Advances in Proximal Inference for Continuous Exposures, Estimation of Ill-Posed Regression, and Non-Inferiority Assessment in Active-Controlled Trials

Abstract

This dissertation advances proximal inference methods for continuous exposures and ill-posed regression problems, alongside non-inferiority assessment in active-controlled trials.An introduction to the topics is provided in Chapter 1. Chapter 2 develops a unifying framework for non-inferiority evaluation in active-controlled trials, where placebo arms are unavailable, enabling systematic comparison of existing methods in terms of type I error, power, and robustness to transportability misspecifications. Chapter 3, motivated by the analysis of immune correlates of protection in COVID-19 vaccine trials, extends the proximal inference framework to identify and estimate the mean outcome under modified treatment policies, enabling causal analysis of continuous exposures in the presence of unmeasured confounding. Chapter 4 addresses the challenge of estimating ill-posed nuisance functions in proximal inference and related settings, developing a novel finite-sample analysis of kernel-based regularized adversarial stabilized estimators and establishing conditions under which debiased, influence-function-based one-step estimators for a broad class of estimands, achieve root-n consistency and asymptotic normality. Together, these contributions support more robust inference in complex causal problems with unmeasured confounding or design constraints.