Aspects of causal inference.

Observational studies differ from experimental studies in that assignment of subjects to treatments is not randomized but rather occurs due to natural mechanisms, which are usually hidden from researchers. Yet objectives of the two studies are frequently the same: identify the causal – rather than merely associational – relationship between some treatment or exposure and an outcome. The statistical issues that arise in properly analyzing observational data for this goal are numerous and fascinating, and these issues are encompassed in the domain of causal inference. The research presented in this dissertation explores several distinct aspects of causal inference. This dissertation is divided into four chapters. Chapter One gives an introduction to major concepts, underlying assumptions, and analytical frameworks encountered in the domain of causal inference. The next three chapters describe extensive research projects that are linked together by those threads. Chapter Two deals with propensity score techniques and, more specifically, how to specify the propensity score model to achieve the best treatment effect estimates. This chapter not only provides a theoretical proof showing that one particular type of specification is best, but also demonstrates an original method for applying that result. The method presented in Chapter Three has a similar purpose – obtaining precise and accurate estimates of causal effects – but views the challenge through a Bayesian, rather than a frequentist, lens. Here, a hierarchical Bayesian model is developed that is grounded in the framework of causal inference. While Chapters Two and Three focus on scenarios involving causal inference from observational data, Chapter Four presents a method that has been designed to apply equally well to experimental data. The intent of the research here is to provide a method for identifying subgroups of the population in which the treatment effect differs from the overall population average treatment effect. Maintaining a central theme of causal inference, the research focuses on avoiding confounding bias while identifying effect modifiers that characterize the subgroups. In all, this dissertation is intended to provide views of causal inference concepts from several distinct angles, demonstrating the complexity and richness of this domain