Cited by 369Advanced Causal Inference TechniquesStatistical Methods and InferenceStatistical Methods and Bayesian Inference

The DOI matches its Crossref record; 54 of the 54 references it cites were found in a registry or an index.

Stable Weights that Balance Covariates for Estimation With Incomplete Outcome Data

Zubizarreta, José R.·2015·Journal of the American Statistical Association

DOI 10.1080/01621459.2015.1023805

Open this paper in CoChat — free account

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.

Integrity signals

Registry

Crossref · 10.1080/01621459.2015.1023805

Cites

54 of 54 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

This paper’s full text isn’t openly available, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Convex Optimization
Boyd, S., & Vandenberghe, L. (2004) · doi:10.1017/cbo9780511804441 · Cited by 56,601
The central role of the propensity score in observational studies for causal effects
ROSENBAUM, P. R., & RUBIN, D. B. (1983) · Biometrika · doi:10.1093/biomet/70.1.41 · Cited by 31,241
The Elements of Statistical Learning
Hastie, T., Tibshirani, R., & Friedman, J. (2009) · Springer Series in Statistics · doi:10.1007/978-0-387-84858-7 · Cited by 25,970
The Elements of Statistical Learning
Hastie, T., Friedman, J., & Tibshirani, R. (2001) · Springer Series in Statistics · doi:10.1007/978-0-387-21606-5 · Cited by 24,162
Statistical Analysis With Missing Data
Lahiff, M., Little, R. J. A., & Rubin, D. B. (1989) · Journal of the American Statistical Association · doi:10.2307/2289883 · Cited by 17,385
Untitled work
(2002) · Cited by 13,211
Statistical Analysis with Missing Data
Little, R. J. A., & Rubin, D. B. (2002) · Wiley Series in Probability and Statistics · doi:10.1002/9781119013563 · Cited by 8,473
Matching Methods for Causal Inference: A Review and a Look Forward
Stuart, E. A. (2010) · Statistical Science · doi:10.1214/09-sts313 · Cited by 5,478
A generalization of sampling without replacement from a finite universe
Horvitz, D. G., & Thompson, D. J. (1952) · Journal of the American Statistical Association · doi:10.1080/01621459.1952.10483446 · Cited by 4,293
Introduction to Nonparametric Estimation
Tsybakov, A. (2008) · Springer Series in Statistics · doi:10.1007/b13794 · Cited by 3,687

Show all 54 references

Research works printed but not linked: 2

Elliott M.R., 2008, Journal of Official Statistics, 24, 517
Rao J. N.K., 2009, Pakistan Journal of Statistics, 25, 371

