Statistical Methods for the Study of Effect Modification and Spatial Causal Inference: Theory and Applications

Abstract

More and more, scientists and policymakers are interested in using quantitative methods to answer complex causal questions across diverse contexts. This thesis proposes and implements statistical methods for inferring causation beyond simple average effects, for example, how causal effects vary across populations or by individual characteristics. It also proposes and develops theory for estimators of causal effects in the kinds of complex spatial settings encountered in practice, where data may not obey classical statistical assumptions like independence. Chapter 1 introduces profile matching, a multivariate matching method for randomized experiments and observational studies that finds the largest possible unweighted samples across multiple treatment groups that are balanced relative to a covariate profile. By selecting the profile appropriately, profile matching can be a flexible tool for investigators to generalize or transport effect estimates across populations while retaining the simple structure of unweighted data. Chapter 2 presents a framework for the study of heterogeneous treatment effects in difference-in-differences designs in a study of the effects of firearm injuries on survivors and their family members. This framework encompasses a novel set of identification assumptions and sensitivity analysis for difference-in-differences with staggered treatment adoption. The method for covariate adjustment combines risk set matching with profile matching, which respects the time alignment of variable measurements while also controlling bias due to observed covariate imbalances in subgroups discovered from the data. Inference on main effects and treatment effect heterogeneity entails randomization-based techniques. Chapter 3 presents and analyzes semiparametric estimators of causal effects in settings where the data exhibit spatial dependence, where the dependence assumptions are considerably weaker than those in the existing causal inference literature. We prove that the treatment effect estimator is asymptotically normal and that the proposed block bootstrap sampling variance estimator is consistent. The proofs of these results rely on novel extensions of central limit and empirical process theory for dependent data.