Abstract
Biomedical data, encompassing genetic profiles, imaging biomarkers, and electronic health records, play a crucial role in advancing precision medicine and clinical decision-making by enabling the estimation of treatment effects, disease progression, and patient-specific risk prediction. However, extracting meaningful and reliable information from such high-dimensional, heterogeneous biomedical data requires advanced statistical and computational methodologies. This dissertation develops novel nonparametric and semiparametric statistical methods across two broad domains: functional and imaging data analysis, and causal inference for multilevel semi-competing risks data.
The first part of this dissertation addresses the analysis of functional and imaging outcomes in neuroimaging studies. In Chapter 2 we propose a longitudinal image-on-scalar regression framework that jointly models nonlinear temporal dynamics and spatially varying covariate effects on brain imaging responses. Multivariate splines over triangulation accommodate irregular brain geometry, and a scalable distributed learning algorithm based on Hilbert space-filling curve domain decomposition enables computation at large scale. In Chapter 3 we develop a framework for estimating the functional conditional average treatment effect (fCATE) to characterize how the spatially distributed effect of multiple treatments on imaging outcomes varies across individuals with heterogeneous clinical and genetic profiles. A double machine learning approach based on Robinson-type orthogonalization and deep learning yields robust, debiased estimates of heterogeneous treatment effects in high-dimensional functional imaging settings. Both methods are evaluated using the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset.
The second part of this dissertation develops a unified semiparametric framework for causal inference in multilevel semi-competing risks data, motivated by population-based comparative effectiveness research using observational healthcare data such as SEER-Medicare. In such settings, patients are clustered within healthcare providers, may experience a non-terminal event (e.g., cancer recurrence) that is subject to dependent censoring by a terminal event (e.g., death), and treatment assignment is subject to confounding. In Chapter 4, we propose a copula-based hierarchical regression model with time-varying coefficients, estimated through a two-stage procedure combining penalized pseudo-likelihood and nonlinear estimating equations, and establish the consistency and asymptotic normality of the proposed estimators. Chapter 5 extends this framework to address confounding using propensity score (PS) weighting via inverse probability of treatment weighting (IPTW), targeting the average treatment effect (ATE) by reweighting the observed sample to balance covariate distributions across treatment groups. Chapter 6 instead employs propensity score matching (PSM) to target the average treatment effect for the treated (ATT), constructing a matched control group that is directly comparable to the treated population. Both PS approaches consider marginal, fixed-effect, and random-effect propensity score models to appropriately account for multilevel data structure, and asymptotic properties are established for each. All three chapters are illustrated through a multi-institutional study of breast cancer data.