Sorted by citations

Items 201–300 of 365

A Calibrated Sensitivity Analysis for Weighted Causal Decompositions
Shen, A. A., Visoki, E., Barzilay, R., & Pimentel, S. D. (2025) · Statistics in Medicine · doi:10.1002/sim.70010 · Cited by 5
“As a result, our general MSM formulation achieves the same inferential conclusions from Zhao, Small, and Bhattacharya (2019) [44] and Soriano et al. (2023) [46].”
Design sensitivity and its implications for weighted observational studies
Huang, M., Soriano, D., & Pimentel, S. D. (2025) · Journal of the Royal Statistical Society Series A (Statistics in Society) · doi:10.1093/jrsssa/qnaf067 · Cited by 4
“For examples of such balancing weights and additional methods and theory, see Hainmueller (2012); Zubizarreta (2015); Ben-Michael et al. (2021).”
A stable and more efficient doubly robust estimator
Zhang, M., & Zhang, B. (2020) · Statistica Sinica · doi:10.5705/ss.202019.0265 · Cited by 4
Recent advances in statistical methodologies in evaluating program for high-dimensional data
Zhan, M., Cai, Z., Fang, Y. G., et al. (2022) · Applied mathematics/Applied Mathematics. A Journal of Chinese Universities/Gao-xiao yingyong shuxue xuebao · doi:10.1007/s11766-022-4489-3 · Cited by 4
“…groups: one depends on modeling the propensity score; see, e.g., the papers by Imai and Ratkovic (2014) and Sant’Anna, Song and Xu (2020), and the other directly aims at the balance weights via optimization designs; see, e.g., the papers by Zubizarreta (2015) and Chan, Yam and Zhang (2016).”
MethodInfluential
Sensitivity analysis for calibrated inverse probability-of-censoring weighted estimators under non-ignorable dropout
Su, L., Seaman, S. R., & Yiu, S. (2022) · Statistical Methods in Medical Research · doi:10.1177/09622802221090763 · Cited by 4
“Note that the function in (9) is convex in λ, which ensures that the solution to (7) is unique and can be found efficiently.”
BackgroundMethod
Matching-adjusted indirect comparison via a polynomial-based non-linear optimization method
Alsop, J. C., & Pont, L. (2022) · Journal of Comparative Effectiveness Research · doi:10.2217/cer-2021-0266 · Cited by 4
Reweighting estimators to extend the external validity of clinical trials: methodological considerations
Kaizar, E. E., Lin, C., Faries, D. E., & Johnston, J. A. (2023) · Journal of Biopharmaceutical Statistics · doi:10.1080/10543406.2022.2162067 · Cited by 5
“The transformations of covariates included as ‘X’ in Equation 7 should reflect the conjectured relationship between covariates and outcomes, where balancing the means is effective for a linear relationship, but higher orders or other transformations may be necessary for approximately unbiased estimation (Zubizarreta 2…”
Background
Balancing Approach for Causal Inference at Scale
Lin, S. Y., Xu, M., Xi, Z., Chao, S.-K., Huang, Y.-K., & Shi, X. (2023) · ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD) · doi:10.1145/3580305.3599778 · Cited by 7
Varying impacts of letters of recommendation on college admissions
Ben‐Michael, E., Feller, A., & Rothstein, J. (2023) · The Annals of Applied Statistics · doi:10.1214/23-aoas1740 · Cited by 4
Causal inference from observational data: Estimating the effect of contributions on visitation frequency atLinkedInPreprint
Bojinov, I., Tu, Y., Liu, M., & XU, Y. N. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1903.07755 · Cited by 4
“l FLAMERoy et al. (2017) CausalGAM Glynn and Quinn (2010) Causalimpact Brodersen et al. (2015) MatchIt Ho et al. (2011) IPW van der Wal et al. (2011) wfe Kim et al. (2017) CEM Iacus et al. (2009) sbw Zubizarreta (2015) lfeGaure (2013) resemble a randomized experiment. Typically, this step is performed by only utilizin…”
Background
Robust Methods for Causal Inference Using Penalized Splines
Zhou, T. (2018) · Deep Blue (University of Michigan) · Cited by 4
A Bayesian Gaussian Process for Estimating a Causal Exposure Response Curve in Environmental EpidemiologyPreprint
Ren, B., Wu, X., Braun, D., Pillai, N. S., & Dominici, F. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2105.03454 · Cited by 8
“An important goal of these approaches is to recover covariate balance either implicitly or explicitly (Zubizarreta, 2012; Zubizarreta et al., 2014; Zubizarreta, 2015; Wang and Zubizarreta, 2019).”
Background
Optimal Covariate Balancing Conditions in Propensity Score EstimationPreprint
B, J. F. A., Imai, K., Lee, I., Liu, H., Ning, Y., & Yang, X. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2108.01255 · Cited by 4
“…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).”
BackgroundInfluential
Nonparametric Heterogeneous Treatment Effect Estimation in Repeated Cross Sectional DesignsPreprint
