U.S.-Netherlands Cooperative Research: Statistical Methods for Analyzing Data Arising from Reliability Studies (Mathematical Sciences)

这是宾夕法尼亚州立大学统计学系Michael G. Akritas教授与荷兰林堡大学医学信息与统计学系Willem Albers教授之间为期两年的合作研究项目。数学家们正在合作研究基于距离测量的测试和估计器，相关的自举技术的使用，以及自举技术在某些排序过程（包括多重比较）中的应用。这项工作可能导致发展一种共同理论，用于使用经过审查和未经审查的数据进行测试和估计，因此与可靠性、寿命测试和医学研究产生的数据有关。将考虑的一些性能方面是：分别对一样本和两样本问题的尾部替代方案和交叉危险替代方案的敏感性，以及估计器的鲁棒性以及这如何依赖于审查的程度。工作的第二个方面涉及应用自举技术来近似零分布或零方差的一些常见的秩统计有或没有审查，以及基于秩的多重比较程序与审查和未审查的数据。本研究涉及发展和改进统计程序，以进行“拟合优度”检验，使人们能够判断所选模型与来自实验观察的数据的拟合程度。特别是，该程序将应用于数据被“审查”的情况，即由于某种原因而缺失的情况，例如当患者在临床研究结束前退出时。例如，这些方法可以比较一种疾病的两种或两种以上治疗方法的有效性，并表明得出的结论应具有多大的可信度。所谓的“自举”技术，一种相对较新的和强大的统计工具，将应用于本研究中，以获得感兴趣参数的真实概率分布的近似值。Akritas教授在将统计方法应用于审查数据方面有丰富的经验。阿尔伯斯教授是渐近理论方面公认的权威，特别强调非参数方法。两位研究人员在这项工作的许多数学和计算方面的合作将大大促进新程序的发展以及与现有统计方法的比较。

This is a two-year cooperative research project between Professor Michael G. Akritas, Department of Statistics, The Pennsylvania State University, and Professor Willem Albers, Department of Medical Informatics and Statistics, University of Limburg, The Netherlands. The mathematicians are cooperating in a study of tests and estimators that are based on distance measures, the associated use of the bootstrap technique, and the application of the bootstrap to certain rank procedures including multiple comparisons. The work may lead to the development of a common theory for testing and estimation with both censored and uncensored data, and so is relevant to data arising from reliability, life testing, and medical studies. Some of the performance aspects that will be considered are: sensitivity to tail alternatives and to crossing hazards alternatives for the one- and two- sample problem, respectively, and robustness of the estimators and how this depends on the degree of censoring. The second aspect of the work is concerned with applications of the bootstrap technique to approximating the null distribution or the null variance of some common rank statistics with or without censoring, and to rank-based multiple comparison procedures with both censored and uncensored data. This study is concerned with developing and refining statistical procedures for making "goodness of fit" tests that permit one to judge how well a chosen model fits data derived from experimental observations. In particular, applications of the procedures will be made to situations in which data are "censored," that is, missing for some reason, as when a patient drops out of a clinical study before the study is over. The methods would permit a comparison of the effectiveness of two or more treatments for a disease, for example, as well as indicate the levels of confidence that should be placed on the conclusions that are drawn. The so-called "bootstrap" technique, a relatively new and powerful statistical tool, will be applied in this study to obtain approximations to the true probability distribution of parameters of interest. Professor Akritas has considerable experience in applying statistical methods to censored data. Professor Albers is a recognized authority in asymptotic theory with special emphasis in nonparametric methods. Collaboration by the two researchers on the many mathematical and computational aspects of this work should greatly facilitate the development of the new procedures as well as their comparison with existing statistical methods.