Balancing Covariates via Propensity Score Weighting

By Fan Li, Kari Lock Morgan, Alan M. Zaslavsky. 2014

998 citations recorded by the source corpus.

ABSTRACT Covariate balance is crucial for unconfounded descriptive or causal comparisons. However, lack of balance is common in observational studies. This article considers weighting strategies for balancing covariates. We define a general class of weights—the balancing weights—that balance the weighted distributions of the covariates between treatment groups. These weights incorporate the propensity score to weight each group to an analyst-selected target population. This class unifies existing weighting methods, including commonly used weights such as inverse-probability weights as special cases. General large-sample results on nonparametric estimation based on these weights are derived. We further propose a new weighting scheme, the overlap weights, in which each unit’s weight is proportional to the probability of that unit being assigned to the opposite group. The overlap weights are bounded, and minimize the asymptotic variance of the weighted average treatment effect among the class of balancing weights. The overlap weights also possess a desirable small-sample exact balance property, based on which we propose a new method that achieves exact balance for means of any selected set of covariates. Two applications illustrate these methods and compare them with other approaches.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/70b328ba320bbbe9ba516d4442ec22b3fecd80e5

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Citations in the corpus

Propensity Score Weighting for Causal Inference with Clustered Data (2017, background): “, the average causal effects over a subset of population [71, 72, 73], including the average causal effect on the treated.”
Overlap in observational studies with high-dimensional covariates (2017, background): “X1:p)} ∈ [η,1 −η]. 4An alternative strategy is to estimate a weighted average of the conditional treatment eﬀect, e.g., τw = E{w(X1:p)τ(X1:p)} with w(X1:p) ∝ e(X1:p){1 − e(X1:p)} (Crump et al., 2006; Li et al., 2018). This estimand downweights the units with propensity scores close to zero and one, ”
A regression discontinuity design for ordinal running variables: Evaluating central bank purchases of corporate bonds (2019, background): “Among the general class of balancing weights, of particular relevance to our application is the overlap weights (Li et al., 2018), (w0 = e(xi), w1 = 1 − e(xi)), corresponding to h(xi) = e(xi)(1−e(xi)), the maximum of which is attained at e(xi) = 0.”
Sensitivity analysis for inverse probability weighting estimators via the percentile bootstrap (2017, background): “Li and Greene (2013), Li et al. (2018) and Zhao (2019)), with the caveat that the corresponding optimization problems (counterparts to problem (4.”
The Augmented Synthetic Control Method (2018, background): “(2016), and Li et al. (2017) for related examples with slightly different forms.”
Augmented minimax linear estimation (2017, background): “, Newey, W. and Robins, J. (2018). Double/De-Biased Machine Learning Using Regularized Riesz Representers.”
Inference on a New Class of Sample Average Treatment Effects (2017, background): “(2)A related literature discusses the idea of an optimal estimand in terms of covariate balance in observational studies (Crump et al., 2009; Li et al., 2016).”
Covariate balancing propensity score by tailored loss functions (2016, methodology): “This corresponds to the “overlap weights” recently proposed by Li et al. (2016), where each observation’s weight is proportional to the probability of being assigned to the opposite group.”
Minimal dispersion approximately balancing weights: asymptotic properties and practical considerations (2017, methodology): “. (2016), Zhao and Percival (2017), Wong and Chan (2018), and Zhao (2018). Earlier and related methods include Deville and Särndal (1992), Hellerstein and Imbens (1999), Imai and Ratkovic (2014), and Li et al. (2018). Two promising methods that use similar weights together with outcome information a”
A Survey on Causal Inference (2020, background): “In [75], the overlap weight is proposed, in which each unit’s weight is proportional to the probability of that unit being assigned to the opposite group.”
Estimating Average Treatment Effects: Supplementary Analyses and Remaining Challenges (2017, background): “This orthogonality property (Neyman and Scott [1948], Lancaster [2000], Chernozhukov et al.”
The Balancing Act in Causal Inference (2021, neutral): “…et al. (2018), Breidt, Opsomer, et al. (2017), Chan et al. (2016), Deville and Särndal (1992), Graham et al. (2012), Hainmueller (2012), Hirshberg and Wager (2018), Imai and Ratkovic (2014), Kallus (2020), Li et al. (2018), Tan (2020), Wong and Chan (2018), Zhao (2019), and Zubizarreta (2015).”
Asymptotic inference of causal effects with observational studies trimmed by the estimated propensity scores (2018, background): “In contrast, another smooth weight function, the overlap weight function ω{e(X )} = e(X ){1 − e(X )} recently proposed by Li et al. (2018), overweighs units with propensity scores close to 0·5 and thus does not target τ(O).”
Contamination Bias in Linear Regressions (2021, positive): “When the treatment is binary, this estimator reduces to the estimator studied in Li et al. (2018).”