Variance-based sensitivity analysis for weighting estimators results in more informative bounds

Weighting methods are popular tools for estimating causal effects, and assessing their robustness under unobserved confounding is important in practice. Current approaches to sensitivity analyses rely on bounding a worst-case error from omitting a confounder. In this paper, we introduce a new sensitivity model called the variance-based sensitivity model, which instead bounds the distributional differences that arise in the weights from omitting a confounder. The variance-based sensitivity model can be parameterized by an R-2 parameter that is both standardized and bounded. We demonstrate, both empirically and theoretically, that the variance-based sensitivity model provides improvements on the stability of the sensitivity analysis procedure over existing methods. We show that by moving away from worst-case bounds, we are able to obtain more interpretable and informative bounds. We illustrate our proposed approach on a study examining blood mercury levels using the National Health and Nutrition Examination Survey.