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Stable Weights that Balance Covariates for Estimation With Incomplete Outcome Data


  • José R. Zubizarreta


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.

Suggested Citation

  • José R. Zubizarreta, 2015. "Stable Weights that Balance Covariates for Estimation With Incomplete Outcome Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 910-922, September.
  • Handle: RePEc:taf:jnlasa:v:110:y:2015:i:511:p:910-922
    DOI: 10.1080/01621459.2015.1023805

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    References listed on IDEAS

    1. Richard K. Crump & V. Joseph Hotz & Guido W. Imbens & Oscar A. Mitnik, 2009. "Dealing with limited overlap in estimation of average treatment effects," Biometrika, Biometrika Trust, vol. 96(1), pages 187-199.
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    3. Andrea Rotnitzky & Quanhong Lei & Mariela Sued & James M. Robins, 2012. "Improved double-robust estimation in missing data and causal inference models," Biometrika, Biometrika Trust, vol. 99(2), pages 439-456.
    4. Donald B. Rubin, 2005. "Causal Inference Using Potential Outcomes: Design, Modeling, Decisions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 322-331, March.
    5. Zhiqiang Tan, 2010. "Bounded, efficient and doubly robust estimation with inverse weighting," Biometrika, Biometrika Trust, vol. 97(3), pages 661-682.
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    7. José R. Zubizarreta, 2012. "Using Mixed Integer Programming for Matching in an Observational Study of Kidney Failure After Surgery," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1360-1371, December.
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