Bayesian Regularized Regression for Treatment Effect Estimation from Observational Data

Hahn, P. Richard; Carvalho, Carlos M.; He, Jingyu; Puelz, David

doi:10.2139/ssrn.2728512

Cited by 5 publications

(5 citation statements)

References 22 publications

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“…Regularization for effect estimation is adopted from a Bayesian perspective in Hahn et al. () by reparameterizing the likelihood and using horseshoe priors on the regression coefficients. Ghosh et al.…”

Section: Introductionmentioning

confidence: 99%

“…Ertefaie et al (2018) addressed the issue of selecting weak confounders in small sample sizes by penalizing a joint likelihood on the exposure and outcome. Regularization for effect estimation is adopted from a Bayesian perspective in Hahn et al (2016) by reparameterizing the likelihood and using horseshoe priors on the regression coefficients. Ghosh et al (2015) utilized penalization in the potential outcomes framework, though their goal is to identify covariates that modify treatment effects.…”

Section: Introductionmentioning

confidence: 99%

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Doubly Robust Matching Estimators for High Dimensional Confounding Adjustment

et al. 2018

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Valid estimation of treatment effects from observational data requires proper control of confounding. If the number of covariates is large relative to the number of observations, then controlling for all available covariates is infeasible. In cases where a sparsity condition holds, variable selection or penalization can reduce the dimension of the covariate space in a manner that allows for valid estimation of treatment effects. In this article, we propose matching on both the estimated propensity score and the estimated prognostic scores when the number of covariates is large relative to the number of observations. We derive asymptotic results for the matching estimator and show that it is doubly robust in the sense that only one of the two score models need be correct to obtain a consistent estimator. We show via simulation its effectiveness in controlling for confounding and highlight its potential to address nonlinear confounding. Finally, we apply the proposed procedure to analyze the effect of gender on prescription opioid use using insurance claims data.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Doubly Robust Matching Estimators for High Dimensional Confounding Adjustment

et al. 2018

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“…Antonelli et al [14] utilized a fully Bayesian approach to estimating treatment effects in high-dimensions that reduces finite sample bias while eliminating the impact of instrumental variables through informative prior distributions on variable inclusion parameters. Hahn et al [15] utilized horseshoe priors on the coefficients from a re-parameterized likelihood to reduce shrinkage of variables that are associated with both the treatment and outcome. A large number of approaches have focused on obtaining uniformly valid inference of causal effects in high-dimensions [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Averaging causal estimators in high dimensions

Antonelli

Cefalu

2020

Journal of Causal Inference

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There has been increasing interest in recent years in the development of approaches to estimate causal effects when the number of potential confounders is prohibitively large. This growth in interest has led to a number of potential estimators one could use in this setting. Each of these estimators has different operating characteristics, and it is unlikely that one estimator will outperform all others across all possible scenarios. Coupling this with the fact that an analyst can never know which approach is best for their particular data, we propose a synthetic estimator that averages over a set of candidate estimators. Averaging is widely used in statistics for problems such as prediction, where there are many possible models, and averaging can improve performance and increase robustness to using incorrect models. We show that these ideas carry over into the estimation of causal effects in high-dimensional scenarios. We show theoretically that averaging provides robustness against choosing a bad model, and show empirically via simulation that the averaging estimator performs quite well, and in most cases nearly as well as the best among all possible candidate estimators. Finally, we illustrate these ideas in an environmental wide association study and see that averaging provides the largest benefit in the more difficult scenarios that have large numbers of confounders.

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“…Shortreed & Ertefaie (2017) used similar ideas by fitting an adaptive lasso to a propensity score model, and show that it leads to the inclusion of only covariates necessary for confounding adjustment or outcome model prediction. Hahn et al (2016) utilized horseshoe priors on a re-parameterized likelihood that aims to reduce shrinkage for important confounders. Athey et al (2016) combined high-dimensional regression with the balancing weights of Zubizarreta (2015) to obtain valid inference of treatment effects even when the true data generating models are not sparse.…”

Section: Introductionmentioning

confidence: 99%

High-Dimensional Confounding Adjustment Using Continuous Spike and Slab Priors

Antonelli¹,

Parmigiani²,

Dominici³

2019

Bayesian Anal.

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In observational studies, estimation of a causal effect of a treatment on an outcome relies on proper adjustment for confounding. If the number of the potential confounders (p) is larger than the number of observations (n), then direct control for all potential confounders is infeasible. Existing approaches for dimension reduction and penalization are generally aimed at predicting the outcome, and are less suited for estimation of causal effects. Under standard penalization approaches (e.g. Lasso), if a variable X j is strongly associated with the treatment T but weakly with the outcome Y , the coefficient β j will be shrunk towards zero thus leading to confounding bias. Under the assumption of a linear model for the outcome and sparsity, we propose continuous spike and slab priors on the regression coefficients β j corresponding to the potential confounders X j . Specifically, we introduce a prior distribution that does not heavily shrink to zero the coefficients (β j s) of the X j s that are strongly associated with T but weakly associated with Y . We compare our proposed approach to several state of the art methods proposed in the literature. Our proposed approach has the following features: 1) it reduces confounding bias in high dimensional settings; 2) it shrinks towards zero coefficients of instrumental variables; and 3) it achieves good coverages even in small sample sizes. We apply our approach to the National Health and Nutrition Examination Survey (NHANES) data to estimate the causal effects of persistent pesticide exposure on triglyceride levels.High-dimensional data; Causal inference; Bayesian variable selection; Shrinkage priors arXiv:1704.07532v5 [stat.ME]

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Bayesian Regularized Regression for Treatment Effect Estimation from Observational Data

Cited by 5 publications

References 22 publications

Doubly Robust Matching Estimators for High Dimensional Confounding Adjustment

Doubly Robust Matching Estimators for High Dimensional Confounding Adjustment

Averaging causal estimators in high dimensions

High-Dimensional Confounding Adjustment Using Continuous Spike and Slab Priors

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