Covariate balancing propensity score by tailored loss functions

By Qingyuan Zhao. Annals of Statistics, 2016

165 citations recorded by the source corpus.

In observational studies, propensity scores are commonly estimated by maxi- mum likelihood but may fail to balance high-dimensional pre-treatment covariates even after specification search. We introduce a general framework that unifies and generalizes several recent proposals to improve covariate balance when designing an observational study. In- stead of the likelihood function, we propose to optimize special loss functions---covariate balancing scoring rules (CBSR)---to estimate the propensity score. A CBSR is uniquely determined by the link function in the GLM and the estimand (a weighted average treatment effect). We show CBSR does not lose asymptotic efficiency to the Bernoulli likelihood in estimating the weighted average treatment effect compared, but CBSR is much more robust in finite sample. Borrowing tools developed in statistical learning, we propose practical strategies to balance covariate functions in rich function classes. This is useful to estimate the maximum bias of the inverse probability weighting (IPW) estimators and construct honest confidence interval in finite sample. Lastly, we provide several numerical examples to demonstrate the trade-off of bias and variance in the IPW-type estimators and the trade-off in balancing different function classes of the covariates.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ca6db7c4903d0026cd49917ffda2836d5614210f

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Citations in the corpus

Synthetic Difference In Differences (2018, unknown): “…some similarity to the work on “balancing” methods for program evaluation under unconfoundedness, including Athey, Imbens, and Wager ( 2018 ) ; Graham, Pinto, and Egel ( 2012 ) ; Hirshberg and Wager ( 2017 ) ; Imai and Ratkovic ( 2014 ) ; Kallus ( 2020 ) ; Zhao ( 2019 ); and Zubizarreta ( 2015 ) .”
The Balancing Act in Causal Inference (2021, background): “See BenMichael, Feller, and Rothstein (2021), Wang and Zubizarreta (2020), and Zhao (2019) for related discussions.”
Augmented minimax linear estimation (2017, unknown): “Imai and Ratkovic, 2014; Kallus, 2016; Wang and Zubizarreta, 2017; Zhao, 2016; Zubizarreta, 2015).”
Matching for Balance (2019, methodology): “Examples of weighting methods for covariate balance include Hainmueller (2012), Imai and Ratkovic (2014), Zubizarreta (2015), Chan et al. (2016), Fan et al. (2016), Zhao and Percival (2017), Athey et al. (2018), Hirshberg and Wager (2018), Zhao (2019), and Wang and Zubizarreta (2017).”
Minimal dispersion approximately balancing weights: asymptotic properties and practical considerations (2017, methodology): “Zhao, Q. (2016). Covariate balancing propensity score by tailored loss functions.”
Covariate balancing propensity score for a continuous treatment: Application to the efficacy of political advertisements (2018, background): “In recent years, several researchers have proposed methods that estimate propensity scores by optimizing covariate balance (e.g., McCaffrey et al., 2004; Tan, 2010; Hainmueller, 2012; Graham et al., 2012; Imai and Ratkovic, 2014; Chan et al., 2015; Hazlett, 2016; Fan et al., 2016; Zhao, 2016).”
Sensitivity analysis for inverse probability weighting estimators via the percentile bootstrap (2017, background): “In principle, our approach can be extended to other causal estimands and propensity score weighting schemes (e.g. Li and Greene (2013), Li et al. (2018) and Zhao (2019)), with the caveat that the corresponding optimization problems (counterparts to problem (4.12)) are not always easy to solve.”