Stable weights that balance covariates for estimation with incomplete outcome data
Abstract
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.
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Modern statistical methods applied to large electronic health record databases to adjust for baseline differences in patients across types of treatment can be used to estimate aggregate treatment effects.
“modern statistical methods applied to large electronic health record databases to adjust for (“balance”) baseline differences in patients across types of treatment can be used to estimate aggregate treatment effects (131, 132).”
From Using Administrative Data to Predict Suicide After Psychiatric Hospitalization in the Veterans Health Administration System (2020) · cites this paper as [132]
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“een treated and control units, rather than balancing them indirectly by rst estimating the propensity score coecients. 3 Examples includeHainmueller(2011),Graham et al.(2012),Imai and Ratkovic(2013),Zubizarreta (2015),Tan(2017), andWang and Zubizarreta(2018). Several also combine weighting and outcome modeling, includ…”
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“Recently, there is an emerging interest, particularly among applied researchers, in directly incorporating covariate balance in the estimation procedure, so there is no need to check covariate balance repeatedly (e.g. Diamond and Sekhon, 2013; Imai and Ratkovic, 2014; Zubizarreta, 2015).”
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“This contrasts with some other methods such as entropy balancing and stable weights that solve a convex optimization problem [Hainmueller (2012), Zubizarreta (2015)].”
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“12Researchers have recently developed more sophisticated methods for estimating causal effects (Imai and Ratkovic 2014), including those that blend insights from operations research (Zubizarreta 2012, Zubizarreta 2015) and machine learning (Athey, Imbens, and Wager forthcoming).”
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BackgroundStable Prediction across Unknown Environments
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“…way of estimating weights is to use a function of the estimated propensity score, a procedure known as inverse probability weighting (IPW), though there have been some developments that bypass estimating the propensity score to estimate the weights directly (Hainmueller, 2012; Zubizarreta, 2015).”
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“…(a) The crucial concept of covariate balance between two groups in causal inference is usually not considered in missing data analysis; see Zubizarreta (2015) for an exception; (b) The widely used Fisher randomization test for causal comparisons has no analog in missing data analysis; see…”
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“Zubizarreta (2015) proposed to solve a problem similar to (22) (the objective is replaced by the coefficient of variation of w and the exact balancing constraints are relaxed to tolerance level).”
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“It is also possible to (approximately) balance many covariates with proper bias control.(37) An obvious advantage of balancing covariates is that it is automatically MIB with a distance based on the sample mean or proportion.”
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“2) are like the balancing conditions of Zubizarreta (2015) and Athey, Imbens, and Wager (2018).”
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“This analysis weights observations to balance the distributions of the compositional and childhood covariates across cohorts, by using stable balancing weights (Zubizarreta 2015), and employs splines to flexibly model the age-arrest relationships.”
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“This approach is a precursor to the literature on calibrated propensity scores (e.g., Imai & Ratkovic 2014) and balancing weights (e.g., Athey et al. 2018b, Fong et al. 2018, Hainmueller 2012, Zhou & Wodtke 2020, Zubizarreta 2015).”
BackgroundGeneralizing Graph Neural Networks on Out-of-Distribution Graphs
Fan, S., Wang, X., Shi, C., Cui, P., & Wang, B. (2023) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2023.3321097 · Cited by 114 · see citing works
“Confounding balancing techniques [51], [52] correct the non-random assignment of treatment variable by balancing the distributions of confounder across different treatment levels.”
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“Zubizarreta [Zubizarreta 2015] learnt the stable balancing weights via minimizing its variance and adjust them for confounder balancing.”
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“…with Algorithm 1 and consider three dispersion measures of the weights: the sum of absolute deviations, f (w) = |w − w̄|; the variance, f (w) = (w − 1/r)2 (Zubizarreta, 2015); D ow nloaded from https://academ ic.oup.com /biom et/article/107/1/93/5602475 by N ew York U niversity user on 23 D ecem…”
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“In addition to strong conceptual support, estimators of the type have been found to perform well in practice across several application areas (Armstrong and Kolesár, 2018; Imbens and Wager, 2017; Kallus, 2016; Zubizarreta, 2015).”
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“In the case of exact calibration (λ = 0), (31)–(33) can be obtained from Chan et al. (2016) with the particular distance measure DCAL(w); see also Zubizarreta (2015) for D ow nloaded from https://academ ic.oup.com /biom et/article-abstract/107/1/137/5658668 by R utgers U niversity…”
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“, δK) is the vector of balance tolerances used in (10).”
