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) <doi:10.1007/978-1-4419-1213-8_14>). There are two examples, one concerning unemployment from Lalive et al. (2006) <doi:10.1111/j.1467-937X.2006.00406.x>, the other concerning smoking and periodontal disease from Rosenbaum (2017) <doi:10.1214/17-STS621>.