  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.
