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Weighting methods that adjust for observed covariates, such as inverse probability weighting, are widely used for causal inference and estimation with incomplete outcome data. Part of the appeal of such methods is that one set of weights can be used to estimate a range of treatment effects based on different outcomes, or a variety of population means for several variables. However, this appeal can be diminished in practice by the instability of the estimated weights and by the difficulty of adequately adjusting for observed covariates in some settings. To address these limitations, this article presents a new weighting method that finds the weights of minimum variance that adjust or balance the empirical distribution of the observed covariates up to levels prespecified by the researcher. This method allows the researcher to balance very precisely the means of the observed covariates and other features of their marginal and joint distributions, such as variances and correlations and also, for example, the quantiles of interactions of pairs and triples of observed covariates, thus, balancing entire two- and three-way marginals. Since the weighting method is based on a well-defined convex optimization problem, duality theory provides insight into the behavior of the variance of the optimal weights in relation to the level of covariate balance adjustment, answering the question, how much does tightening a balance constraint increases the variance of the weights? Also, the weighting method runs in polynomial time so relatively large datasets can be handled quickly. An implementation of the method is provided in the new package sbw for R. This article shows some theoretical properties of the resulting weights and illustrates their use by analyzing both a dataset from the 2010 Chilean earthquake and a simulated example.

This article presents a new method for optimal matching in observational studies based on mixed integer programming. Unlike widely used matching methods based on network algorithms, which attempt to achieve covariate balance by minimizing the total sum of distances between treated units and matched controls, this new method achieves covariate balance directly, either by minimizing both the total sum of distances and a weighted sum of specific measures of covariate imbalance, or by minimizing the total sum of distances while constraining the measures of imbalance to be less than or equal to certain tolerances. The inclusion of these extra terms in the objective function or the use of these additional constraints explicitly optimizes or constrains the criteria that will be used to evaluate the quality of the match. For example, the method minimizes or constrains differences in univariate moments, such as means, variances, and skewness; differences in multivariate moments, such as correlations between covariates; differences in quantiles; and differences in statistics, such as the Kolmogorov–Smirnov statistic, to minimize the differences in both location and shape of the empirical distributions of the treated units and matched controls. While balancing several of these measures, it is also possible to impose constraints for exact and near-exact matching, and fine and near-fine balance for more than one nominal covariate, whereas network algorithms can finely or near-finely balance only a single nominal covariate. From a practical standpoint, this method eliminates the guesswork involved in current optimal matching methods, and offers a controlled and systematic way of improving covariate balance by focusing the matching efforts on certain measures of covariate imbalance and their corresponding weights or tolerances. A matched case–control study of acute kidney injury after surgery among Medicare patients illustrates these features in detail. A new R package called mipmatch implements the method.

A distinctive feature of a clustered observational study is its multilevel or nested data structure arising from the assignment of treatment, in a nonrandom manner, to groups or clusters of units or individuals. Examples are ubiquitous in the health and social sciences including patients in hospitals, employees in firms, and students in schools. What is the optimal matching strategy in a clustered observational study? At first thought, one might start by matching clusters of individuals and then, within matched clusters, continue by matching individuals. But as we discuss in this article, the optimal strategy is the opposite: in typical applications, where the intracluster correlation is not one, it is best to first match individuals and, once all possible combinations of matched individuals are known, then match clusters. In this article, we use dynamic and integer programming to implement this strategy and extend optimal matching methods to hierarchical and multilevel settings. Among other matched designs, our strategy can approximate a paired clustered randomized study by finding the largest sample of matched pairs of treated and control individuals within matched pairs of treated and control clusters that is balanced according to specifications given by the investigator. This strategy directly balances covariates both at the cluster and individual levels and does not require estimating the propensity score, although the propensity score can be balanced as an additional covariate. We illustrate our results with a case study of the comparative effectiveness of public versus private voucher schools in Chile, a question of intense policy debate in the country at the present.

Ballot initiatives allow the public to vote directly on public policy. The literature in political science has attempted to document whether the presence of an initiative can increase voter turnout. We study this question for an initiative that appeared on the ballot in 2008 in Milwaukee, Wisconsin, using a natural experiment based on geography. This form of natural experiment exploits variation in geography where units in one geographic area receive a treatment whereas units in another area do not. When assignment to treatment via geographic location creates as-if random variation in treatment assignment, adjustment for baseline covariates is unnecessary. In many applications, however, some adjustment for baseline covariates may be necessary. As such, analysts may wish to combine identification strategies—using both spatial proximity and covariates. We propose a matching framework to incorporate information about both geographic proximity and observed covariates flexibly which allows us to minimize spatial distance while preserving balance on observed covariates. This framework is also applicable to regression discontinuity designs that are not based on geography. We find that the initiative on the ballot in Milwaukee does not appear to have increased turnout.