Nie, X., Lu, C., & Wager, S. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1905.11622 · Cited by 4
Microbiome data integration via shared dictionary learning
Yuan, B., & Wang, S. (2025) · Nature Communications · doi:10.1038/s41467-025-63425-y · Cited by 7
Learning Disentangled Latent Factors for Individual Treatment Effect Estimation Using Variational Generative Adversarial Nets
Bao, Q., Mao, Z., & Chen, L. (2022) · International Conference on Computer Supported Cooperative Work in Design (CSCWD) · doi:10.1109/cscwd54268.2022.9776065 · Cited by 3
Linear high-dimensional mediation models adjusting for confounders using propensity score method
Luo, L., Yan, Y., Cui, Y., Yuan, X., & Yu, Z. (2022) · Frontiers in Genetics · doi:10.3389/fgene.2022.961148 · Cited by 3
“In addition, applying other weighting methods such as the stable weights proposed by Zubizarreta (2015) in the PSW and PSU models might help to enhance the model robustness.”
Method
Propensity score weighting methods for causal subgroup analysis with time-to-event outcomes
Yang, S., Zhou, R., Li, F., & Thomas, L. E. (2023) · Statistical Methods in Medical Research · doi:10.1177/09622802231188517 · Cited by 3
“In the context of linear models for continuous outcome, Zubizarreta 32 shows a weighting estimator for the overall mean is unbiased when the overall covariate means are balanced.”
Background
Minimizing confounding in comparative observational studies with time-to-event outcomes: An extensive comparison of covariate balancing methods using Monte Carlo simulation
Cafri, G., Fortin, S., & Austin, P. C. (2024) · Statistical Methods in Medical Research · doi:10.1177/09622802241262527 · Cited by 4
“…propensity score often considered in past published simulations (e.g. greedy pair matching, average treatment effect on the treated (ATT) weighting), 6 newer balancing methods (e.g. stable balance weighting 3 ), and pairing some older balancing methods with a covariate balancing propensity score.”
Influential
Causal analysis methods for estimating the impact of drought and cold events on crop yields in France
Mendes, C., Aldebert, K., Brun, F., et al. (2025) · European Journal of Agronomy · doi:10.1016/j.eja.2025.127743 · Cited by 3
Combining Propensity Scores and Common Items for Test Score Equating
Laukaityte, I., Wallin, G., & Wiberg, M. (2025) · Applied Psychological Measurement · doi:10.1177/01466216251363240 · Cited by 3
“Other methods for balancing covariates include weighting techniques, such as the minimum-variance balancing method proposed by Zubizarreta (2015), which adjusts the empirical distribution of covariates to achieve a prespeci ﬁ ed level of balance.”
Some Solutions Inspired by Survey Sampling Theory to Build Effective Clinical Trials
Tillé, Y. (2022) · International Statistical Review · doi:10.1111/insr.12498 · Cited by 3
“This programme is also studied in Zubizarreta (2015).”
Background
RKHS-based covariate balancing for survival causal effect estimation
Wu, X., Zhang, X., Chan, K. C. G., & Wong, R. K. W. (2023) · Lifetime Data Analysis · doi:10.1007/s10985-023-09590-y · Cited by 3
“To alleviate the challenge of extreme weights, various covariate balancing methods havebeendeveloped(e.g.,ImaiandRatkovic2014;Zubizarreta2015;Chanetal.2016; Fongetal.2018;NeweyandRobins2018;Zhao2019;WangandZubizarreta2020; Zhangetal.2021;HirshbergandWager2021).”
Characterizing Imbalance in the Tails of the Propensity Score Distribution
DiPrete, B. L., Girman, C. J., Mavros, P., et al. (2023) · American Journal of Epidemiology · doi:10.1093/aje/kwad200 · Cited by 3
Effekte unbegleiteter Lockerungen aus der Sozialtherapie auf die Beschäftigungssituation bei Entlassung
Suhling, S., & Guéridon, M. (2023) · Monatsschrift für Kriminologie und Strafrechtsreform · doi:10.1515/mks-2023-0047 · Cited by 3
Causation, Comparison, and Regression
Chattopadhyay, A., & Zubizarreta, J. R. (2024) · Harvard Data Science Review · doi:10.1162/99608f92.87c6125f · Cited by 3
Large Sample Properties of Matching for Balance
Wang, Z., & Zubizarreta, J. R. (2021) · Statistica Sinica · doi:10.5705/ss.202020.0343 · Cited by 3
Covariate balancing for causal inference on categorical and continuous treatments
Lee, S.-H., Yanyuan Ma, B., & de Luna, X. (2022) · Econometrics and Statistics · doi:10.1016/j.ecosta.2022.01.007 · Cited by 3
“As other recent proposals for the binary treatment case (Athey et al. 2018, Wang & Zubizarreta 2019, Wong & Chan 2017, Zubizarreta 2015), the method presented here does not necessarily try to achieve exact balance when this is not possible, although in practice exact balance can always be targeted…”
Method
Characterizing Subpopulations with Better Response to Treatment Using Observational Data – an Epilepsy Case StudyPreprint
