Model-Based Methods for the Analyses of Weighted Data

描述（由申请人提供）：拟议研究的目的是通过开发基于模型的方法，将设计方法的稳健性与通过模型可获得的最优性相结合，开发用于分析具有高差异纳入概率的数据的方法。在以人口为基础的全国性复杂样本设计健康调查中经常发现的非等选择概率样本设计中，选择概率与抽样数据之间的相关性可能导致偏差。通常使用与选择概率的倒数相等的权重来抵消这种偏差。高度不成比例的样本设计具有较大的权重，这可能会在统计数据中引入不必要的可变性，例如总体均值估计。权值调整将大权值减少到固定的切点值，并调整低于此值的权值以保持未调整的权值总和。这以引入一些偏差为代价减少了可变性。标准方法不是“数据驱动的”：它们不使用数据来进行适当的偏差-方差权衡，或者以一种非常低效的方式进行权衡。我们建议开发基于模型的“权重修剪”方法，以补充非比例纳入概率设计中标准的、基于特别设计的方法，其中样本权重的方差超过了偏差校正。我们还将考虑使用这些模型来估计线性和广义线性回归模型中的总体参数。我们在分层和后分层已知概率样本设计的背景下开发了这些模型，并将其应用扩展到更一般的多阶段聚类样本设计中。我们计划开发贝叶斯模型，因为我们相信它们为传统的频率分析提供了理论和实践上的优势，并且它们在调查数据分析中的使用被忽视了。我们会考虑三个主要的应用：使用儿童乘客安全合作伙伴基于人口的监测数据集进行分析，以确定乘用车碰撞中儿童受伤的预测因素和机制；利用国家健康和营养检查调查来探索儿童心血管危险因素的发展，并利用结合行为风险因素监测调查和国家健康访谈调查数据开发的校准估计器来确定成年人中吸烟和癌症筛查行为的流行程度。

DESCRIPTION (provided by applicant): The purpose of the proposed research is to develop methodologies for the analysis of data with highly differential probabilities of inclusion by developing model-based methods that combine the robustness of the design approach with the optimality obtainable through a model. In unequal-probability-of-selection sample designs often found in national, population-based, complex-sample-design health surveys, correlations between the probability of selection and the sampled data can induce bias. Weights equal to the inverse of the probability of selection are often used to counteract this bias. Highly disproportional sample designs have large weights, which can introduce unnecessary variability in statistics such as the population mean estimate. Weight trimming reduces large weights to a fixed cutpoint value and adjusts weights below this value to maintain the untrimmed weight sum. This reduces variability at the cost of introducing some bias. Standard approaches are not "data-driven": they do not use the data to make the appropriate bias-variance tradeoff, or else do so in a highly inefficient fashion. We propose to develop model-based methods for "weight trimming" to supplement standard, ad-hoc design-based methods in disproportional probability-of-inclusion designs where variances due to sample weights exceeds bias correction. We will also consider the use of these models to estimate population parameters in linear and generalized linear regression models. We develop these models in the context of stratified and poststratified known-probability sample designs, and extend their use into more general multistage cluster sample designs. We plan to develop Bayesian models, as we believe that they offer both theoretical and practical advantages to traditional frequentist analyses and that their use has been neglected in the analysis of survey data. We will consider three major applications: analyses to determine predictors and mechanisms of injury to children in passenger vehicle crashes using the population-based surveillance dataset of the Partners for Child Passenger Safety, to explore the development of cardiovascular risk factors in children using the National Health and Nutrition Examination Survey and to determine the prevalence of smoking and cancer screening behavior among adults using calibration estimators developed to combine data from the Behavioral Risk Factor Surveillance Survey and the National Health Interview Survey.