Sensitivity Analysis for Causal Inference with Unobserved Confounding

Many questions in social and biomedical sciences are causal in nature. For example, sociologists and policy-makers often want to know the effects of social programs on poverty and upward mobility; medical professionals are interested in how drugs impact the progression of disease. Unfortunately, estimating causal effects from non-experimental data is very difficult due to unobserved confounders, which can lead to spurious causal conclusions about the treatment's effect on the outcome. Sensitivity analysis, which explores how sensitive our causal conclusions are to potential unobserved confounding, can help us understand the potential impacts of confoundedness. However, existing sensitivity analyses are often at odds with modern machine learning (ML) tools for causal inference, which emphasize flexible models over interpretability. Besides, modern problems require new methods which account for the existence of multiple concurrent treatment variables and/or high dimensional outcomes. In this dissertation, we provide new tools that help improve communication and transparency about the robustness of analysis results to unmeasured confoundedness for important applications of observational causal inference, especially in high-dimensional settings. In chapter 1, we introduce the two most prevalent frameworks for causal inference studies, define the relevant quantities and notations, and discuss the importance of sensitivity analysis. In Chapters 2, we propose a sensitivity analysis method by reparametering latent confounder models, and in Chapter 3, we extend a sensitivity analysis method based on the Tukey's factorization to cases where treatments are ordinal variable with multiple levels, where both methods clearly separate the identifiable part from the unidentifiable part. In Chapter 4 and 5, we focus on high-dimensional settings, respectively considering the multi-treatment and multi-outcome cases, where the multivariate correlation structure could provide additional information about unobserved confounders, but the causal effects are still not point identifiable in general and the high-dimensional variables would largely complicate the analysis. To address the issue, we present novel sensitivity analysis methods based on copula factorization, which can show how much is gained by leveraging latent structure in a given application while leave the observed data modeling untouched