Causal Inference for Error-Prone and Multi-Source Data

Abstract

This dissertation presents statistical methods for the estimation of causal effects in the presence of measurement error and data arising from multiple, heterogeneous sources. As the use of real-world data for the support of clinical decision making continues to grow, these factors are increasingly arising as sources of bias across observational data sources that can invalidate inferences when left unaddressed. Chapters 1 and 2 are motivated by observational studies based on EHR data, where key variables of interest are often measured with substantial error. In Chapter 1 we present efficient estimators of causal effects when exposure variables are subject to measurement error, but one is able to collect gold-standard exposure measurements for a subset of the overall dataset, typically referred to as the validation data. Our proposed methods leverage the small subset of gold-standard exposure measurements to obtain unbiased estimates, while utilizing information from the remaining error-prone exposure measurements to improve efficiency of the final proposed estimator. By making use of estimation procedures from the generalizability and transportability literatures, our proposed methods can accommodate a wide range of validation data sampling schemes, and enable the use of machine learning to estimate nuisance functions while still obtaining valid inferences. Chapter 2 considers scenarios where both outcomes and treatment variables are measured with error, and the availability of validation samples can depend on the error-prone measurements themselves. In constructing estimators for the average treatment effect, we make connections between two previously disconnected strands of the semiparametric efficiency theory literature to derive two asymptotically equivalent estimators. We identify factors that can lead to meaningfully finite sample behavior in the estimators arising from each approach, and propose an ensemble estimator which optimally combines these two estimators while attaining a tractable asymptotic distribution. In both Chapters 1 and 2, we demonstrate the utility of our methods on real-world EHR data from the Vanderbilt Comprehensive Care Clinic. Chapter 3 is dually motivated by the growth in multi-source data agreements, as well as the increasing biomedical focus on treatment effect heterogeneity. We consider scenarios where one is able to train counterfactual prediction models on data collected from a source population, and wishes to construct counterfactual prediction intervals for individuals in a separate target population. These prediction intervals can serve as informative inputs in high-stakes decision making contexts. We accommodate settings where in the target population, one is unable to collect all possible confounders of the treatment-outcome relationship. This situation, which often arises due to resource and logistical constraints, is commonly referred to as runtime confounding. Contributing to the literature on conformal prediction---a powerful framework for constructing valid prediction intervals under minimal assumptions---we present a debiased machine learning algorithm for the construction of valid counterfactual prediction intervals under runtime confounding. Through both theoretical results and numerical experiments, we demonstrate that our approach can attain desired coverage rates under less stringent conditions than standard approaches, while also partially protecting against model misspecification.