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A fundamental limitation of causal inference in observational studies is thatperceived evidence for an effect might instead be explained by factors notaccounted for in the primary analysis. Methods for assessing the sensitivity ofa study's conclusions to unmeasured confounding have been established under theassumption that the treatment effect is constant across all individuals. In thepotential presence of unmeasured confounding, it has been argued that certainpatterns of effect heterogeneity may conspire with unobserved covariates torender the performed sensitivity analysis inadequate. We present a new methodfor conducting a sensitivity analysis for the sample average treatment effectin the presence of effect heterogeneity in paired observational studies. Ourrecommended procedure, called the studentized sensitivity analysis, representsan extension of recent work on studentized permutation tests to the case ofobservational studies, where randomizations are no longer drawn uniformly. Themethod naturally extends conventional tests for the sample average treatmenteffect in paired experiments to the case of unknown, but bounded, probabilitiesof assignment to treatment. In so doing, we illustrate that concerns aboutcertain sensitivity analyses operating under the presumption of constanteffects are largely unwarranted.

Studentized sensitivity analysis for the sample average treatment effect in paired observational studies