  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.
