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Abstract:
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We demonstrate that when performing multiple comparisons in an observational study, the loss in power from controlling the familywise error rate can be attenuated when assessing the robustness of the study's findings to unmeasured confounding. This is because unmeasured confounding cannot have a different impact on the probability of assignment to treatment for a given individual depending on the outcome being analyzed. Existing methods for testing the overall truth of multiple hypotheses allow this to occur by combining the results of sensitivity analyses performed on individual outcomes. By solving a quadratically constrained linear program, we are able to perform a sensitivity analysis while avoiding this logical inconsistency. We show that this allows for uniform improvements in the power of a sensitivity analysis when compared to combining individual sensitivity analyses. This is true not only for testing the overall null across outcomes, but also for testing null hypotheses on specific outcome variables when using certain sequential rejection procedures. We illustrate our method through an example examining the impact of smoking on naphthalene levels in the body.
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