Flexible sensitivity analysis for observational studies without observable implications
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A fundamental challenge in observational causal inference is that assumptions about unconfoundedness are not testable from data. Assessing sensitivity to such assumptions is therefore important in practice. Unfortunately, existing model-based sensitivity analysis approaches typically force investigators to make a choice between a restrictive model for the data or a well-defined sensitivity analysis. To address this issue, we propose a framework that allows (1) arbitrary, flexible models for the observed data and (2) clean separation of the identified and unidentified parts of the sensitivity model. Our approach treats the causal inference problem as a missing data problem, and applies a factorization of missing data densities first attributed to John Tukey and more recently termed "the extrapolation factorization." This name arises because we extrapolate from the observed potential outcome distributions to the missing potential outcome distributions by proposing unidentified selection functions. We demonstrate the flexibility of this approach for estimating both average treatment effects and quantile treatment effects using Bayesian nonparametric models for the observed data. We provide a procedure for interpreting and calibrating the sensitivity parameters and apply this approach to two examples.
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