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Innovative Strategies, Statistical Solutions and Simulations for Modern Clinical Trials
Journal of the American Statistical Association ( IF 3.7 ) Pub Date : 2020-04-02 , DOI: 10.1080/01621459.2020.1759987
Ionut Bebu 1
Affiliation  

Owen (1988, 1990) proposed an innovative empirical likelihood (EL) approach for the confidence interval of mean based on the complete data. EL is a pure nonparametric approach, which has been applied in numerous research fields due to the excellent performance for the small sample compared to other existing methods. It is preferable to other parametric and bootstrap methods, in particular when the distribution of the data is unknown. For example, the EL interval estimate has more accurate coverage probability than asymmetric confidence intervals. It also obeys the range of parameters of interest, and shares the Bartlett correction property. It has been three decades since the EL was proposed by Owen (1988). The book by Vexler and Yu presents many useful procedures for EL inference for biomedicine and health research, and discusses the properties of those statistical procedures in detail. This well-written book gives a very nice and systematic overview of EL techniques and computational procedures with many working examples from health research. The book uses deep EL theory to deal with biomedical and health data with complex structures including bivariate data, missing data, skewed data, etc. This book is appropriate for being used as a textbook for an advanced graduate course. Some material in the book is suitable and understandable for graduate students. Other material would be of interest to postgraduate researchers, and is useful as a reference when the researchers conduct a novel research using modern empirical likelihood methods. This book not only introduces the technical details about EL theory, powerful statistical procedures, derivations of theorems, but also contains many examples related to clinical and epidemiological datasets. In addition, the book offered numerous R codes for the implementation of proposed EL procedures, which are readily used by the readers. In Chapter 1, this book provides a nice overview of hypothesis tests. After discussing the likelihood ratio tests and maximum likelihood, this chapter introduces the EL as a datadriven likelihood, which is a powerful and nonparametric approach. The advantages and benefits of EL approach are discussed. Chapter 2 covers basic ingredients of the EL. This chapter starts with an overview of the idea of classical EL. Then, it presents several interesting topics including densitybased EL methods, Bayesian procedures, Bartlett correction, comparison with bootstrap approach, etc. Chapter 3 introduces an innovative method, which incorporates EL in the Bayesian frame work. It proposes nonparametric Bayesian interval estimation with adjustment for skewed data and posterior expectations of general functionals. The probability weighted moments (PWMs) is the subject of Chapter 4. It develops the interval estimation of the PWMs and shows an application to the Gini index. The performance comparisons are carried out in this chapter. Chapter 5 covers new approach for two-group comparison. It shows how to combine empirical likelihoods and parametric models together to make statistical inference based on incomplete data. Chapter 6 discusses quantile comparisons based on EL approach. It considers testing one group and two groups. Both the standard EL and plug-in method are used in the testing problem. Chapter 7 tackles EL inference problem for a U-statistic constraint. The chapter begins with some background on U statistics, and then proposes the EL ratio test with the U-statistic type constraints. It offers an EL approach for multivariate two-group U-statistic with applications to receiver operating characteristic (ROC) curves and crossover designs, etc. Chapter 8 presents an EL approach for ROC curve analysis. It begins with the introduction of ROC curves. Then, it proposes EL method to derive the correct variance estimate for the partial area under ROC curve in details. Chapter 9 provides challenging topics about EL, which include censored data analysis, missing data analysis, longitudinal data analysis, survey sampling, etc. It shows that EL methods can be used to many interesting problems by formulating as an estimating equation. The first book about EL is Owen (2001), which presents the foundation of EL theory and basic methods. The second EL book is Zhou (2015), which studies modern survival analysis problems with right censored data using censored empirical likelihood. The book by Vexler and Yu is the third EL book with the focus on health research applications. The coverage of the book ranges broadly from medicine diagnostic, Bayesian data analysis, to the comparison of quantiles, health science research, etc. This book is extensive in its coverage of EL methods with many useful applications. In my opinion, it can form the advanced nonparametric statistics course with the concentration in EL theory and method with applications in biostatistics taught in PhD-level programs. In summary, this is an interesting and comprehensive book. This book with many topics in biostatistics and EL will provide an appealing and invaluable reference to instructors and researchers.

