Sensitivity analysis for unmeasured confounding in principal stratification settings with binary variables.

Within causal inference, principal stratification (PS) is a popular approach for dealing with intermediate variables, that is, variables affected by treatment that also potentially affect the response. However, when there exists unmeasured confounding in the treatment arms--as can happen in observational studies--causal estimands resulting from PS analyses can be biased. We identify the various pathways of confounding present in PS contexts and their effects for PS inference. We present model-based approaches for assessing the sensitivity of complier average causal effect estimates to unmeasured confounding in the setting of binary treatments, binary intermediate variables, and binary outcomes. These same approaches can be used to assess sensitivity to unknown direct effects of treatments on outcomes because, as we show, direct effects are operationally equivalent to one of the pathways of unmeasured confounding. We illustrate the methodology using a randomized study with artificially introduced confounding and a sensitivity analysis for an observational study of the effects of physical activity and body mass index on cardiovascular disease.