Sensitivity analysis for certain permutation inferences in matched observational studies

In observational studies, treatments are not randomly assigned to experimental units, so that randomization tests and their associated interval estimates are not generally applicable. In an effort to compensate for the lack of randomization, treated and control units are often matched on the basis of observed covariates; however, the possibility remains of bias due to residual imbalances in unobserved covariates. A general though simple method is proposed for displaying the sensitivity of permutation inferences to a range of assumptions about unobserved covariates in matched observational studies. The sensitivity analysis is applicable to Wilcoxon's signed rank test, to the McNemar-Cox test for paired binary responses, and to some matching problems with a variable number of controls.