Ozery-Flato, M., El‐Hay, T., Aharonov, R., Parush, N., Goldschmidt, Y., Borghs, S., Chan, J., Haddad, N., Pierre‐Louis, B. J., & Kalilani, L. (2018) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/290585 · Cited by 3
LaLonde (1986) after Nearly Four Decades: Lessons LearnedPreprint
Xu, Y., & Imbens, G. W. (2024) · SSRN Electronic Journal · doi:10.2139/ssrn.4849285 · Cited by 3
sbw: Stable Balancing Weights for Causal Inference and Missing Data
Zubizarreta, J. R., Li, Y., & Kim, K. (2019) · doi:10.32614/cran.package.sbw · Cited by 3
Estimating drug concentration–response relationships by applying causal inference methods for continuous point exposures and time-to-event outcomes
Yiu, S., Wang, Q., Mercier, F., Manfrini, M., Koendgen, H., Kletzl, H., & Model, F. (2023) · Statistical Methods in Medical Research · doi:10.1177/09622802231212274 · Cited by 2
Therapeutic Drug Monitoring of Thiopurines in Patients With Inflammatory Bowel Disease: Observations From Daily Practice
Lovrić, M., Dukić, K., Čuković‐Čavka, S., et al. (2025) · Therapeutic Drug Monitoring · doi:10.1097/ftd.0000000000001327 · Cited by 2
Balancing Weights for Estimating Treatment Effects in Educational Studies
Keele, L. J., Ben‐Michael, E., Lenard, M., & Page, L. C. (2025) · Journal of Research on Educational Effectiveness · doi:10.1080/19345747.2025.2483775 · Cited by 2
“Various proposals include entropy balancing weights (Hainmueller, 2012), and stable balancing weights (Zubizarreta, 2015), among others (e.g., Ben-Michael et al., 2023; Chan et al., 2016; Tan, 2020).”
Influential
What to Observe When Assuming Selection on Observables
Quinn, K. M., Liu, G., Epstein, L., & Martin, A. D. (2025) · Political Analysis · doi:10.1017/pan.2025.10003 · Cited by 2
“We refer to these estimators as balancing weights estimators (for examples of such estimators, see Hainmueller 2012; Hazlett 2020; Wang and Zubizarreta 2020; Zubizarreta 2015).”
Joint subgraph independence for graph out-of-distribution generalization
Yu, H., Liu, W., Wang, Y., et al. (2025) · Pattern Recognition · doi:10.1016/j.patcog.2025.112551 · Cited by 2
Balancing Weights for Causal Inference in Observational Factorial Studies
Yu, R., & Ding, P. (2026) · Journal of the American Statistical Association · doi:10.1080/01621459.2025.2602837 · Cited by 8
“…weighting [Hahn, 1998, Robins et al., 2000, Hirano and Imbens, 2001, Hirano et al., 2003] and balancing weighting [Hainmueller, 2012, Zubizarreta, 2015, Chan et al., 2016, Li et al., 2018, Wong and Chan, 2018, Zhao, 2019, Wang and Zubizarreta, 2020, Bruns-Smith and Feller, 2022,…”
Effectiveness of Doxycycline in Combination With Other Antibiotics for Gram-Positive Periprosthetic Joint Infections: A Causal Inference Study
Godon, J., Sow, A.-K., Neves, S. D., et al. (2026) · Open Forum Infectious Diseases · doi:10.1093/ofid/ofag098 · Cited by 2
“If the initial propensity score model based on logistic regression failed to achieve adequate covariate balance (defined as standardized mean differences exceeding 0.1), an alternative weighting approach—stable balancing weights (SBW)—[19] was applied using the WeightIt package in R [20].”
Influential
Penalizing women MPs: the approval of women-initiated bills in the Turkish parliament
Alemán, E., & Unal, S. K. (2023) · Journal of Legislative Studies · doi:10.1080/13572334.2023.2195142 · Cited by 2
“The goal is to balance the distributions of the observed covariates to remove bias produced by cofounding and produce stable estimates (Zubizarreta, 2015).”
Intended and Unintended Consequences of ERP System Implementation
Walton, S., Wheeler, P. R., & Zhang, Y. (2023) · Accounting Horizons · doi:10.2308/horizons-2020-192 · Cited by 2
Assessing a Community-Based Maternal Self-Efficacy Intervention in Rural India using a Quasi-Experimental Design
Jiwani, Z. (2024) · The Counseling Psychologist · doi:10.1177/00110000231215842 · Cited by 2
“Typically, IPWs are calculated using logistic regression, but this approach does not target the balancing of covariates and can lead to unstable estimates (Li & Li, 2021; Zubizarreta, 2015).”
Method
Copula-based pairwise estimator for quantile regression with hierarchical missing data
Verhasselt, A., Flórez, A. J., Molenberghs, G., et al. (2024) · Statistical Modelling · doi:10.1177/1471082x231225806 · Cited by 2
“Nevertheless, instability in the estimates can be encountered when some of the calculated weights are large (Zubizarreta, 2015).”
Optimal refinement of strata to balance covariates
Brumberg, K., Small, D. S., & Rosenbaum, P. R. (2024) · Biometrics · doi:10.1093/biomtc/ujae061 · Cited by 2
Robust weights that optimally balance confounders for estimating marginal hazard ratios
Santacatterina, M. (2023) · Statistical Methods in Medical Research · doi:10.1177/09622802221146310 · Cited by 2
