On Sensitivity Value of Pair-Matched Observational Studies

ABSTRACT

This article 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 the presence of unmeasured confounding using a microarray dataset. Supplementary materials for this article are available online.

KEYWORDS:

• Effect modification
• Genomics screening
• Signed score test
• Study design
• U-statistics

Supplementary Materials

The supplementary file includes R code to reproduce the results in this article.

Acknowledgments

The author thanks Paul Rosenbaum and Dylan Small for their constructive suggestions.