Mathematical Sciences: Asymptotic Methods for Order Restricted Inference in Survival Analysis

题目：生存分析中顺序限制推理的渐近方法摘要：研究的目的是在未知参数表现出顺序限制的情况下，发展从生存数据推断的大样本理论。这种限制在生存分析中经常出现。例如，如果一项临床试验涉及在研究队列中增加剂量的药物，那么计算每组的生存曲线应该根据剂量水平排序。在连锁分析中，为了绘制数量遗传性状的图谱，可能会发现所研究的性状在一种基因型中比在其他基因型中更为普遍。虽然已知这些情况下的适当估计量，但尚未研究它们的分布性质。因此，当次序限制方法可能有助于数据分析时，通常不使用它。出于估计的目的，它将给估计器提供更高的准确度。为了测试的目的，它将给予更大的权力，能够考虑次序限制的替代方案。研究的重点是调查存在订单限制的统计方法。这些限制经常出现在生物技术问题中。例如，在确定药物疗效的临床试验中，经常会出现药物剂量增加的情况。在遗传连锁分析中，人们通常知道，某种基因型比其他可能的基因型更能缩短发病时间。如果兴趣在于确定药物功效（在第一种情况下）或找出基因的位置（在第二种情况下），那么将数据中的噪声与信号分离的统计方法必须包含这些已知的顺序。调查人员研究整合这些信息的方法。他们认为，所得的统计方法将比目前处理生物技术数据的方法更合适，因为这种排序是存在的。

Proposal: DMS 9504891 PI: Jens Praestgaard Institution: University of Iowa Title: Asymptotic Methods for Order Restricted Inference in Survival Analysis ABSTRACT: The purpose of the research is to develop large-sample theory for inference from survival data when the unknown parameters exhibit order restrictions. Such restrictions occur frequently in survival analysis. For example, if a clinical trial involves administering a drug in increasing doses to the cohorts under study, then the survival curves computed for each group should be ordered according to dose level. In linkage analysis, for the purpose of mapping a quantitative genetic trait, it may be known that the trait under study is more prevalent for one genotype than for others. Although appropriate estimators in these settings are known, their distributional properties have not been studied. Thus, order restricted methods are often not used when it would potentially help the data analysis. For estimation purposes it would give estimators with higher degree of accuracy. For testing purposes it would give higher power to be able to consider order restricted alternatives. The research centers on investigating statistical methods in the presence of order restrictions. These restrictions occur often in biotechnological problems. For instance, in a clinical trial to determine drug efficacy, it is often the case that the drug is administered in increasing doses. In genetical linkage analysis it is often known that a certain genotype lowers the time until the onset of a disease more than do other possible genotypes. If the interest is on determining the drug efficacy (in the first case) or finding out where the gene is located (second case), then the statistical methods, which separate the noise in the data from the signal, must incorporate these known orderings. The investigators study ways of incorporating such information. They believe that the resulting statistical method ology will be more appropriate than present methods for dealing with biotechnological data where such orderings are present.