Flexible sensitivity analysis for observational studies without observable implications

TL;DR

This paper introduces a flexible sensitivity analysis framework for observational causal inference that separates identified and unidentified parts, allowing for modern, nonparametric models and easier interpretation of sensitivity parameters.

Contribution

It extends Tukey's factorization to causal inference, enabling flexible modeling of observed data and clearer sensitivity analysis without restrictive assumptions.

Findings

Framework effectively separates identified and unidentified components.

Allows calibration of sensitivity parameters using observable data.

Demonstrated with Bayesian models for treatment and quantile effects.

Abstract

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, some existing sensitivity analysis approaches inadvertently impose restrictions that are at odds with modern causal inference methods, which emphasize flexible models for observed data. To address this issue, we propose a framework that allows (1) flexible models for the observed data and (2) clean separation of the identified and unidentified parts of the sensitivity model. Our framework extends an approach from the missing data literature, known as Tukey's factorization, to the causal inference setting. Under this factorization, we can represent the distributions of unobserved potential outcomes in terms of unidentified selection functions that posit an unidentified relationship between the treatment assignment indicator and the observed potential outcomes. The sensitivity parameters in this framework are easily interpreted, and we provide heuristics for calibrating these parameters against observable quantities. We demonstrate the flexibility of this approach in two examples, where we estimate both average treatment effects and quantile treatment effects using Bayesian nonparametric models for the observed data.