Analysis of Longitudinal or Multivariate Data with Nonignorable Missing Values

University Of Wisconsin-Madison, Madison WI

Investigators

Abstract

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.