Tilted sensitivity analysis in matched observational studies

We present a new procedure for conducting a sensitivity analysis in matched observational studies. For any candidate test statistic, the approach defines tilted modifications dependent upon the proposed strength of unmeasured confounding. The framework subsumes both (i) existing approaches to sensitivity analysis for sign-score statistics; and (ii) sensitivity analyses using conditional inverse probability weighting, wherein one weights the observed test statistic based upon the worst-case assignment probabilities for a proposed strength of hidden bias. Unlike the prevailing approach to sensitivity analysis after matching, there is a closed form expression for the limiting worst-case distribution when matching with multiple controls. Moreover, the approach admits a closed form for its design sensitivity, a measure used to compare competing test statistics and research designs, for matching with multiple controls, whereas the conventional approach generally only does so for pair matching. The tilted sensitivity analysis improves design sensitivity under a host of generative models. The proposal may also be adaptively combined with the conventional approach to attain a design sensitivity no smaller than the maximum of the individual design sensitivities. Data illustrations indicate that tilting can provide meaningful improvements in the reported robustness of matched observational studies.