“As discussed by Yiu and Su,21 by minimizing the variance of the weights while controlling for a measure of balance, ROW is constructed in the spirit of SBW.19 However, differently from SBW which has not been adapted to deal with continuous treatments to date, ROW can also be used to estimate effects of continuous trea…”
Background
Statistical Inference for Causal Effects in Clinical Psychology
Mozer, R., Rubin, D. B., & Zubizarreta, J. R. (2020) · Cambridge University Press eBooks · doi:10.1017/9781316995808.038 · Cited by 2
An introduction to flexible methods for policy evaluation
Huber, M. (2021) · Edward Elgar Publishing eBooks · doi:10.4337/9781788976480.00010 · Cited by 2
Generalized full matching and extrapolation of the results from a large-scale voter mobilization experimentPreprint
Sävje, F., Higgins, M., & Sekhon, J. S. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1703.03882 · Cited by 3
Estimating Average Treatment Effects: Supplementary Analyses and Remaining ChallengesPreprint
Athey, S. C., Imbens, G. W., Pham, T., & Wager, S. (2017) · RePEc: Research Papers in Economics · doi:10.48550/arxiv.1702.01250 · Cited by 2
Optimal Estimation of Generalized Average Treatment Effects using Kernel Optimal MatchingPreprint
Kallus, N., & Santacatterina, M. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1908.04748 · Cited by 2
“Zubizarreta (2018). Handling limited overlap in observational studies with cardinality matching. Observational Studies 4, 217–249. Waterman, B. R., P. J. Belmont Jr, and A. J. Schoenfeld (2012). Low back pain in the united states: incidence and risk factors for presentation in the emergency setting.”
BackgroundInfluential
Double Robust Representation Learning for Counterfactual PredictionPreprint
Zeng, S., Assaad, S., Tao, C., Datta, S., Carin, L., & Li, F. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2010.07866 · Cited by 2
“Important directions for future research include exploring other balancing weights methods (Deville & Särndal, 1992; Kallus, 2019; Zubizarreta, 2015) and generalizing into the learning problem with panel data (Abadie et al.”
Method
Treatment Effects Estimation by Uniform TransformerPreprint
Yu, R., & Wang, S. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2008.03738 · Cited by 2
“In order to make weighting methods more robust, several optimization-based weighting methods have been proposed recently (Imai and Ratkovic, 2014; Zubizarreta, 2015; Chan et al., 2016; Fan et al., 2016; Zhao, 2019; Wang and Zubizarreta, 2020).”
BackgroundMethodInfluential
Semiparametric Single-Index Estimation for Average Treatment EffectsPreprint
Huang, D., Gao, J., & Oka, T. (2022) · SSRN Electronic Journal · doi:10.2139/ssrn.4134564 · Cited by 3
A Computational Framework for Solving Nonlinear Binary Optimization Problems in Robust Causal Inference
Islam, M. S., Morshed, M. S., & Noor‐E‐Alam, M. (2022) · INFORMS journal on computing · doi:10.1287/ijoc.2022.1226 · Cited by 1
“In recent years, discrete optimization models have been developed [1, 14, 8, 15] to solve matching problems that directly aim to minimize the imbalance metrics.”
Background
Scalable kernel balancing weights in a nationwide observational study of hospital profit status and heart attack outcomes
Kim, K.-H., Niknam, B. A., & Zubizarreta, J. R. (2023) · Biostatistics · doi:10.1093/biostatistics/kxad032 · Cited by 1
“…program with linear constraints, which are efficiently solved via a specialized first-order alternating direction method of multipliers (Stellato et al. 2020), yielding the stable kernel balancing weights of minimum dispersion that approximately balance the covariate functions (Zubizarreta 2015).”
BackgroundMethodInfluential
Entropy balancing versus vector-based kernel weighting for causal inference in categorical treatment settings
Feyman, Y., Lum, J., Asfaw, D. A., et al. (2024) · Health Services and Outcomes Research Methodology · doi:10.1007/s10742-024-00331-8 · Cited by 1
“…it has not been compared against VBKW. Understanding the relative performance of EB is important, particularly in the broader context of optimal weighting strategies that minimize weight variability while satisfying balancing constraints (Zubizarreta 2015; Santacatterina and Bottai 2018).”
Cauchy-Schwarz bounded trade-off weighting for causal inference with small sample sizes
Qin, M., Tu, S., & Xu, L. (2024) · International Journal of Approximate Reasoning · doi:10.1016/j.ijar.2024.109311 · Cited by 1
Accommodating informative visit times for analysing irregular longitudinal data: a sensitivity analysis approach with balancing weights estimators
Yiu, S., & Su, L. (2025) · Journal of the Royal Statistical Society Series C (Applied Statistics) · doi:10.1093/jrsssc/qlaf002 · Cited by 1
