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Abstract 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 R2 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. 

Abstract Matching in observational studies faces complications when units enroll in treatment on a rolling basis. While each treated unit has a specific time of entry into the study, control units each have many possible comparison, or “pseudo-treatment,” times. Valid inference must account for correlations between repeated measures for a single unit, and researchers must decide how flexibly to match across time and units. We provide three important innovations. First, we introduce a new matched design, GroupMatch with instance replacement, allowing maximum flexibility in control selection. This new design searches over all possible comparison times for each treated-control pairing and is more amenable to analysis than past methods. Second, we propose a block bootstrap approach for inference in matched designs with rolling enrollment and demonstrate that it accounts properly for complex correlations across matched sets in our new design and several other contexts. Third, we develop a falsification test to detect violations of the timepoint agnosticism assumption, which is needed to permit flexible matching across time. We demonstrate the practical value of these tools via simulations and a case study of the impact of short-term injuries on batting performance in major league baseball. 

Abstract Assessing sensitivity to unmeasured confounding is an important step in observational studies, which typically estimate effects under the assumption that all confounders are measured. In this paper, we develop a sensitivity analysis framework for balancing weights estimators, an increasingly popular approach that solves an optimization problem to obtain weights that directly minimizes covariate imbalance. In particular, we adapt a sensitivity analysis framework using the percentile bootstrap for a broad class of balancing weights estimators. We prove that the percentile bootstrap procedure can, with only minor modifications, yield valid confidence intervals for causal effects under restrictions on the level of unmeasured confounding. We also propose an amplification—a mapping from a one-dimensional sensitivity analysis to a higher dimensional sensitivity analysis—to allow for interpretable sensitivity parameters in the balancing weights framework. We illustrate our method through extensive real data examples.