Primary Submission Category: Sensitivity Analysis
Controlling the False Discovery Proportion in Observational Studies with Hidden Bias
Authors: Mengqi Lin, Colin Fogarty,
Presenting Author: Mengqi Lin*
We propose an approach to exploratory data analysis in matched observational studies. We consider the setting where a single intervention is thought to potentially impact multiple outcomes, and the researcher would like to investigate which of these causal hypotheses come to bear while accounting not only for the possibility of false discoveries, but also the possibility that the study is plagued by unmeasured confounding. For any candidate set of hypotheses, our method provides sensitivity intervals for the false discovery proportion (FDP). For a set $cR$, the method describes how much unmeasured confounding would need to exist for us to believe that the proportion of true hypotheses is $0/|cR|$,$1/|cR|$,…,$|cR|/|cR|$. Moreover, the resulting confidence statements intervals are valid simultaneously over all possible choices for the rejected set, allowing the researcher to look in an ad hoc manner for promising subsets of outcomes that maintain a large estimated fraction of correct discoveries even if a large degree of unmeasured confounding is present. The approach is particularly well suited to sensitivity analysis, as conclusions that some fraction of outcomes were affected by the treatment exhibit larger robustness to unmeasured confounding than the conclusion that any particular outcome was affected. While the method involves solving quadratically constrained integer programs, we demonstrate that they can be efficiently handled or typically bypassed in large samples.