Causal Inference Methods for Measurement Error and Mediation

Causal inference provides a principled way to investigate causal effects in public health, neuroscience and other areas. This thesis addresses two topics in causal inference: (i) the estimation of causal effects using covariates measured with error, and (ii) the investigation of mechanisms underlying causal effects. Although covariate measurement error is often present, methods for handling covariate measurement error in propensity score methods have not been widely investigated. We develop an imputation-based solution to using mismeasured covariates in propensity score methods that provide an estimate of a causal treatment effect, and use it to estimate the effects of living in a disadvantaged neighborhood on adolescent mental health and substance use. Furthermore, we can use mediation analysis to study how the causal effect that a treatment X has on an outcome variable Y is influenced by some intermediate variable M. Standard approaches toward assessing mediation require that each of the variables X, M, and Y take scalar values. However, in many situations this may not be reasonable or practical. We extend the standard and causal mediation framework, allowing one or more of the variables to be considered continuous functions of time. But making causal statements about mediation always poses a problem because, even if we can randomize the intervention, it is often difficult - or impossible - to randomize the assignment of the mediator. Within-subject designs, common in neuroscience experiments using functional Magnetic Resonance Imaging, open new possibilities for identification of the mediation counterfactuals. We establish a new set of identifiability conditions for estimating causal mediation effects and develop an estimation procedure that is robust to baseline confounding of the mediator-outcome relation. This thesis advances the causal inference literature in innovative ways, enriching the principled thinking about effects and mediation with contributions from the measurement error and functional data analysis literature