“…likelihood estimation (MLE), which dramatically improved the performance of inverse probability weighted estimators for handling missing data in cross-sectional settings and dropout in longitudinal studies (e.g., see Graham et al., 2012; Zubizarreta, 2015; Han, 2016; Tan, 2020; Yiu and Su, 2022).”
Robust propensity score estimation via loss function calibration
Shang, Y., Chiu, Y., & Kong, L. (2025) · Statistical Methods in Medical Research · doi:10.1177/09622802241308709 · Cited by 1
“19,20 To test the robustness of our proposed method under model misspeciﬁcation, we replicated this simulation setting and examined the empirical performance of the proposed method under different model misspeciﬁcations.”
Economic and clinical outcomes of cesarean deliveries with skin closure using 2-octyl cyanoacrylate plus polymer mesh tape versus conventional smooth sutures plus waterproof wound dressings
Johnston, S. S., Gunja, N. J., Jha, A., et al. (2025) · The Journal of Maternal-Fetal & Neonatal Medicine · doi:10.1080/14767058.2025.2463390 · Cited by 1
“To retain all patients in the 2OPMT group, patients in the CS-WWD cohort were weighted to resemble those in the 2OPMT cohort on the study covariates using optimization-based stable balancing weights [19].”
IJMPR Didactic Paper: Weighting for Causal Inference in Mental Health Research
Cohn, E. R., & Zubizarreta, J. R. (2025) · International Journal of Methods in Psychiatric Research · doi:10.1002/mpr.70018 · Cited by 1
“The marginal and interaction designs implement the stable balancing weights (SBW) approach of (Zubizarreta 2015) which maximizes the effective sample size subject to approximate balance constraints on the basis functions, where the degree of approximate balance and the basis functions are inputs to…”
Statistical balancing as an unconstrained optimisation problem
Longford, N. T. (2025) · Australian & New Zealand Journal of Statistics · doi:10.1111/anzs.70004 · Cited by 1
Multi-level phenotypic models of cardiovascular disease and obstructive sleep apnea comorbidities: A longitudinal Wisconsin sleep cohort study
Nguyen, D. T., Hoang, C., Truong, T., Nguyen, D. H., Lam, H. G., Sharma, A., Le, T., & Huynh, P. K. (2025) · PLoS ONE · doi:10.1371/journal.pone.0327977 · Cited by 5
Confounding adjustment with propensity scores for overlap weighting in observational studies: a concise primer
Rizk, J. G. (2025) · Expert Review of Clinical Pharmacology · doi:10.1080/17512433.2025.2546151 · Cited by 1
“In contrast, prasugrel is typically prescribed to younger patients at higher ischemic risk, such as those with diabetes [17,18].”
Covariate Balancing With Measurement Error
Wen, X., & Yan, Y. (2025) · Statistics in Medicine · doi:10.1002/sim.70300 · Cited by 1
The Consequences of Elite Action Against Elections
Porter, R., Harden, J. J., Anderson, E. J., de Freitas, G., Dobson, M. R., Hemmen, A., & Schroeder, E. (2025) · British Journal of Political Science · doi:10.1017/s0007123425100926 · Cited by 1
1-Year Outcomes of TAVR With ACURATE neo2 vs SAPIEN/Evolut
Rück, A., Settergren, M., Saleh, N., et al. (2025) · JACC: Cardiovascular Interventions · doi:10.1016/j.jcin.2025.09.025 · Cited by 1
A study on the impact of open doors: investigating the influence of short leave and open prison on recidivism rates
Neumann, M., Schüttler, H., & Klatt, T. (2026) · Journal of Experimental Criminology · doi:10.1007/s11292-026-09741-9 · Cited by 3
Integration of aggregate data in causally interpretable meta-analysis by inverse weighting
Vo, T., Le, T. T. K., Afach, S., & Vansteelandt, S. (2026) · Biometrics · doi:10.1093/biomtc/ujag107 · Cited by 8
Doubly robust augmented weighting estimators for the analysis of externally controlled single-arm trials and unanchored indirect treatment comparisons
Campbell, H., & Remiro‐Azócar, A. (2026) · Research Synthesis Methods · doi:10.1017/rsm.2026.10106 · Cited by 2
“Moreover, one could go beyond the marginal moments of individual covariates and also balance joint covariate distributions; for instance, by including quantiles of interactions for pairs or triples of covariates.”
Reweighted nonparametric likelihood inference for linear functionals
Adusumilli, K., Otsu, T., & Qiu, C. (2023) · Electronic Journal of Statistics · doi:10.1214/23-ejs2168 · Cited by 1
A Weighted Sample Framework to Incorporate External Calculators for Risk Modeling
Ghosh, D., & Sabel, M. S. (2021) · Statistics in Biosciences · doi:10.1007/s12561-021-09325-3 · Cited by 1
Causal Reasoning Methods in Medical Domain: A Review
Wu, X., Li, J., Qian, Q., et al. (2022) · Lecture notes in computer science · doi:10.1007/978-3-031-08530-7_16 · Cited by 1
