Estimating Process Capability Index C PM Using a Bootstrap Sequential Sampling Procedure

Construction of a confidence interval for process capability index C _PM is often based on a normal approximation with fixed sample size. In this article, we describe a different approach in constructing a fixed-width confidence interval for process capability index C _PM with a preassigned accuracy by using a combination of bootstrap and sequential sampling schemes. The optimal sample size required to achieve a preassigned confidence level is obtained using both two-stage and modified two-stage sequential procedures. The procedure developed is also validated using an extensive simulation study.     

Moments of the decisive sample number and of the average time to termination of sequential tests

The moments of the decisive sample number and of the average time to termination of sequential tests are derived. All moments depend only on the probability of continuation of the sequential test at each step, or at each instant of time for time processes. Two theorems are proved. Although the second theorem may be proved by quoting a result used in Barlow and Proschan (1965), p. 33, or both theorems from a lemma in Govindarajulu (1975), pp. 518-519, the author’s direct proofs illuminate the results.     

Point estimation after early stopping in a repeated measures trial

When the individual measurements are statistically independent, the maximum likelihood estimator calculated at the end of a sequential procedure overestimates the underlying effect. There are many clinical trials in which we are interested in comparing changes in responses between two treatment groups sequentially. Lee and DeMets (1991, JASA 86, 757–762) proposed a group sequential method for comparing rates of change when a response variable is measured for eaeh patient at successive follow-up visits. They assumed that the response follows the linear mixed effects model and derived the asymptotic joint distribution of the sequentially computed statistics. In this article, we consider the maximum likelihood estimator (MLE), the median unbiased estimator (MUE) and the midpoint of a 100(1-α)% confidence interval as point estimators for the rate of change in the linear mixed effects model, and investigate their properties by Monte Carlo simulation.     

Bayes sequential estimation for a Poisson process under a LINEX loss function

In this paper, within the framework of a Bayesian model, we consider the problem of sequentially estimating the intensity parameter of a homogeneous Poisson process with a linear exponential (LINEX) loss function and a fixed cost per unit time. An asymptotically pointwise optimal (APO) rule is proposed. It is shown to be asymptotically optimal for the arbitrary priors and asymptotically non-deficient for the conjugate priors in a similar sense of Bickel and Yahav [Asymptotically pointwise optimal procedures in sequential analysis, in Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, University of California Press, Berkeley, CA, 1967, pp. 401–413; Asymptotically optimal Bayes and minimax procedures in sequential estimation, Ann. Math. Statist. 39 (1968), pp. 442–456] and Woodroofe [A.P.O. rules are asymptotically non-deficient for estimation with squared error loss, Z. Wahrsch. verw. Gebiete 58 (1981), pp. 331–341], respectively. The proposed APO rule is illustrated using a real data set.     

城镇化、工业化对农业全要素生产率增长的影响研究——来自重庆37个县(区)面板数据的证据

文章基于2000—2016年重庆37个县（区）面板数据，使用序列DEA方法测算了重庆农业全要素生产率变动，在此基础上探讨了重庆农业全要素生产率增长的时间演变，并从理论和实证层面系统考察了城镇化和工业化对农业全要素生产率增长的影响。结果表明：首先，2000—2016年间重庆市农业全要素生产率呈上升趋势，2007年后重庆市农业全要素生产率增长更为明显，并且重庆市各地区呈现出明显的空间不平衡性。其次，动态面板模型的实证结果表明城镇化对农业全要素生产率增长具有显著正向影响，工业化对农业全要素生产率增长也具有显著正向影响。最后，研究还发现基础设施、教育水平以及金融发展程度对农业全要素生产率增长均具有显著正向影响，而产业结构对农业全要素生产率增长具有显著负向影响。     

Bias Reduction using Stochastic Approximation

The paper studies stochastic approximation as a technique for bias reduction. The proposed method does not require approximating the bias explicitly, nor does it rely on having independent identically distributed (i.i.d.) data. The method always removes the leading bias term, under very mild conditions, as long as auxiliary samples from distributions with given parameters are available. Expectation and variance of the bias-corrected estimate are given. Examples in sequential clinical trials (non-i.i.d. case), curved exponential models (i.i.d. case) and length-biased sampling (where the estimates are inconsistent) are used to illustrate the applications of the proposed method and its small sample properties.     

象似性及其对英语词汇教学的启示

本文从这四个方面论述了词汇象似性,并探讨象似性对英语词汇教学的启示,以提高英语词汇学习和英语课堂词汇教学的效率。     

Adaptive designs for IVPT data with mixed scaled average bioequivalence

In vitro permeation tests (IVPT) offer accurate and cost-effective development pathways for locally acting drugs, such as topical dermatological products. For assessment of bioequivalence, the FDA draft guidance on generic acyclovir 5% cream introduces a new experimental design, namely the single-dose, multiple-replicate per treatment group design, as IVPT pivotal study design. We examine the statistical properties of its hypothesis testing method—namely the mixed scaled average bioequivalence (MSABE). Meanwhile, some adaptive design features in clinical trials can help researchers make a decision earlier with fewer subjects or boost power, saving resources, while controlling the impact on family-wise error rate. Therefore, we incorporate MSABE in an adaptive design combining the group sequential design and sample size re-estimation. Simulation studies are conducted to study the passing rates of the proposed methods—both within and outside the average bioequivalence limits. We further consider modifications to the adaptive designs applied for IVPT BE trials, such as Bonferroni's adjustment and conditional power function. Finally, a case study with real data demonstrates the advantages of such adaptive methods.     

Modifications of sequential designs in bioequivalence trials

Bioequivalence (BE) studies are designed to show that two formulations of one drug are equivalent and they play an important role in drug development. When in a design stage, it is possible that there is a high degree of uncertainty on variability of the formulations and the actual performance of the test versus reference formulation. Therefore, an interim look may be desirable to stop the study if there is no chance of claiming BE at the end (futility), or claim BE if evidence is sufficient (efficacy), or adjust the sample size. Sequential design approaches specially for BE studies have been proposed previously in publications. We applied modification to the existing methods focusing on simplified multiplicity adjustment and futility stopping. We name our method modified sequential design for BE studies (MSDBE). Simulation results demonstrate comparable performance between MSDBE and the original published methods while MSDBE offers more transparency and better applicability. The R package MSDBE is available at https://sites.google.com/site/modsdbe/ . Copyright © 2015 John Wiley & Sons, Ltd.     

Group sequential monitoring based on the weighted log‐rank test statistic with the Fleming–Harrington class of weights in cancer vaccine studies

In recent years, immunological science has evolved, and cancer vaccines are now approved and available for treating existing cancers. Because cancer vaccines require time to elicit an immune response, a delayed treatment effect is expected and is actually observed in drug approval studies. Accordingly, we propose the evaluation of survival endpoints by weighted log‐rank tests with the Fleming–Harrington class of weights. We consider group sequential monitoring, which allows early efficacy stopping, and determine a semiparametric information fraction for the Fleming–Harrington family of weights, which is necessary for the error spending function. Moreover, we give a flexible survival model in cancer vaccine studies that considers not only the delayed treatment effect but also the long‐term survivors. In a Monte Carlo simulation study, we illustrate that when the primary analysis is a weighted log‐rank test emphasizing the late differences, the proposed information fraction can be a useful alternative to the surrogate information fraction, which is proportional to the number of events. Copyright © 2016 John Wiley & Sons, Ltd.