Causal Estimators for Non-Standard Scenarios: Individual Versus Population-Level Causal Effects in Transplantation Treatment Regimes, and Clinical Trials where Compliance is Measured with Error

Abstract

Inferring and explaining causal relationships is frequently one of the primary goals in public health research. Randomized controlled trials (RCTs) are the gold standard for establishing causal effects, but often RCTs are infeasible or unethical, and we must rely on observational data for inference. Even in the case where RCTs can be conducted causal inference is often difficult due to patient noncompliance. Statistical methods for causal inference are needed in such cases. Although there exist well-established statistical causal inference methods, in this dissertation we develop methods for non-standard scenarios. In Chapter 2, we consider treatment regimes for solid organ transplantation. In Chapters 3 and 4, we consider estimating causal effects in RCTs in the presence of noncompliance. In all cases, we develop novel weighted estimators that are similar to inverse probability of compliance weighted estimators, but the weights are a ratio of probabilities rather than an inverse probability. For solid organ transplantation, these weights are needed so that our estimators have the desired interpretation, and in the case of RCTs in the presence of noncompliance, these weights are needed so that our estimators actually correspond to a causal effect of interest when traditional assumptions about noncompliance are not valid.