Bounding causal effects under uncontrolled confounding using counterfactuals.

Common sensitivity analysis methods for unmeasured confounders provide a corrected point estimate of causal effect for each specified set of unknown parameter values. This article reviews alternative methods for generating deterministic nonparametric bounds on the magnitude of the causal effect using linear programming methods and potential outcomes models. The bounds are generated using only the observed table. We then demonstrate how these bound widths may be reduced through assumptions regarding the potential outcomes under various exposure regimens. We illustrate this linear programming approach using data from the Cooperative Cardiovascular Project. These bounds on causal effect under uncontrolled confounding complement standard sensitivity analyses by providing a range within which the causal effect must lie given the validity of the assumptions.