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

An important strategy for identifying principal causal effects, which are often used in settings with noncompliance, is to invoke the principal ignorability (PI) assumption which equates unobserved principal-stratum-specific outcome distributions (or their means). 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), and consider two sensitivity analysis approaches anchoring on and deviating from the mean version and the distribution version of PI. In the mean-based approach, we propose a range of sensitivity parameters (suitable for different outcome types) representing how (within levels of covariates) the mean of potential outcome under control (Y0) is assumed to differ between compliers and noncompliers. In the distribution-based approach, we introduce association between Y0 and principal stratum (within levels of covariates) via a monotonic mapping between Y0 and the probability of belonging to the stratum given covariates and Y0. The mean-based approach is simpler, but can suffer from out-of-range prediction. The distribution-based approach requires additional modeling but avoids this problem. With a view to facilitate practice, the paper offers pairings of sensitivity analysis with several types of main analysis methods. We illustrate the proposed methods using different outcomes from the JOBS II study, and provide code in an R-package.