False discovery rate control for effect modification in observational studies

Abstract

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 as non-causal 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 the effect modifiers that will be tested. For observational studies, we address simultaneously the problem of accounting for the multiplicity involved in choosing effect modifiers to test among many possible effect modifiers by looking at the data and conducting a proper sensitivity analysis. We develop an approach that provides finite sample false discovery rate control for a collection of adaptive hypotheses identified from the data on matched-pairs design. Along with simulation studies, an empirical study is presented on the effect of cigarette smoking on lead level in the blood using data from the U.S. National Health and Nutrition Examination Survey. Other applications of the suggested method are briefly discussed.