal incidence for CHD was almost the same as the lower bound for which subjects with competing events were assumed to be censored at the end of all follow-up. This result provided reassurance that the results in KLIS were robust to competing risks.     

Estimation of ratio of population means in two-occasion successive sampling

ABSTRACT

This article considers the problem of estimation of the ratio of population means at the current occasion based on the samples selected over two occasions. Using auxiliary information on both the occasions, some classes of estimators have been proposed. Properties of the proposed estimators have been studied and their respective optimum replacement strategies are discussed. The gains in efficiency of the proposed classes of estimators over the direct estimator where no past information is used are computed. Theoretical results have been interpreted through empirical studies which are followed by suitable recommendations.     

More powerful permutation test based on multistage ranked set sampling

Many researches have used ranked set sampling (RSS) method instead of simple random sampling (SRS) to improve power of some nonparametric tests. In this study, the two-sample permutation test within multistage ranked set sampling (MSRSS) is proposed and investigated. The power of this test is compared with the SRS permutation test for some symmetric and asymmetric distributions through Monte Carlo simulations. It has been found that this test is more powerful than the SRS permutation test; its power increased by set size and/or number of cycles and/or number of stages. Symmetric distributions power increased better than asymmetric distributions power.     

A New Proof of Murthy's Estimator which Applies to Sequential Sampling

Murthy's estimator has been used for constructing an unbiased estimator of a population total or mean from a sample of fixed size when there is unequal probability sampling without replacement. Traditionally, the estimator is derived by constructing an unordered version of Raj's ordered unbiased estimator. This paper presents an elementary proof of Murthy's estimator which applies the Rao–Blackwell theorem to a very simple estimator. This proof includes any sequential sampling scheme, thus extending the usefulness of Murthy's estimator. We demonstrate this extension by deriving unbiased estimators for inverse sampling.     

Inverse Probability of Censoring Weighted U‐statistics for Right‐Censored Data with an Application to Testing Hypotheses

Abstract. A right‐censored version of a U ‐statistic with a kernel of degree m 1 is introduced by the principle of a mean preserving reweighting scheme which is also applicable when the dependence between failure times and the censoring variable is explainable through observable covariates. Its asymptotic normality and an expression of its standard error are obtained through a martingale argument. We study the performances of our U ‐statistic by simulation and compare them with theoretical results. A doubly robust version of this reweighted U ‐statistic is also introduced to gain efficiency under correct models while preserving consistency in the face of model mis‐specifications. Using a Kendall's kernel, we obtain a test statistic for testing homogeneity of failure times for multiple failure causes in a multiple decrement model. The performance of the proposed test is studied through simulations. Its usefulness is also illustrated by applying it to a real data set on graft‐versus‐host‐disease.     

Statistical adjustment of network degree in respondent-driven sampling estimators: Venue attendance as a proxy for network size among young MSM

We introduce a new venue-informed network degree measure, which we applied to respondent-driven sampling (RDS) estimators. Using data collected from 746 young MSM in 2014–2016 in Chicago, IL, and Houston, TX, we estimated the population seroprevalence of HIV and syphilis and risk/protective behaviors, using RDS estimates with self-reported network size as a standard degree measure as well as our proposed venue-informed degree measure. The results indicate that the venue-informed degree measure tended to be more efficient (smaller variance) and less biased than the other measure in both cities sampled. Venue attendance-adjusted network size may provide a more reliable and accurate degree measure for RDS estimates of the outcomes of interest.     

浅谈反三角函数概念的教学

利用知识发生过程的教学方法 ,围绕反三角函数的概念 ,培养学生分析变通能力     

西部地区公众灾害意识的综合评判及抽样分析

公众的灾害意识影响着公众和政府防灾减灾的行为与决策。本文构建了灾害意识水平的综合评价体系,并依此对西部地区公众的灾害意识状况进行了调查分析,结果发现,尽管西部地区公众的灾害意识水平有所提高,但总体而言并不乐观;另外,灾害意识的4个具体维度在性别、年龄、职业、文化和居住地五个人类个性特征上表现出一定的差异。加强灾害教育是提高公众灾害意识必然选择。