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“Some of these methods can alternatively achieve approximate balance while minimizing weight variance (Zubizarreta, 2015).”
BackgroundMethodInfluentialStatistical data integration in survey sampling: a review
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“ion can be naturally incorporated into the framework and machine learning methods, such as boosting, can be used. The covariate balancing condition, or calibration condition, in (13), can be relaxed. Zubizarreta (2015) relaxed the exact balancing constraints to some tolerance level. Wong et al. (2019) used the theory…”
Kernel-based covariate functional balancing for observational studies
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“Based on these considerations, weighting-based covariate balancing methods have been proposed by Qin & Zhang (2007), Hainmueller (2012), Imai & Ratkovic (2014), Zubizarreta (2015) and Chan et al. (2016).”
Pragmatic Precision Psychiatry—A New Direction for Optimizing Treatment Selection
Kessler, R. C., & Luedtke, A. R. (2021) · JAMA Psychiatry · doi:10.1001/jamapsychiatry.2021.2500 · Cited by 74 · see citing works
Estimating Treatment Effect in the Wild via Differentiated Confounder Balancing
Kuang, K., Cui, P., Li, B., Jiang, M., & Yang, S. (2017) · ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD) · doi:10.1145/3097983.3098032 · Cited by 69 · see citing works
“Recently, researchers proposed new weighting based estimators by focusing on confounder balancing directly [2, 7, 11, 12, 26].”
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Estimating Average Treatment Effects: Supplementary Analyses and Remaining Challenges
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Generalized Optimal Matching Methods for Causal InferencePreprint
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“This trade o↵ between bias and variance is well understood in matching [24, 25, 26, 13].”
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“It may be that there is more promise, as has been shown in the binary settings, when using optimization based weighting methods that seek to directly optimize “covariate balance” (Hainmueller 2012; Imai and Ratkovic 2014; Zubizarreta 2015; Vegetabile et al.”
MethodPropensity score weighting for causal subgroup analysis
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“When focusing on additive models, Zubizarreta19 showed that the weighting estimator for the population mean is unbiased when the covariate means are balanced.”
BackgroundMethodInfluentialPenalized Spline of Propensity Methods for Treatment Comparison
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“The results without truncation are in Figure 10 (see Zubizarreta (2015) for an alternative that minimizes weight variance while retaining covariate balance).”
BackgroundImproving Trial Generalizability Using Observational Studies
Lee, D., Yang, S., Dong, L., Wang, X., Zeng, D., & Cai, J. (2021) · Biometrics · doi:10.1111/biom.13609 · Cited by 60 · see citing works
“A special case is the stable balancing weights method (SBW; Zubizarreta, 2015; Chattopadhyay et al. , 2020) which finds weights with the minimum variance that achieves covariate balance approximately.”
Setodji, C. M., McCaffrey, D. F., Burgette, L. F., Almirall, D., & Griffin, B. A. (2017) · Epidemiology · doi:10.1097/ede.0000000000000734 · Cited by 58 · see citing works
Robust estimation of causal effects via a high-dimensional covariate balancing propensity score
Ning, Y., Sida, P., & Imai, K. (2020) · Biometrika · doi:10.1093/biomet/asaa020 · Cited by 69 · see citing works
Kessler, R. C., Bauer, M. S., Bishop, T. M., Demler, O. V., Dobscha, S. K., Gildea, S. M., Goulet, J. L., Karras, E., Kreyenbuhl, J., Landes, S. J., et al. (2020) · Frontiers in Psychiatry · doi:10.3389/fpsyt.2020.00390 · Cited by 52 · see citing works
Evaluation of subset matching methods and forms of covariate balance
Resa, M. D. L. A., & Zubizarreta, J. (2016) · Statistics in Medicine · doi:10.1002/sim.7036 · Cited by 59 · see citing works
Zhang, Z., Yuan, F., Chen, R., Li, Y., Ma, J., Yan, X., Wang, L., Zhang, F., Tao, H., Guo, D. L., et al. (2020) · Frontiers in Immunology · doi:10.3389/fimmu.2020.01173 · Cited by 51 · see citing works
“Optimization-based methods were utilized to balance the baseline covariates between different groups (29).”
MethodYiu, S., & Su, L. (2018) · Biometrika · doi:10.1093/biomet/asy015 · Cited by 46 · see citing works
“Finally, our method can be implemented with standard statistical software by solving a convex optimization problem that identifies minimum-variance weights subject to our conditions (Zubizarreta, 2015).”