Balancing weights for region-level analysis: The effect of Medicaid expansion on the uninsurance rate among states that did not expand Medicaid
Rubinstein, M., Haviland, A. M., & Choi, D. S. (2023) · The Annals of Applied Statistics · doi:10.1214/22-aoas1678 · Cited by 1
“…to generate weights that enforce covariate balance between the treated and control units (see, e.g., Hainmueller (2012), Imai and Ratkovic (2014), Zubizarreta (2015)).1 From an applied perspective, there are at least four benefits of this approach: first, it does not require iterating propensity…”
BackgroundMethodInfluential
Statistical Challenges for Causal Inference Using Time-to-Event Real-World Data
Wang, J., Zhang, H., & Tiwari, R. C. (2023) · Springer eBooks · doi:10.1007/978-3-031-26328-6_13 · Cited by 1
Mortality analysed by propensity score matching: an application to national neonatal audit
Longford, N. T. (2023) · Brazilian Journal of Biometrics · doi:10.28951/bjb.v41i4.617 · Cited by 1
“For example, mipmatch (Zubizarreta, 2012), sbw (Zubizarreta, 2015) and rcbalance (Pimentel, 2016), are packages implemented in R .”
Self-reported preoperative depressive symptoms and survival after cardiac surgery
Falk, A. S., Sartipy, U., & Stenman, M. (2024) · European Journal of Cardio-Thoracic Surgery · doi:10.1093/ejcts/ezae076 · Cited by 1
Mahalanobis balancing: A multivariate perspective on approximate covariate balancing
Dai, Y., & Yan, Y. (2024) · Scandinavian Journal of Statistics · doi:10.1111/sjos.12721 · Cited by 1
“The MDABW method (Wang & Zubizarreta, 2020; Zubizarreta, 2015) ∑ , where 𝛿 = ( 𝛿 1 , … , 𝛿 K ) ⊤ , suggesting that A 1 is controlled by the MDABW method.”
Influential
How should we estimate inverse probability weights with possibly misspecified propensity score models?
Katsumata, H. (2024) · Political Science Research and Methods · doi:10.1017/psrm.2024.23 · Cited by 1
“This novel perspective, while acknowledged in previous works (Hainmueller, 2012; Zubizarreta, 2015; Li et al. , 2018), remains largely unexplored.”
BackgroundMethodInfluential
YKL-40 as a risk stratification marker in acute pancreatitis: A prospective study
Blažević, N., Trkulja, V., Rogić, D., Pelajić, S., Miler, M., Glavčić, G., Misir, Z., Živković, M., Nikolić, M., Lerotić, I., et al. (2024) · Pancreatology · doi:10.1016/j.pan.2024.11.024 · Cited by 1
A two-stage feature selection approach for robust evaluation of treatment effects in high-dimensional observational data
Islam, M. S., Shikalgar, S., & Noor‐E‐Alam, M. (2025) · IISE Transactions on Healthcare Systems Engineering · doi:10.1080/24725579.2024.2447715 · Cited by 3
“A wide variety of matching methods are employed to make ( t, c ) pairs (or subset C ⊂ C and T ∈ T ) as similar as possible (Zubizarreta, 2012, 2015; Rosenbaum and Rubin, 1983; Nikolaev et al., 2013) in terms of the covariate set X .”
Semiparametric single-index estimation for average treatment effects
Huang, D., Gao, J., & Oka, T. (2025) · Econometric Reviews · doi:10.1080/07474938.2025.2457561 · Cited by 1
“…of our proposed method with recent approaches to propensity score estimation based on covariates balancing (e.g., Imai and Ratkovic, 2014; Sant’Anna, Song, and Xu, 2022; Zubizarreta, 2015) and high-dimensional selection (e.g., Belloni et al., 2017; Chernozhukov et al., 2018; Sun and Tan, 2021).”
Influential
Continuous‐Time Causal Inference With Marked Point Process Weights: An Example on Sodium‐Glucose Co‐Transporters 2 Inhibitor Medications and Urinary Tract Infection
Kalia, S., Saarela, O., Chen, T., O’Neill, B. G., Meaney, C. A., Moineddin, R., Aliarzadeh, B., Sullivan, F., & Greiver, M. (2025) · Statistics in Medicine · doi:10.1002/sim.70102 · Cited by 2
Use of coronary artery bypass graft surgery and percutaneous coronary intervention and associated outcomes in the ISCHEMIA trial
White, H. D., O’Brien, S. M., Boden, W. E., Fremes, S. E., Bangalore, S., Reynolds, H. R., Stone, G. W., Ali, Z. A., Parakh, N., Lopez-Sendon, J. L., et al. (2025) · American Heart Journal · doi:10.1016/j.ahj.2025.05.009 · Cited by 1
Targeted quality measurement of health care providers
Li, Y., Keating, N. L., Landrum, M. B., & Zubizarreta, J. R. (2025) · Journal of the Royal Statistical Society Series A (Statistics in Society) · doi:10.1093/jrsssa/qnaf027 · Cited by 2
Covariates Distributions Balancing for Continuous Treatment
Jiang, Q., Xu, L. H., & Huang, C. (2022) · Economics Letters · doi:10.1016/j.econlet.2022.110644 · Cited by 1
Retrospective Comparison of Clinical and Economic Outcomes of Non-Donor Patients Undergoing Radical Nephrectomy Using One of Two Different Linear Stapler Technologies for Transection of the Renal Vessels: Fixed-Height Gripping Surface Reloads vs Variable-Height Reloads
