This dissertation explores statistical methodologies, particularly causal inference methods and Functional Data Analysis (FDA) methods, applied to problems in social and biomedical sciences. The work is divided into three distinct parts.
The first part studies the integration of external data in randomized controlled trials (RCTs), which is gaining interest from the FDA and industry, particularly when RCTs face limitations. The research has two main objectives: first, to introduce causal weighting estimators for improved statistical power while maintaining type I error rates. Second, we propose causal inference methods for estimating long-term treatment effects in the open-label extension phase of phase III studies, where subjects switch from placebo to the experimental treatment after the primary endpoint. The practical application of these methods is demonstrated through a phase III clinical trial in rare disease.
The second part studies the U.S. Supreme Court dynamics by analyzing the temporal evolution of the underlying policy positions of the Supreme Court Justices as reflected by their actual voting data, using functional data analysis methods. The flexible nonparametric method makes it possible to represent highly complex dynamic trajectories by a few principal components and dissect the time-dynamics of policy positions at the level of individual Justices, as well as providing a comprehensive view of the ideology evolution over the history of Supreme Court since its establishment. In addition to quantifying individual Justice's policy positions, we uncover average changes over time and also the major patterns of change over time.
The third part studies gerrymandering. While the Court has been hesitant to intervene in partisan gerrymandering, it has been more willing to address racial gerrymandering due to the clear constitutional protections against racial discrimination in voting. Legislators engaged in partisan gerrymandering may use race as a proxy, targeting racial voting blocs to either concentrate or dilute their power. This can lead to situations where partisan gerrymandering inadvertently results in racial gerrymandering, creating a loophole in litigation. First, we introduce a novel metric of representation weight to measure individual voter representation in redistricting, filling a gap in existing research. Second, we estimate the quantile treatment effect to quantify the distributional impact of partisan redistricting on representation weight and the racial disparities in those effects. The utility of our framework is demonstrated through analyses of current redistricting litigations in Alabama, Florida, and Texas.