中文翻译:

现代临床试验的创新策略、统计解决方案和模拟

Owen (1988, 1990) 针对基于完整数据的均值置信区间提出了一种创新的经验似然 (EL) 方法。EL 是一种纯非参数方法,由于与其他现有方法相比,它在小样本方面具有出色的性能,因此已应用于众多研究领域。它比其他参数和引导方法更可取,特别是当数据的分布未知时。例如,EL 区间估计比非对称置信区间具有更准确的覆盖概率。它还遵守感兴趣的参数范围,并共享 Bartlett 校正属性。自欧文 (Owen) (1988) 提出 EL 以来,已经过去了三十年。Vexler 和 Yu 的书介绍了许多用于生物医学和健康研究的 EL 推理的有用程序,并详细讨论了这些统计程序的特性。这本写得很好的书对 EL 技术和计算程序进行了非常好的和系统的概述,其中包含许多来自健康研究的工作示例。本书使用深度EL理论处理具有复杂结构的生物医学和健康数据,包括双变量数据、缺失数据、倾斜数据等。本书适合作为研究生高级课程的教科书。本书中的一些材料适合研究生并且易于理解。其他材料可能会引起研究生研究人员的兴趣,并且在研究人员使用现代经验似然方法进行新研究时可用作参考。本书不仅介绍了EL理论的技术细节,强大的统计程序,定理的推导,但也包含许多与临床和流行病学数据集相关的例子。此外,本书还提供了大量 R 代码来实现所提议的 EL 程序,读者可以很容易地使用这些代码。在第 1 章,本书很好地概述了假设检验。在讨论了似然比检验和最大似然之后,本章介绍了 EL 作为数据驱动的似然,这是一种强大的非参数方法。讨论了 EL 方法的优点和好处。第 2 章介绍了 EL 的基本要素。本章首先概述经典 EL 的思想。然后,它提出了几个有趣的主题,包括基于密度的 EL 方法、贝叶斯程序、巴特利特校正、与引导方法的比较等。第 3 章介绍了一种创新方法,它在贝叶斯框架中结合了 EL。它提出了非参数贝叶斯区间估计,调整了偏斜数据和一般泛函的后验期望。概率加权矩 (PWM) 是第 4 章的主题。它开发了 PWM 的区间估计并展示了对基尼指数的应用。本章进行了性能比较。第 5 章介绍了两组比较的新方法。它展示了如何将经验似然和参数模型结合在一起,以基于不完整数据进行统计推断。第 6 章讨论基于 EL 方法的分位数比较。它考虑测试一组和两组。标准EL和插件方法都用于测试问题。第 7 章解决了 U 统计约束的 EL 推理问题。本章首先介绍了 U 统计的一些背景知识,然后提出了具有 U 统计类型约束的 EL 比率检验。它为多元两组 U 统计量提供了一种 EL 方法,适用于接收器操作特征 (ROC) 曲线和交叉设计等。第 8 章介绍了 ROC 曲线分析的 EL 方法。它从引入 ROC 曲线开始。然后,详细地提出了EL方法来推导出ROC曲线下局部面积的正确方差估计。第 9 章提供了有关 EL 的具有挑战性的主题,包括删失数据分析、缺失数据分析、纵向数据分析、调查抽样等。它表明 EL 方法可以通过公式化为估计方程来解决许多有趣的问题。关于 EL 的第一本书是 Owen (2001),介绍了EL理论和基本方法的基础。第二本 EL 书是 Zhou (2015),它使用删失的经验似然研究了右删失数据的现代生存分析问题。Vexler 和 Yu 的这本书是第三本专注于健康研究应用的 EL 书。本书涵盖的范围很广,从医学诊断、贝叶斯数据分析到分位数比较、健康科学研究等。本书涵盖了具有许多有用应用的 EL 方法。在我看来,它可以形成以EL理论和方法为重点的高级非参数统计课程,并在博士课程中教授生物统计学。总而言之,这是一本有趣而全面的书。
更新日期:2020-04-02
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