Latent Confounder adjustment in Multivariate Analysis

Latent confounding—unobserved factors that influence both covariates and outcomes—poses a fundamental challenge to valid inference in modern multivariate regression. Such confounders are pervasive in biomedical, epidemiologic, and genomic studies, where biological processes, environmental exposures, and measurement artifacts induce structured dependence across variables. When ignored, latent confounding can bias effect estimates, inflate false discoveries, and compromise replicability. Despite substantial progress in high-dimensional regression and multiple testing, general and computationally efficient methods for latent confounder adjustment remain limited, especially for correlated binary outcomes. This dissertation develops a unified theoretical and methodological foundation for latent confounder adjustment in multivariate regression and extends these ideas to continuous, binary, and high-dimensional settings. The work proceeds in three interrelated components. First, we establish a unifying latent-factor regression framework showing that several widely used approaches—such as negative-control (NC) methods, robust regression (RR), and surrogate-variable analysis (SVA)—are special cases of a general model under distinct identifiability conditions. This theoretical perspective clarifies when unbiased estimation is possible, provides sufficient conditions for identifiability, and reveals common structure among methods previously viewed as distinct. Second, we extend this framework to multivariate binary data through a generalized linear latent variable model (GLLVM), which formally characterizes identifiability under logistic links. We develop likelihood-based estimation procedures, including adaptive Gaussian quadrature and Laplace approximations, and demonstrate their effectiveness in simulation and real-world applications such as vaccine safety surveillance. Finally, motivated by modern large-scale studies, we design scalable inference algorithms for high-dimensional binary outcomes that circumvent high-dimensional integration. These include variational and Pólya–Gamma–based approximations that maintain interpretability while enabling efficient computation. Collectively, these approaches establish a continuum of accuracy–efficiency trade-offs for latent confounder adjustment in large-scale data. Across simulations and applications, the proposed methods achieve accurate, stable estimation under diverse confounding structures and substantially improve interpretability compared to standard analyses. Taken together, this work unifies disparate lines of research on latent-factor modeling and confounding adjustment, establishes general identifiability theory for multivariate regression, and delivers practical algorithms suited to modern high-dimensional biomedical data.