Hybrid likelihood methods

PI: McKeague, Ian w.s nnsf项目：统计机构：哥伦比亚大学标题：混合似然方法经验似然正在向三个方向扩展：允许在估计方程中插入有害参数的估计，比根n的收敛速度慢，以及与样本量相比有相对大量的估计方程的设置。这项工作的部分动机是需要更有效地比较临床试验和队列研究中的生存分布。寻找分裂点置信区间的方法，如在更广泛的半参数模型中的参数回归模型中的跳跃所表示的，也正在研究中。这涉及到开发混合似然方法的立方根渐近性。通过对非混合似然比统计量进行反演，构造了一个新的置信集。该项目的这一部分的动机是应用于开发大沼泽地的磷阈值标准。最后，正在开发用于艾滋病毒疫苗功效试验的混合可能性技术，在试验中必须考虑到感染的相对风险与感染艾滋病毒的差异之间的依赖关系。混合似然提供了一种统一的方法来看待以某种方式适应非参数似然方法的技术，例如，通过使用插件估计干扰参数，或者通过使用从工作（但不是“真实”）模型派生的似然。近年来，混合似然的使用变得越来越普遍，在许多应用领域都很有吸引力，因为它结合了基于似然方法的力量，以及需要找到复杂统计问题的易于处理和易于实施的解决方案的实用意识。研究者正在扩大混合似然方法在各种设置的范围。方法学工作主要围绕三个具体主题展开：应用于生存分析的经验似然，应用于估计污染阈值的分裂点置信区间，以及应用于检测HIV疫苗功效试验中病毒差异的标记特异性相对风险的比较。

ABSTRACTProp ID: DMS-0505201 PI: McKeague, Ian W.NSF Program: STATISTICS Institution: Columbia University Title: Hybrid likelihood methods Empirical likelihood is being extended in three directions: to allow for plug-in estimates of nuisance parameters in estimating equations, slower than root-n rates of convergence, and settingsin which there are a relatively large number of estimating equationscompared to the sample size. This work is motivated in partby the need to more effectively compare survival distributions in clinical trials and cohort studies.Methods of finding confidence intervals for split points, as represented by jumps in parametric regression models withinbroader semiparametric models, are also being investigated. This involves developing cube-root asymptotics for hybrid likelihood methods. A new confidence set is constructed by inverting ahybrid likelihood ratio statistic. This part of the project is motivated by an application to the development of a phosphorus threshold standard for the Everglades. Finally, hybrid likelihood techniques are being developed for use in HIV vaccine efficacy trials in which it is important to take into account dependence of the relative risk of infection on the divergence of infecting HIV viruses.Hybrid likelihood provides a unified way of looking at techniquesthat adapt a nonparametric likelihood based approach in some way, for example through the use of plug-in estimates for nuisance parameters, or by the use of a likelihood derived from a working (but not "true") model. The use of hybrid likelihood has become increasinglycommon in recent years and is attractive in many applied areas because it combines the power of likelihood based methods with a pragmatic sense of the need to find tractable and easily implementedsolutions to complex statistical problems. The investigator is extending the scope of hybrid likelihood methods in a variety of settings. Methodological work is conducted on three specific topics:empirical likelihood with applications in survival analysis,confidence intervals for split points with application to the estimation of pollution thresholds, and comparison of mark-specific relative risks with application to the detection ofviral divergence in HIV vaccine efficacy trials.