  Causal inference with observational studies often suffers from unmeasured
confounding, yielding biased estimators based on the unconfoundedness
assumption. Sensitivity analysis assesses how the causal conclusions change
with respect to different degrees of unmeasured confounding. Most existing
sensitivity analysis methods work well for specific types of statistical
estimation or testing strategies. We propose a flexible sensitivity analysis
framework that can deal with commonly used inverse probability weighting,
outcome regression, and doubly robust estimators simultaneously. It is based on
the well-known parametrization of the selection bias as comparisons of the
observed and counterfactual outcomes conditional on observed covariates. It is
attractive for practical use because it only requires simple modifications of
the standard estimators. Moreover, it naturally extends to many other causal
inference settings, including the causal risk ratio or odds ratio, the average
causal effect on the treated units, and studies with survival outcomes. We also
develop an R package saci to implement our sensitivity analysis estimators.
