Bayesian and Causal Inference Methods for Panel Data in Observational Studies

Abstract

Environmental and policy datasets, when combined with electronic health records or other health outcome data, can be leveraged for large-scale studies of population health and policy effectiveness. However, such observational data pose statistical challenges because exposures are not randomized, treatment or policy timing may be staggered, and complex temporal structures (e.g., lags, varying durations, or early adoption behavior) are rarely accommodated by standard methods. This dissertation develops and applies Bayesian and causal inference methods for panel data that address these challenges, with a focus on environmental health impacts and the evaluation of policy interventions using observational data. In Chapter 1, we investigate the short- to medium‑term health impacts of severe flooding on older adults across the contiguous United States. Leveraging 17 years of nationwide Medicare inpatient claims linked to satellite‑based flood maps, we implement a self‑matched panel design with conditional quasi‑Poisson regression to estimate cause‑specific hospitalization rate changes during and after 72 major flood events. We quantify flood-attributable impacts for 13 well-defined disease categories and characterize heterogeneity across a wide range of effect modifiers, including flood features, population demographics, and hospitalization patterns. This chapter provides one of the first nationwide, multi-decade assessments of flood-related health effects across a broad spectrum of previously understudied diseases in vulnerable sub-populations, including older adults and racially minoritized individuals, using a unified, analytic approach. Chapter 2 addresses a key limitation of existing environmental epidemiology modeling, by formulating a flexible way to model health effects of environmental events whose durations/lengths vary across units, such as floods, heat waves, or wildfires. We propose an exposure duration varying‑coefficient model (EDVCM) formulated within an area‑level self‑matched design and estimated via Bayesian conditional Poisson regression. The EDVCM introduces duration‑ and exposure‑day specific effect coefficients with a two‑dimensional Gaussian process prior that enables principled information sharing across both event duration and time point within the event, while accommodating post‑event lags. We apply the method to nationwide Medicare data and high‑resolution satellite flood maps to characterize how musculoskeletal hospitalization risks evolve over the course of flood events of different lengths. In Chapter 3, we focus on the evaluation of policy interventions in panel data when units may respond before formal policy enactment. Motivated by state‑level prescription drug monitoring program (PDMP) laws, which often feature a prolonged period of voluntary database access prior to mandated prescriber use, we define and formalize early adoption effects within a potential outcomes framework for staggered treatment timing. We decompose the overall impact of a policy into early adoption and post‑enactment components and propose a two‑stage estimation procedure that integrates with existing synthetic control methods. We apply our early adoption-aware estimation approach to assess the effects of state-level PDMP laws on per-capita opioid dispensing, after accounting for early adoption. Together, the statistical methods developed in this dissertation provide flexible tools for analyzing panel data in observational settings, including Bayesian modeling of complex temporal exposures and robust policy evaluation in the presence of early adoption. Applications to flood-related hospitalizations and opioid policies demonstrate the practical utility of these approaches and yield new insights in both environmental and health policy contexts.