BackgroundMethodInfluentialEnergy balancing of covariate distributions
Huling, J. D., & Mak, S. (2024) · Journal of Causal Inference · doi:10.1515/jci-2022-0029 · Cited by 47 · see citing works
“…on the estimation of the propensity model which encourage moment balance of the covariates [12] or by (ii) altogether avoiding direct modeling of the propensity score and instead estimating weights that explicitly balance moments of the covariates either exactly [13,14] or approximately [15].”
BackgroundDesigning an environmental impact bond for wetland restoration in Louisiana
Herrera, D., Cunniff, S. E., DuPont, C., et al. (2019) · Ecosystem Services · doi:10.1016/j.ecoser.2018.12.008 · Cited by 46 · see citing works
Machine Learning Methods Economists Should Know AboutPreprint
Athey, S. C., & Imbens, G. W. (2019) · RePEc: Research Papers in Economics · doi:10.48550/arxiv.1903.10075 · Cited by 46 · see citing works
Building Representative Matched Samples With Multi-Valued Treatments in Large Observational Studies
Bennett, M., Vielma, J. P., & Zubizarreta, J. R. (2020) · Journal of Computational and Graphical Statistics · doi:10.1080/10618600.2020.1753532 · Cited by 46 · see citing works
“Using, for example, the method by Zubizarreta (2015), it is also possible to relax our matching approach into a weighting approach, with weights that are not required to be constant (and therefore that will not produce a self-weighted sample), and further improve power, yet under a different mode…”
MethodChen, S., & Mallory, A. B. (2021) · Social Science & Medicine · doi:10.1016/j.socscimed.2021.114308 · Cited by 50 · see citing works
Athey, S. C., Imbens, G. W., & Wager, S. (2016) · arXiv (Cornell University) · Cited by 43 · see citing works
Propensity score analysis methods with balancing constraints: A Monte Carlo study
Li, Y., & Li, L. (2021) · Statistical Methods in Medical Research · doi:10.1177/0962280220983512 · Cited by 41 · see citing works
High-Dimensional Confounding Adjustment Using Continuous Spike and Slab Priors
Antonelli, J., Parmigiani, G., & Dominici, F. (2018) · Bayesian Analysis · doi:10.1214/18-ba1131 · Cited by 40 · see citing works
On two approaches to weighting in causal inference
Hirshberg, D. A., & Zubizarreta, J. R. (2017) · Epidemiology · doi:10.1097/ede.0000000000000735 · Cited by 38 · see citing works
“This requires that we ask for approximate balance instead of exact balance, either by imposing a sufficienly loose constraint on the maximal imbalance IF(γ) or by minimizing IF(γ)(2) + ψ(γ), where ψ(γ) is a proxy for the variance.(11;12;13;14;15) The behavior of these methods is in some ways more similar to methods th…”
MethodImmunotherapy beyond progression in patients with advanced non-small cell lung cancer
Ge, X., Zhang, Z., Zhang, S., et al. (2020) · Translational Lung Cancer Research · doi:10.21037/tlcr-20-1252 · Cited by 38 · see citing works
“An optimization-based method was used to eliminate the standardized mean difference in an attempt to balance the distribution of covariates between the IBP and non-IBP groups (19).”
Learning Decomposed Representations for Treatment Effect Estimation
Wu, A., Yuan, J., Kuang, K., Li, B., Wu, R., Zhu, Q., Zhuang, Y. T., & Wu, F. Q. (2022) · IEEE Transactions on Knowledge and Data Engineering · doi:10.1109/tkde.2022.3150807 · Cited by 38 · see citing works
“weight by entropy balancing, residual balancing and stable balancing [17], [18], [38], [39].”
BackgroundMethodDeepMatch: Balancing Deep Covariate Representations for Causal Inference Using Adversarial TrainingPreprint
Kallus, N. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1802.05664 · Cited by 37 · see citing works
“A variety of work has recently taken the approach of directly optimizing imbalance metrics for various causal inference tasks (Athey et al., 2016; Bert-simas et al., 2015; Kallus, 2016, 2017, 2018; Zubizarreta, 2012, 2015).”