Johnston, S. S., Johnson, B. H., Chakke, D., et al. (2022) · Medical Devices Evidence and Research · doi:10.2147/mder.s372629 · Cited by 1
“Statistical Analyses We used stable balancing weights (SBW), an optimization-based analogue to inverse propensity score weighting, to balance all study covariates listed above.(13) SBW directly targets covariate balance by treating weighting as an”
Method
Comparison of Clinical Outcomes of Gripping Surface Technology Staple Reloads versus Standard Staple Reloads Used with Manual Linear Surgical Staplers
Fortin, S., Petraiuolo, W. J., Cafri, G., et al. (2022) · Medical Devices Evidence and Research · doi:10.2147/mder.s393881 · Cited by 1
“To address potential confounding and systematic bias due to differences in baseline characteristics between study comparison groups, we performed covariate balancing using stable balancing weights, an optimization algorithm that finds the optimal set of weights meeting a set of prespecified balance criteria.(8) Specif…”
Method
Rejoinder: Estimands and their Estimators for Clinical Trials Impacted by the COVID-19 Pandemic: A Report from the NISS Ingram Olkin Forum Series on Unplanned Clinical Trial Disruptions
Lancker, K. V., Tarima, S. S., Bartlett, J. W., Bauer, M., Dharan, B., Bretz, F., Flournoy, N., Michiels, H., Parra, C. O., Rosenberger, J. L., et al. (2023) · Statistics in Biopharmaceutical Research · doi:10.1080/19466315.2022.2162958 · Cited by 1
“A more principled approach is to estimate the weights in a way that promotes stability, that is, prevents extreme weights (e.g., Imai and Ratkovic 2014; Zubizarreta 2015; Avagyan and Vansteelandt 2021).”
Background
Balancing Method for High Dimensional Causal InferencePreprint
Pham, T. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1702.04473 · Cited by 1
“Balancing weights has a long literature in machine learning, speciﬁcally in covariate shift problems (Reddi et al., 2015) as well as in causal inference area (Zubizarreta, 2015; Athey et al., 2016) among others; the latter focuses mostly on average treatment effect estimation though.”
Covariate Balancing by Uniform TransformerPreprint
Yu, R., & Wang, S. (2020) · arXiv (Cornell University) · Cited by 1
The Impact of Early Digital Movie Releases on Box Office Revenue: Evidence from the Korean MarketPreprint
Liang, Y., Burtch, G., Cho, D., & Smith, M. D. (2020) · SSRN Electronic Journal · doi:10.2139/ssrn.3749476 · Cited by 1
Statistical Analysis with Non-probability Survey Samples
Chen, Y. (2020) · UWSpace (University of Waterloo) · Cited by 1
Marginalization of Regression-Adjusted Treatment Effects in Indirect Comparisons with Limited Patient-Level DataPreprint
Remiro‐Azócar, A., Heath, A., & Baio, G. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2008.05951 · Cited by 3
Optimal transport weights for causal inferencePreprint
Dunipace, E. A. (2021) · RePEc: Research Papers in Economics · doi:10.48550/arxiv.2109.01991 · Cited by 1
Feature Selection for Causal Inference from High Dimensional Observational Data with Outcome Adaptive Elastic Net.Preprint
Islam, S., & Noor-E-Alam (2021) · arXiv (Cornell University) · Cited by 1
Data Imputation for Clinical Trial Emulation: A Case Study on Impact of Intracranial Pressure Monitoring for Traumatic Brain InjuryPreprint
Zhao, Z., Liu, R., Groner, J. I., Xiang, H., & Zhang, P. (2023) · medRxiv · doi:10.1101/2023.01.29.23285172 · Cited by 1
optweight: Optimization-Based Stable Balancing Weights
Greifer, N. (2018) · doi:10.32614/cran.package.optweight · Cited by 1
Essays on Cloud Pricing and Causal Inference
Kilcioglu, C. (2016) · doi:10.7916/d8r78f9q
“, 2012), entropy balancing (Hainmueller, 2012), stable balancing weights (Zubizarreta, 2015), calibration weighting (Chan et al.”
Background
Essays on Matching and Weighting for Causal Inference in Observational Studies
Juárez, R. (2017) · doi:10.7916/d8959w4h
“…(Normand et al., 2001), but the fact that two covariates have distributions with similar first moments does not imply that differences in other moments do not introduce bias in the effect estimates (see sections 2.4 and 2.5; a related formal argument is proposition 4.2 of Zubizarreta (2015)).”
BackgroundInfluential
Mathematical programming for optimal probability weighting
Santacatterina, M. (2018) · Figshare

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
DOI: 10.1080/01621459.2015.1023805
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

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

Stable Weights that Balance Covariates for Estimation With Incomplete Outcome Data

Abstract

Overview

Integrity signals

Verification

Claims the paper makes

Claims other papers make about this one

Citations

Cites

Cited by

Related

Metadata

Record

About these checks