Conditional Sensitivity Analysis for Matched Observational Studies

A d-statistic tests the null hypothesis of no treatment effect in a matched, nonrandomized study of the effects caused by treatments. A d-statistic focuses on subsets of matched pairs that demonstrate insensitivity to unmeasured bias in such an observational study, correcting for double-use of the data by conditional inference. This conditional inference can, in favorable circumstances, substantially increase the power of a sensitivity analysis (Rosenbaum (2010) ). There are two examples, one concerning unemployment from Lalive et al. (2006) , the other concerning smoking and periodontal disease from Rosenbaum (2017) .