BackgroundMethodStable inverse probability weighting estimation for longitudinal studies
Avagyan, V., & Vansteelandt, S. (2021) · Scandinavian Journal of Statistics · doi:10.1111/sjos.12542 · Cited by 36 · see citing works
“Through extensive simulation results, we demonstrate that, under a wide variety of settings, our proposed methodology performs well in terms of several statistical measures compared with the traditional maximum likelihood propensity score estimator (MLE), the covariate balancing propensity score (CBPS) estimator (Imai…”
BackgroundMethodInfluentialFramework for identifying drug repurposing candidates from observational healthcare data
Ozery-Flato, M., Goldschmidt, Y., Shaham, O., Ravid, S., & Yanover, C. (2020) · JAMIA Open · doi:10.1093/jamiaopen/ooaa048 · Cited by 30 · see citing works
On the implied weights of linear regression for causal inference
Chattopadhyay, A., & Zubizarreta, J. R. (2022) · Biometrika · doi:10.1093/biomet/asac058 · Cited by 32 · see citing works
Local border reforms and economic activity
Egger, P. H., Koethenbuerger, M., & Loumeau, G. (2021) · Journal of Economic Geography · doi:10.1093/jeg/lbab030 · Cited by 31 · see citing works
Kernel Balancing: A Flexible Non-Parametric Weighting Procedure for Estimating Causal EffectsPreprint
Hazlett, C. J. (2016) · SSRN Electronic Journal · doi:10.2139/ssrn.2746753 · Cited by 31 · see citing works
A method to reduce imbalance for site-level randomized stepped wedge implementation trial designs
Lew, R., Miller, C. J., Kim, B., Wu, H.-S., Stolzmann, K. L., & Bauer, M. (2019) · Implementation Science · doi:10.1186/s13012-019-0893-3 · Cited by 18 · see citing works
A unifying approach for doubly-robust $\ell_1$ regularized estimation of causal contrastsPreprint
Smucler, E., Rotnitzky, A. G., & Robins, J. M. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1904.03737 · Cited by 30 · see citing works
“Z) among the units with observed data, i.e. it satises the "balancing" property P n[˚(Z)] ˇP n 2 4 D expit hb b;˚(Z)i ˚(Z) 3 5: 10 Estimators satisfying this property have been used in Zubizarreta (2015); Athey et al. (2018); Chan et al. (2016); Tan (2017); Imai and Ratkovic (2014); Hirshberg and Wager (2017…”
MethodCafri, G., Wang, W., Chan, P., & Austin, P. (2018) · Statistical Methods in Medical Research · doi:10.1177/0962280218799540 · Cited by 31 · see citing works
Antonelli, J., Papadogeorgou, G., & Dominici, F. (2020) · Biometrics · doi:10.1111/biom.13417 · Cited by 29 · see citing works
Learning L2 Continuous Regression Functionals via Regularized Riesz RepresentersPreprint
Chernozhukov, V., Newey, W. K., & Singh, R. (2018) · arXiv (Cornell University) · Cited by 29 · see citing works
Alternative weighting schemes when performing matching‐adjusted indirect comparisons
Jackson, D., Rhodes, K. M., & Ouwens, M. (2020) · Research Synthesis Methods · doi:10.1002/jrsm.1466 · Cited by 28 · see citing works
“One main contribution of this paper is to show that the methodology proposed by Zubizarreta15 can be used to maximise the ESS when performing a MAIC in this way.”
BackgroundMethodInfluentialMultiply Robust Estimation of Causal Effects under Principal Ignorability
Jiang, Z., Yang, S., & Ding, P. (2022) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/rssb.12538 · Cited by 28 · see citing works
“We can also construct balancing weights for estimating the PCEs based on Theorem 4, similar to the strategies for estimating the average causal effect (Zubizarreta, 2015; Tan, 2020).”
MethodEgger, P. H., & Tarlea, F. (2020) · Economica · doi:10.1111/ecca.12361 · Cited by 27 · see citing works
“One such weighting approach is entropy balancing, which is based on optimally-chosen weights as a function of the distributions of observables for the treated and the untreated (see Hainmüller, 2012; Imai and Ratkovic, 2014; Zubizarreta, 2015).”
Multilevel Calibration Weighting for Survey Data
Ben‐Michael, E., Feller, A., & Hartman, E. (2023) · Political Analysis · doi:10.1017/pan.2023.9 · Cited by 26 · see citing works
“First, there has been a renewedpush to find calibrationweights that allow for approximate balance on covariates, rather than exact balance (Guggemos and Tillé 2010; Park and Fuller 2009; Zubizarreta 2015).”
