On sensitivity value of pair-matched observational studies

TL;DR

This paper introduces the 'sensitivity value' to quantify how strong unmeasured confounders must be to alter causal conclusions in pair-matched observational studies, aiding in study design and hypothesis screening.

Contribution

It defines the sensitivity value, establishes its asymptotic normality, and demonstrates its use in power approximation, study design, and hypothesis screening under unmeasured confounding.

Findings

Sensitivity value asymptotically normal in pair-matched studies

Method to approximate power of sensitivity analysis

Application to microarray hypothesis screening

Abstract

An observational study may be biased for estimating causal effects by failing to control for unmeasured confounders. This paper proposes a new quantity called the "sensitivity value", which is defined as the minimum strength of unmeasured confounders needed to change the qualitative conclusions of a naive analysis assuming no unmeasured confounder. We establish the asymptotic normality of the sensitivity value in pair-matched observational studies. The theoretical results are then used to approximate the power of a sensitivity analysis and select the design of a study. We explore the potential to use sensitivity values to screen multiple hypotheses in presence of unmeasured confounding using a microarray dataset.