Causal Inference in the Presence of Unmeasured Confounding: Advances in Mendelian Randomization and Proximal Causal Inference

Abstract

Observational data are indispensable for causal inference, particularly when randomized controlled trials are infeasible due to ethical, logistical, or economic constraints. However, observational data are subject to unmeasured confounding, where unobserved variables influence both the treatment and the outcome, potentially leading to biased estimates and spurious findings. This dissertation aims to develop statistical methods for causal inference in the presence of unmeasured confounding, focusing on multivariable Mendelian randomization (MVMR) using summary-level data and proximal causal inference using individual-level data. MVMR uses genetic variants as instrumental variables (IVs) to infer the direct causal effects of multiple exposures on an outcome. In the first project, we develop a general asymptotic regime for many weak instruments, which allows for varying degrees of IV strengths across exposures, offering a more accurate asymptotic framework for studying MVMR estimators. We then propose a novel spectral regularized inverse-variance weighted estimator for estimating causal effects, and show that it is consistent and asymptotically normal under many weak IVs. The second project extends this work to settings involving many potentially highly correlated exposures. We develop a new estimator which minimizes a penalized debiased objective function that reduces weak instrument bias while yielding interpretable estimates with theoretical guarantees for variable selection. To enable valid post-selection inference, we adapt a data-thinning strategy to summary-data MVMR. In the third project, we aim to identify and estimate the average treatment effect (ATE) in a target population using data from an observational source study conducted within another population. To address unmeasured confounding within the source study and unmeasured effect modification, we adopt proximal causal inference, leveraging observed variables as proxies for unmeasured confounders and effect modifiers.