BackgroundMethodInfluentialOptimal Covariate Balancing Conditions in Propensity Score Estimation
Fan, J., Imai, K., Lee, I., Liu, H., Ning, Y., & Yang, X. (2021) · Journal of Business and Economic Statistics · doi:10.1080/07350015.2021.2002159 · Cited by 27 · see citing works
“…estimation of the propensity score by optimizing covariate balance rather than maximizing the accuracy of predicting treatment assignment (e.g., Hainmueller 2012; Graham, Pinto, and Egel 2012; Imai and Ratkovic 2014; Chan, Yam, and Zhang 2016; Zubizarreta 2015; Zhao and Percival 2017; Zhao 2019).”
BackgroundInfluentialCounterfactual Representation Learning with Balancing WeightsPreprint
Assaad, S., Zeng, S., Tao, C., Datta, S., Mehta, N., Henao, R., Li, F., & Carin, L. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2010.12618 · Cited by 25 · see citing works
“Without careful adjustment, this leads to a biased estimate of the causal effect (Zubizarreta, 2015).”
BackgroundMethodInfluentialCheng, D. T.-Y., Ayyagari, R., & Signorovitch, J. (2020) · The Annals of Applied Statistics · doi:10.1214/20-aoas1359 · Cited by 24 · see citing works
“MAIC is similar in spirit to a number of other re-weighting methods that seek to balance covariates between treatment groups to estimate causal effects (Zubizarreta, 2015; Li, Morgan and Zaslavsky, 2017) and identical to the covariate balancing propensity score used to estimate average treatment effects on the treated…”
BackgroundMethodA Review of Causal Inference for External Comparator Arm Studies
Rippin, G., Ballarini, N. M., Sanz, H., Largent, J. A., Quinten, C., & Pignatti, F. (2022) · Drug Safety · doi:10.1007/s40264-022-01206-y · Cited by 25 · see citing works
Díaz, I., & van der Laan, M. V. (2017) · Statistics in Medicine · doi:10.1002/sim.7389 · Cited by 26 · see citing works
“Covariate balanced estimators have been traditionally used to reduce bias in observational studies and missing data models (e.g., Hainmueller, 2011; Imai and Ratkovic, 2014; Zubizarreta, 2015), but covariate selection for balancing remains an open problem.”
MethodSengewald, M.-A. D.-P., Steiner, P. M., & Pohl, S. (2018) · British Journal of Mathematical and Statistical Psychology · doi:10.1111/bmsp.12146 · Cited by 27 · see citing works
The role of covariate balance in observational studies
Sauppe, J. J., & Jacobson, S. H. (2017) · Naval Research Logistics (NRL) · doi:10.1002/nav.21751 · Cited by 23 · see citing works
“Additionally, the strongest assumption presented here, Assumption 6, is standard for any regression approach [60].”
BackgroundMethodResultInfluentialWhen is a Match Sufficient? A Score-based Balance Metric for the Synthetic Control Method
Parast, L. M., Hunt, P., Griffin, B. A., & Powell, D. (2020) · Journal of Causal Inference · doi:10.1515/jci-2020-0013 · Cited by 22 · see citing works
“For example, one could consider an approach similar to the stable balancing weights proposed in Zubizarreta (2015) [31] which would constrain the absolute difference in means of the weighted pre-intervention outcomes to be less than user-specified thresholds.”
MethodResidual Balancing: A Method of Constructing Weights for Marginal Structural Models
Zhou, X., & Wodtke, G. T. (2020) · Political Analysis · doi:10.1017/pan.2020.2 · Cited by 21 · see citing works
“2018) or the variance (Zubizarreta 2015), could also be used to construct the weights.”
MethodCounterfactual Prediction for Bundle Treatment
Zou, H., Cui, P., Li, B., Shen, Z., Ma, J., Yang, H., & He, Y. (2020) · neural information processing systems · Cited by 22 · see citing works
Keele, L. J., & Small, D. S. (2020) · The American Statistician · doi:10.1080/00031305.2020.1867638 · Cited by 21 · see citing works
“The next replication uses the results from an investigation of the effect of the Chilean earthquake in 2010 on mental health (Zubizarreta et al. 2013).”
MethodSong, Z., & D, K. B. A. (2021) · Health Affairs · doi:10.1377/hlthaff.2020.01808 · Cited by 21 · see citing works
Treatment Effect Estimation via Differentiated Confounder Balancing and Regression
Kuang, K., Cui, P., Li, B., Jiang, M., Wang, Y., Wu, F. Q., & Yang, S. (2019) · ACM Transactions on Knowledge Discovery from Data · doi:10.1145/3365677 · Cited by 20 · see citing works
“Recently, researchers proposed new weighting based estimators by focusing on confounder balancing directly [2, 9, 15, 17, 45, 46], bypassing propensity score estimation.”
