Analysis of Longitudinal or Multivariate Data with Nonignorable Missing Values

在许多统计应用中，由于各种原因，抽样单位的一些数据会丢失。在大多数调查问题中，一些抽样单位在调查中合作，但不能对部分或全部调查项目提供答案。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往往是可观的，特别是当数据是纵向的和/或多变量的时候(例如，调查中的许多问题)。当数据缺失仅依赖于观测数据时，缺失机制或倾向称为可忽略。否则，丢失的数据是不可忽视的。有大量关于处理可忽略的丢失数据的方法的文献。不可忽略的缺失数据比不可忽略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，必须强加假设以确保未知量的可辨识性和可估计性，而这些假设不能使用数据来检验，因为存在缺失值。所提出的研究侧重于基于具有不可忽略的缺失值的纵向或多变量数据的估计和推断。调查员研究了三个一般性的主题。(1)当缺失数据不可忽略时，应用已有的针对可忽略缺失数据情况的方法会导致有偏估计。需要进行研究来得出感兴趣参数的近似无偏和一致的估计值。在对无响应情况下的遗漏倾向和/或数据分布的一些假设下，研究了几种构造渐近有效估计的方法。这些方法都是半参数的，并利用协变量在不可忽略的缺失情况下帮助识别参数(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、广义矩方法、数据变换、近似条件似然、推算以及一些测量误差的处理技术。对于调查数据，采用模型辅助的方法。(2)除了偏差和相合性外，研究者还研究了估计量的渐近有效性。对于具有不可忽略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。将努力使用更多或全部观测数据。(3)为了进行误差评估，大多数调查都要求每个调查估计值都有一个方差估计值。统计推断，如设置置信集，也需要方差估计器。对方差估计量的一个基本要求是它们的近似无偏和一致性。在每个建议的研究主题中，研究人员在得到有效的估计量之后，使用线性化、替换或重采样等方法来研究方差估计。由于建议的研究主题的动机是人口普查局、劳工统计局和加拿大统计局等调查机构的问题，或者是医疗和健康研究中的数据集，因此建议的研究结果将对处理缺失数据和变异性估计的方法产生重大影响。由于对不可忽视的缺失数据，特别是对多变量或纵向数据的研究还远未完成，这一建议的结果将为这一领域的进一步科学研究提供参考。

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.