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Abstract:
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In an observational study, a difference between the treatment and control group's outcome might reflect the bias in treatment assignment rather than a true treatment effect. A sensitivity analysis determines the magnitude of this bias that would be needed to explain away a significant treatment effect from a naive analysis that assumed no bias. Effect modification is the interaction between a treatment and a pretreatment covariate. In an observational study, there are often many possible effect modifiers and it is desirable to be able to look at the data to identify hypotheses of interest. For observational studies, we address simultaneously the problem of accounting for the multiplicity involved at looking at many possible effect modifiers and conducting a proper sensitivity analysis. We prove that for such type of inference we can provide finite sample false discovery rate control for the collection of adaptive hypotheses identified from the data. Along with a simulation study an empirical study is presented of the effect of cigarette smoking on lead level in the blood using data from the U.S. National Health and Nutrition Examination Survey.
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