Sensitivity Analysis for Informative Missingness with Semiparametric Models

Michigan State University, East Lansing MI

Investigators

Abstract

Missing data are common in almost all empirical research. Examples abound in epidemiologic studies, clinical trials, social science studies (for example sample surveys) and other substantive investigations of scientific inquiry. With incomplete data, a long-standing question in statistical research concerns how to conduct unbiased and reliable inferences, especially when the missingness process depends on the unobserved data. This question has become particularly relevant in this era of big data, where empirical data, albeit massive, may be subject to a selective nonresponse. Motivated by practical problems in medical imaging data, functional and longitudinal data, this research project will develop new methods and practical tools for handling incomplete data, focusing on sensitivity analysis. Results obtained from this research will have significant impacts on sensitivity analysis methods for nonrandom missing data under semiparametric estimation and inference. With recent technological advances in this era of big data, many missing data models arising in various substantive applications involve infinite-dimensional parameters that are only identifiable on the grounds of unverifiable assumptions about the data generating process. A popular approach for addressing identifiability concerns, at least in the context of finite-dimensional parameter settings, has been to impose some structural constraints on the model upon which the parameters of primary interest are presumed identified. Inferences are then conducted within the framework of a sensitivity analysis to accommodate uncertainties resulting from these untestable restrictions. Despite its popularity, this approach has not been systematically studied when the working population model involves a nonparametric component in addition to the parametric component. This project proposes to fill this gap by formalizing inferences via rigorous sensitivity analyses when there are identifiability concerns under semiparametric estimation and inference. Unlike in finite-dimensional parametric models, conducting such analyses is not trivial owing to the complexity of the theoretical arguments and the computational burden. The goal of this project is to further our understanding of the theory that embeds inference in non- and weakly-identified semiparametric models arising in missing data problems within the framework of a sensitivity analysis. Conducting a sensitivity analysis under semiparametric formulations is technically not trivial owing to the inferential strategy posing substantial challenges beyond those encountered with finite-dimensional parametric models. In this project, asymptotic expansions, resampling techniques including the bootstrap, related techniques from empirical processes and computer-aided simulations will be employed to study the central theoretical properties and the finite sample performance of the proposed procedures. The foundational nature of the proposal in establishing the connection between the empirical process theory and sensitivity analysis is transformative. This connection within the class of semiparametric models arising in both classical and modern statistics will be explored and studied. A further part of the intellectual merit lies in its interdisciplinary approach with the transfer of ideas between high level computing, empirical process techniques, and subject matter science informing the model describing complex systems with many parameters. 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.