UC Irvine

A central goal in health research is to estimate the causal effect of a treatment or exposure on an outcome of interest. When randomization cannot be achieved due to ethical, feasibility, or monetary constraints, we must turn to observational studies to isolate causal effects. One core challenge in this setting is controlling for confounding, or extraneous factors that cause both the exposure and outcome. Observational studies are prone to bias due to unmeasured confounding, which renders methods like confounder adjustment and propensity scores ineffective. This has motivated the instrumental variable (IV) approach where we use a variable that influences the exposure but is otherwise not associated with the outcome, to quasi-randomize the exposure, hence producing unbiased causal effects. This dissertation makes three important contributions to enhance the utility of IVs in their application to observational data. First, in the linear setting, we analytically quantify the relative trade-offs between the confounder and the IV approach under the violation of key causal identification assumptions including unmeasured confounding, the exclusion restriction, independence of the IV, and unmeasured treatment effect heterogeneity. We further provide guidelines for practice and develop a sensitivity analysis procedure to quantify these relative trade-offs. In the next contribution, we move to the topic of nonparametric identification of the local average treatment effect (LATE), the estimand targeted by IVs, by developing an influence function (IF) based estimator to incorporate unknown sampling weights to replicate causal estimates across populations – an important facet of enhancing confidence in observational study findings. Via the use of cross-fitting, our method is able to use machine learning (ML) to flexibly model nuisance functions, including the sampling weights. Furthermore, we extend this framework to provide weighted bounds on the ATE. Our final contribution extends the nonparametric, IF-based framework for identifying the LATE to the time-to-event setting. With time-to-event outcomes, causal inference with IVs is often limited by the proportional hazards assumption and the non-collapsibility of the hazard ratio (HR). Therefore, rather than targeting the HR, we extend the accelerated failure time (AFT) model and the Buckley-James (BJ) imputation procedure to nonparametrically identify the percentage difference in the median survival time among compliers for a binary exposure. With this approach, we are able to circumvent several issues involving the application of IVs to estimate the causal HR and, furthermore, protect against misspecification via the incorporation of ML with cross-fitting and double-robustness properties.