Methodology

This work develops advanced statistical modeling techniques to build efficient and scalable computational frameworks for investigating decision-making in behavioral tasks, integrating data across multiple tasks, uncovering latent dynamics, and elucidating brain–behavior relationships. We aim to identify and quantify distinctive decision-making patterns associated with mental health conditions and diverse cognitive strategies, localize brain regions activated by specific tasks, and determine the causal effects of brain activity on behavior.

This work introduces statistical methodologies for integrating data from multiple randomized controlled trials, which may share a common treatment arm but differ in their alternative treatment options, to learn more robust and reliable individualized treatment rules. In addition, this work develops methods to integrate electronic health records from multiple hospitals while respecting data privacy and institutional sharing constraints, enabling more comprehensive and generalizable analyses across heterogeneous healthcare systems.

This work extends boosting methods by developing multiple strategies to handle missing and interval-censored response variables. These strategies are implemented using functional gradient descent, and we establish rigorous theoretical guarantees. Numerical studies demonstrate that the proposed methods perform well in finite-sample settings.

This work investigates joint models for genetic association involving longitudinal biomarkers and time-to-event outcomes. We develop and validate a closed-form sample size formula for assessing the overall effects of single-nucleotide polymorphisms. To improve robustness against model misspecification due to nonlinear trajectories in the longitudinal traits, we incorporate spline functions to capture subject-specific nonlinear evolutions.

This work addresses key challenges in missing data analysis by proposing a unified modeling framework based on generalized additive models. The framework flexibly accommodates a wide range of missing data mechanisms without relying on strong parametric assumptions. To enable simultaneous estimation and variable selection, it incorporates a regularized likelihood approach. The proposed method is supported by rigorous theoretical guarantees and demonstrates strong empirical performance across a variety of settings.