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Abstract When there are multiple outcome series of interest, Synthetic Control analyses typically proceed by estimating separate weights for each outcome. In this paper, we instead propose estimating a common set of weights across outcomes, by balancing either a vector of all outcomes or an index or average of them. Under a low-rank factor model, we show that these approaches lead to lower bias bounds than separate weights, and that averaging leads to further gains when the number of outcomes grows. We illustrate this via a re-analysis of the impact of the Flint water crisis on educational outcomes. 

Abstract Research documents that Black patients experience worse general surgery outcomes than White patients in the U.S. In this paper, we focus on an important but less-examined category: the surgical treatment of emergency general surgery (EGS) conditions, which refers to medical emergencies where the injury is internal, such as a burst appendix. Our goal is to assess racial disparities in outcomes after EGS treatment using administrative data. We also seek to understand the extent to which differences are attributable to patient-level risk factors vs. hospital-level factors, as well as to the decision to operate on EGS patients. To do so, we develop a class of linear weighting estimators that reweight White patients to have a similar distribution of baseline characteristics to Black patients. This framework nests many common approaches, including matching and linear regression, but offers important advantages over these methods in terms of controlling imbalance between groups, minimizing extrapolation, and reducing computation time. Applying this approach to the claims data, we find that disparities estimates that adjust for the admitting hospital are substantially smaller than estimates that adjust for patient baseline characteristics only, suggesting that hospital-specific factors are important drivers of racial disparities in EGS outcomes. 

In multisite trials, learning about treatment effect variation across sites is critical for understanding where and for whom a program works. Unadjusted comparisons, however, capture “compositional” differences in the distributions of unit-level features as well as “contextual” differences in site-level features, including possible differences in program implementation. Our goal in this article is to adjust site-level estimates for differences in the distribution of observed unit-level features: If we can reweight (or “transport”) each site to have a common distribution of observed unit-level covariates, the remaining treatment effect variation captures contextual and unobserved compositional differences across sites. This allows us to make apples-to-apples comparisons across sites, parceling out the amount of cross-site effect variation explained by systematic differences in populations served. In this article, we develop a framework for transporting effects using approximate balancing weights, where the weights are chosen to directly optimize unit-level covariate balance between each site and the common target distribution. We first develop our approach for the general setting of transporting the effect of a single-site trial. We then extend our method to multisite trials, assess its performance via simulation, and use it to analyze a series of multisite trials of adult education and vocational training programs. In our application, we find that distributional differences are potentially masking cross-site variation. Our method is available in the balancer R package. 

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. 

ImportanceAbortion bans may lead to births among those who are unable to overcome barriers to abortion. The population-level effects of these policies, particularly their unequal impacts across subpopulations in the US, remain unclear. ObjectiveTo assess heterogeneity in the association of abortion bans with changes in fertility in the US, within and across states. Design, Setting, and ParticipantsDrawing from birth certificate and US Census Bureau data from 2012 through 2023 for all 50 states and the District of Columbia, this study used a bayesian panel data model to evaluate state-by-subgroup-specific changes in fertility associated with complete or 6-week abortion bans in 14 US states. The average percent and absolute change in the fertility rate among females aged 15 through 44 years was estimated overall and by state, and within and across states by age, race and ethnicity, marital status, education, and insurance payer. ExposureComplete or 6-week abortion ban. Main outcome and MeasuresFertility rate (births per 1000 reproductive-aged females) overall and by subgroups. ResultsThere were an estimated 1.01 (95% credible interval [CrI], 0.45-1.64) additional births above expectation per 1000 females aged 15 through 44 years (reproductive age) in states following adoption of abortion bans (60.55 observed vs 59.54 expected; 1.70% increase; 95% CrI, 0.75%-2.78%), equivalent to 22 180 excess births, with evidence of variation by state and subgroup. Estimated differences above expectation were largest for racially minoritized individuals (≈2.0%), unmarried individuals (1.79%), individuals younger than 35 years (≈2.0%), Medicaid beneficiaries (2.41%), and those without college degrees (high school diploma, 2.36%; some college, 1.58%), particularly in southern states. Differences in race and ethnicity and education across states explain most of the variability in the state-level association between abortion bans and fertility rates. Conclusion and RelevanceThese findings provide evidence that fertility rates in states with abortion bans were higher than would have been expected in the absence of these policies, with the largest estimated differences among subpopulations experiencing the greatest structural disadvantages and in states with among the worst maternal and child health and well-being outcomes.