Variable Selection, Instrument Search and Estimation in Problems with Nonignorable Missing Data

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Missing data are ubiquitous in many applications including sample surveys, clinical trials and medical/health studies. Handling incomplete data is particularly challenging when the missingness is related to the unobserved data. This project seeks to develop statistical models and methods for analyzing datasets with nonignorable missing values. The research topics are motivated by problems encountered by survey agencies as well as in data sets from biomedical/health studies. The results will have significant impact both in terms of new methodological development for handling incomplete data as well as in applications to real datasets from a number of scientific fields. When the missing data mechanism depends on unobserved data, the missing data are referred to as nonignorable. Handling nonignorable missing data is a challenging problem as the unobserved values follow a distribution different from that of the observed data leading to issues of identifiability and estimability of the underlying unknown parameters. The proposed research focuses on the following three areas: (1) Instrument search and model selection. A recent method for handling nonignorable missing data is built on the use of a covariate (called an instrument) that enables researchers to identify and estimate population parameters. In applications, however, such an instrument must be constructed from a given set of observed covariates. The proposed research will develop methods for finding instruments in different situations, including semiparametric propensity models, pseudo likelihood methods, and problems with both missing responses and covariate values. Together with instrument search, model selection regarding the parametric component will be also investigated. (2) High dimension reduction and variable selection. In many big data applications, the dimension of the covariate vector is often very large, however, only a few covariates are useful. While there is extensive research related to dimension reduction and variable selection over the past two decades, there are no results available in the presence of nonignorable missing responses. The proposed research focuses on covariate selection or dimension reduction under two semiparametric frameworks. (3) Multivariate data with nonignorable missing values. The proposed research will develop methods for problems with both missing responses and covariates, survival analysis with survival-dependent missing covariates, and personalized medicine with longitudinal data having dropouts.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.