Analysis of Longitudinal or Multivariate Data with Nonignorable Missing Values

具有不可忽略缺失值的纵向或多变量数据分析

• 批准号: 1305474
• 负责人: Jun Shao
• 金额: $ 18万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-09-15 至 2017-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1305474&HistoricalAwards=false
• 关键词: Analysis; Longitudinal; Multivariate; Data; Nonignorable

In many statistical applications, some data from sampled units are missing because of various reasons. In most survey problems, some sampled units cooperate in the survey but fail to provide answers to some or all survey items. In medical or health studies, data are often longitudinal and many patients drop out before the end of the study. The rates of missing data in surveys or medical studies are often appreciable, especially when data are longitudinal and/or multivariate (e.g., many questions in a survey). When data missing depends on observed data only, the missingness mechanism or propensity is called ignorable. Otherwise, missing data are nonignorable. There is a rich literature on methodology for handling ignorable missing data. Nonignorable missing data are much more difficult to handle compared with ignorable missing data, since missingness propensity depends on unobserved values and, thus, model fitting is very challenging. For example, assumptions have to be imposed to ensure the identifiability and estimability of unknown quantities and these assumptions cannot be checked using data because of the presence of missing values. The proposed research focuses on estimation and inference based on longitudinal or multivariate data with nonignorable missing values. The investigator studies three general topics. (1) When missing data are nonignorable, applying existing methods developed for the case of ignorable missing data leads to biased estimators. Research is needed to derive approximately unbiased and consistent estimators for parameters of interest. Under some assumptions on the missingness propensity and/or the data distribution for the case of no nonresponse, the investigator studies several approaches for constructing asymptotically valid estimators. These approaches are all semiparametric and make use of a covariate that helps to identify parameters under nonignorable missingness (and is therefore named as a nonresponse instrument). Adopted estimation methods include pseudo likelihood, estimating equations, generalized method of moments, data transformation, approximate conditional likelihood, imputation, and some techniques of handling measurement errors. For survey data, the model-assisted approach is adopted. (2) In addition to the bias and consistency, the investigator studies the asymptotic efficiency of estimators. For longitudinal or multivariate data with nonignorable missing values, it is difficult to make use of observed data from units having incomplete data. Efforts will be made to use more or all observed data. (3) Most surveys require a variance estimator for each survey estimator for the purpose of error assessment. Statistical inference such as setting confidence sets also requires variance estimators. A basic requirement for variance estimators is their approximate unbiasedness and consistency. In each proposed research topic, the investigator studies variance estimation after a valid estimator is derived, using methods such as linearization, substitution, or resampling.Since the proposed research topics are motivated by problems in survey agencies such as the Census Bureau, the Bureau of Labor Statistics, and Statistics Canada, or by data sets in medical and health studies, results obtained from this proposed research will have significant impact on the methodology of handling missing data and variability estimation. Since research on nonignorable missing data, especially for multivariate or longitudinal data, is far from complete, results from this proposal will shed light on further scientific research in this area.

在许多统计应用中，由于各种原因，抽样单位中的一些数据会丢失。在大多数调查问题中，一些抽样单位在调查中合作，但未能提供部分或全部调查项目的答案。在医学或健康研究中，数据通常是纵向的，许多患者在研究结束前退出。调查或医学研究中的数据缺失率通常是可观的，特别是当数据是纵向和/或多变量时（例如，调查中的许多问题）。当数据缺失仅取决于观测数据时，缺失机制或倾向被称为可验证的。否则，丢失的数据是不可重复的。有丰富的文献方法处理可验证的缺失数据。与可验证的缺失数据相比，不可验证的缺失数据更难处理，因为缺失倾向取决于未观察到的值，因此模型拟合非常具有挑战性。 例如，必须施加假设以确保未知量的可识别性和可估计性，并且由于缺失值的存在，这些假设无法使用数据进行检查。建议的研究重点是基于纵向或多变量数据的估计和推理不可重复的缺失值。研究人员研究了三个一般性主题。(1)当缺失数据是不可估计的，应用现有的方法开发的情况下，可估计的缺失数据导致有偏估计。需要进行研究以获得感兴趣的参数的近似无偏和一致的估计。在缺失倾向和/或无应答情况下的数据分布的一些假设下，研究者研究了几种构建渐近有效估计量的方法。这些方法都是半参数的，并利用协变量，有助于确定参数下non-responsive missingness（因此被称为无响应工具）。所采用的估计方法包括伪似然法、估计方程、广义矩法、数据变换、近似条件似然法、插补法以及处理测量误差的一些技巧。对于调查数据，采用模型辅助方法。(2)除了偏倚和一致性，研究者还研究估计量的渐近有效性。对于具有不可重复缺失值的纵向或多变量数据，很难利用来自具有不完整数据的单元的观测数据。将努力使用更多或所有观察到的数据。(3)大多数调查都需要为每个调查估计量提供方差估计量，以便进行误差评估。统计推断，如设置置信集也需要方差估计。方差估计量的基本要求是近似无偏性和一致性。在每个研究主题中，研究者使用线性化、替代或回归等方法推导出有效的估计量后，研究方差估计。由于研究主题的动机是调查机构（如人口普查局、劳工统计局和加拿大统计局）的问题，或医学和健康研究的数据集，本研究的结果将对缺失数据的处理方法和变异性估计产生重大影响。由于对不可重复缺失数据的研究，特别是对多变量或纵向数据的研究，还远未完成，因此该建议的结果将为该领域的进一步科学研究提供启示。