In public health science research, inference about causality often relies on the strong assumption that there is no hidden bias due to omitted confounders. Through a sensitivity analysis, the analyst attempts to determine whether a conclusion could be easily
reversed by a plausible violation of this key assumption. Without a careful sensitivity analysis, a study is considered incomplete. A new approach to sensitivity analysis, on the basis of weighting, extends a number of existing propensity score weighting methods
for identifying the average treatment effect on the treated (ATT), the average treatment effect (ATE), and the indirect effect and the direct effect that decompose the ATE. This new approach conveniently assesses bias associated with one or more omitted confounders.
In its essence, the discrepancy between a new weight that adjusts for the omitted confounders and an initial weight that omits them captures the role of the confounders. The effect size of a hidden bias is represented as a function of a small number of meaningful
sensitivity parameters. This approach reduces the reliance on functional form assumptions and removes constraints on measurement scales. Several real data applications illustrate its broad utility.