Observational Data With A Continuous Exposure: Study Design And Outcome Analysis

Subclassification and matching are often used in empirical studies to adjust for observed covariates; however, they are largely restricted to relatively simple study designs with a binary exposure and less developed for designs with a continuous exposure. This thesis contains three papers discussing aspects of study design and outcome analysis with a continuous exposure. The first paper presents a new full match methodology for data with a continuous exposure that achieves good subclass homogeneity, preservation of all study units, dose separation when desired, and control over the size of subclasses. There are two types of empirical studies where matching with a continuous exposure could be useful: studies with a continuous treatment dose and studies with a continuous instrumental variable (IV). The second paper analyzes social mobility data during the COVID-19 pandemic using non-bipartite matching, and proposes a simple randomization test for a structured dose-response relationship. We rejected a primary analysis null hypothesis that stated the social distancing from April 27, 2020, to June 28, 2020, had no effect on the COVID-19-related death toll from June 29, 2020, to August 2, 2020 (p-value < 0.001), and found that it took more reduction in mobility to prevent exponential growth in case numbers for non-rural counties compared to rural counties. The third paper studies how to embed retrospective observational data into a cluster-randomized encouragement experiment using non-bipartite matching, and the associated statistical inference problems. Both the first and third papers are motivated by health outcomes research concerning the effect of intraoperative TEE monitoring during CABG surgery on patients' post-surgery clinical outcomes.