Advancing Design and Inference in a Causal Framework

Abstract

Causal inference, or the assessment of the effect of interventions on outcomes of interest, is ubiquitous in many fields. Often causal inference is made on the basis of the randomization of units to treatments, focusing on the design of an experiment or, in observational studies, how to approximate an experiment. The focus on randomization has allowed for results that do not depend on the classic structural assumptions needed in, for instance, linear regression. However, the beautifully simple idea of using randomization as the basis for inference can induce many subtle problems. This dissertation examines three such problems in causal inference. First, we explore the gains of blocked designs, as compared to non-blocked designs. Conservative variance estimators for the case of many blocks of variable size are built, leading to more general inference tools than previously established. Next, we examine the use of conditioning in causal inference, drawing parallels to analyzing an experiment as if another experiment had been run. Finally, we identify challenges in the analysis of observational data with multiple treatments and provide a framework on which to build inference.