The outbreak of the B.1.1.529 lineage of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) (Omicron) has caused an unprecedented number of Coronavirus Disease 2019 (COVID-19) cases, including pediatric hospital admissions. Policymakers urgently need evidence of vaccine effectiveness in children to balance the costs and benefits of vaccination campaigns, but, to date, the evidence is sparse. Leveraging a population-based cohort in Chile of 490,694 children aged 3–5 years, we estimated the effectiveness of administering a two-dose schedule, 28 days apart, of Sinovac’s inactivated SARS-CoV-2 vaccine (CoronaVac). We used inverse probability-weighted survival regression models to estimate hazard ratios of symptomatic COVID-19, hospitalization and admission to an intensive care unit (ICU) for children with complete immunization over non-vaccination, accounting for time-varying vaccination exposure and relevant confounders. The study was conducted between 6 December 2021 and 26 February 2022, during the Omicron outbreak in Chile. The estimated vaccine effectiveness was 38.2% (95% confidence interval (CI), 36.5–39.9) against symptomatic COVID-19, 64.6% (95% CI, 49.6–75.2) against hospitalization and 69.0% (95% CI, 18.6–88.2) against ICU admission. The effectiveness against symptomatic COVID-19 was modest; however, protection against severe disease was high. These results support vaccination of children aged 3–5 years to prevent severe illness and associated complications and highlight the importance of maintaining layered protections against SARS-CoV-2 infection. CoronaVac protects young children from severe COVID-19 during a SARS-CoV-2 Omicron surge, supporting the effectiveness and importance of vaccinating this pediatric population.

Objective Inverse probability weighting is a fundamental and general methodology for estimating the causal effects of exposures and interventions, but standard approaches to constructing such weights are often suboptimal. Methods In this paper, we describe a recent approach for constructing such weights that directly balances covariates while optimizing the stability of the resulting weighting estimator. Results To illustrate the use of this approach in mental health research, we present an exploratory study of the effects of exposure to violence on the risk of suicide attempt. Conclusions The direct balancing approach to weighting should be given strong consideration in empirical research due to its robustness and transparency in building weighting estimators.

In a claims-based study involving 3790 affected youths, parental firearm injury was associated with increases in psychiatric diagnoses — especially trauma-related disorders — and in mental health visits among children.

In 2010, a magnitude 8.8 earthquake hit Chile, devastating parts of the country. Having just completed its national socioeconomic survey, the Chilean government reinterviewed a subsample of respondents, creating unusual longitudinal data about the same persons before and after a major disaster. The follow-up evaluated posttraumatic stress symptoms (PTSS) using Davidson's Trauma Scale. We use these data with two goals in mind. Most studies of PTSS after disasters rely on recall to characterize the state of affairs before the disaster. We are able to use prospective data on preexposure conditions, free of recall bias, to study the effects of the earthquake. Second, we illustrate recent developments in statistical methodology for the design and analysis of observational studies. In particular, we use new and recent methods for multivariate matching to control 46 covariates that describe demographic variables, housing quality, wealth, health, and health insurance before the earthquake. We use the statistical theory of design sensitivity to select a study design with findings expected to be insensitive to small or moderate biases from failure to control some unmeasured covariate. PTSS were dramatically but unevenly elevated among residents of strongly shaken areas of Chile when compared with similar persons in largely untouched parts of the country. In 96% of exposed-control pairs exhibiting substantial PTSS, it was the exposed person who experienced stronger symptoms (95% confidence interval = 0.91-1.00).

Conventionally, the construction of a pair-matched sample selects treated and control units and pairs them in a single step with a view to balancing observed covariates x and reducing the heterogeneity or dispersion of treated-minus-control response differences, Y. In contrast, the method of cardinality matching developed here first selects the maximum number of units subject to covariate balance constraints and, with a balanced sample for x in hand, then separately pairs the units to minimize heterogeneity in Y. Reduced heterogeneity of pair differences in responses Y is known to reduce sensitivity to unmeasured biases, so one might hope that cardinality matching would succeed at both tasks, balancing x, stabilizing Y. We use cardinality matching in an observational study of the effectiveness of for-profit and not-for-profit private high schools in Chile—a controversial subject in Chile—focusing on students who were in government run primary schools in 2004 but then switched to private high schools. By pairing to minimize heterogeneity in a cardinality match that has balanced covariates, a meaningful reduction in sensitivity to unmeasured biases is obtained.