Sensitivity analysis for principal ignorability violation in estimating complier and noncomplier average causal effects

TL;DR

This paper develops sensitivity analysis methods to assess how violations of principal ignorability assumptions affect causal effect estimates in noncompliance studies, providing tools for robust inference.

Contribution

It introduces a flexible sensitivity analysis framework for principal causal effects that accounts for violations of principal ignorability in various forms.

Findings

Sensitivity analysis techniques tailored to multiple PI violation models

Application to JOBS II study data demonstrating practical utility

Theoretical results on asymptotic normality of estimators with nonparametric nuisance estimation

Abstract

An important strategy for identifying principal causal effects, which are often used in settings with noncompliance, is to invoke the principal ignorability (PI) assumption. As PI is untestable, it is important to gauge how sensitive effect estimates are to its violation. We focus on this task for the common one-sided noncompliance setting where there are two principal strata, compliers and noncompliers. Under PI, compliers and noncompliers share the same outcome-mean-given-covariates function under the control condition. For sensitivity analysis, we allow this function to differ between compliers and noncompliers in several ways, indexed by an odds ratio, a generalized odds ratio, a mean ratio, or a standardized mean difference sensitivity parameter. We tailor sensitivity analysis techniques (with any sensitivity parameter choice) to several types of PI-based main analysis methods, including outcome regression, influence function (IF) based and weighting methods. We illustrate the proposed sensitivity analyses using several outcome types from the JOBS II study. This application estimates nuisance functions parametrically -- for simplicity and accessibility. In addition, we establish rate conditions on nonparametric nuisance estimation for IF-based estimators to be asymptotically normal -- with a view to inform nonparametric inference.