BackgroundInterpretable sensitivity analysis for balancing weights
Soriano, D., Ben‐Michael, E., Bickel, P. J., Feller, A., & Pimentel, S. D. (2023) · Journal of the Royal Statistical Society Series A (Statistics in Society) · doi:10.1093/jrsssa/qnad032 · Cited by 20 · see citing works
“(2019) in order to handle balancing weights estimators that achieve approximate (rather than exact) balance on covariates, such as the stable balancing weights of Zubizarreta (2015). In Section 4 we then introduce an amplification that allows us to better interpret and calibrate marginal sensitivity analyses.”
BackgroundCausal inference in the absence of positivity: The role of overlap weights
Matsouaka, R., & Zhou, Y. (2024) · Biometrical Journal · doi:10.1002/bimj.202300156 · Cited by 21 · see citing works
Sufficient dimension reduction for average causal effect estimation
Cheng, D., Li, J., Liu, L., Le, T. D., Liu, J., & Yu, K. (2022) · Data Mining and Knowledge Discovery · doi:10.1007/s10618-022-00832-5 · Cited by 18 · see citing works
“achine learning models have been designed for causal inference such as trees-based methods (Hill 2011; Athey and Imbens 2016; Kunzel et al. 2019),¨ and re-weighting methods (Rosenbaum and Rubin 1983; Zubizarreta 2015; Kuang et al. 2017). Since they do not involve representation learning, these methods are not directly…”
ResultKallonen, J., Korsholm, K., Bredin, F., et al. (2022) · Pulmonary Circulation · doi:10.1002/pul2.12093 · Cited by 19 · see citing works
Doubly robust identification for causal panel data models
Arkhangelsky, D., & Imbens, G. W. (2022) · Econometrics Journal · doi:10.1093/ectj/utac019 · Cited by 19 · see citing works
Targeted optimal treatment regime learning using summary statistics
Chu, J., Lu, W., & Yang, S. (2023) · Biometrika · doi:10.1093/biomet/asad020 · Cited by 19 · see citing works
“Zhang, 2007), entropy-based covariate balancing methods (Hainmueller, 2012), and quadratic loss based covariate balancing methods (Zubizarreta, 2015).”
Fixed Effects and the Generalized Mundlak Estimator
Arkhangelsky, D., & Imbens, G. W. (2023) · The Review of Economic Studies · doi:10.1093/restud/rdad089 · Cited by 19 · see citing works
Rizk, J. G. (2025) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2025.111942 · Cited by 18 · see citing works
Covariate distribution balance via propensity scores
Sant’Anna, P. H. C., Song, X., & Xu, Q. L. (2022) · Journal of Applied Econometrics · doi:10.1002/jae.2909 · Cited by 21 · see citing works
Socioeconomic Status and Risk of Bleeding After Mechanical Aortic Valve Replacement
Dalén, M., Persson, M., Glaser, N., & Sartipy, U. (2022) · Journal of the American College of Cardiology · doi:10.1016/j.jacc.2022.04.030 · Cited by 18 · see citing works
Sparsity Double Robust Inference of Average Treatment EffectsPreprint
Bradić, J., Wager, S., & Zhu, Y. (2019) · RePEc: Research Papers in Economics · doi:10.48550/arxiv.1905.00744 · Cited by 18 · see citing works
“…as follows (the ˆ β ( w ) are estimated via the lasso): Conceptually, this approach is related to several papers that stress the important of covariate balance for accurate estimation of treatment effects [Chan et al., 2015, Imai and Ratkovic, 2014, Kallus, 2018, Zhao, 2019, Zubizarreta, 2015].”
BackgroundMethod
- Authors
- Zubizarreta, J. R.
- Affiliations
- Columbia University (US)
- Corresponding author
- Zubizarreta, José R.
- ORCID
- Zubizarreta, José R.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 2015-07-03
- Volume
- 110
- Issue
- 511
- Pages
- 910-922
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2120817734
- Semantic Scholar
- 2425738e5b67fc909c6c41d7609e9d57e6791eb7
- Cited by
- 369
- References
- 54
- Citations by year
- 2026: 21 · 2025: 53 · 2024: 31 · 2023: 47 · 2022: 41 · 2021: 52 · 2020: 44 · 2019: 31 · 2018: 23 · 2017: 18 · 2016: 8
- FWCI
- 14.99
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of the American Statistical Association (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Keywords
- covariate balance, inverse probability weighting, convex optimization, duality theory, treatment effect estimation, causal inference
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