Tilted sensitivity analysis in matched observational studies

Music City Center 

A sensitivity analysis assesses the robustness of an observational study's conclusions to unmeasured
confounding of increasing strength. We present a new approach to conducting a sensitivity analysis in matched observational studies within Rosenbaum's sensitivity model. For any candidate test statistic, the approach introduces 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 the researcher 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 in matched observational studies, there is a closed form expression for the limiting worst-case distribution even when matching with multiple controls. Moreover, the approach admits a closed form solution for its design sensitivity, a measure used to compare competing test statistics and research designs, when matching with multiple controls, whereas the conventional approach only does so for pair matching. The tilted sensitivity analysis improves design sensitivity relative to the conventional approach 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 max of the individual design sensitivities. Beyond the aforementioned computational and theoretical benefits, data illustrations indicate that tilting can provide meaningful improvements in reported robustness of matched observational studies to hidden bias.

Sensitivity analysis

Matching

Design-based causal inference