Bayesian Analysis of Treatment Effect Models

Li, Mingliang; Tobias, Justin L.

doi:10.1002/9781118771051.ch3

Cited by 10 publications

(3 citation statements)

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“…In terms of implementation, this paper builds explicitly on the work of ; see also Gramacy and Lee (2008) and Murray (2017). Other notable work on Bayesian treatment effect estimation includes Gustafson and Greenland (2006), Zigler and Dominici (2014), Heckman et al (2014), Li and Tobias (2014), Roy et al (2017) and Taddy et al (2016).…”

Section: Relationship To Previous Literaturementioning

confidence: 99%

Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects (with Discussion)

2020

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This paper presents a novel nonlinear regression model for estimating heterogeneous treatment effects, geared specifically towards situations with small effect sizes, heterogeneous effects, and strong confounding by observables. Standard nonlinear regression models, which may work quite well for prediction, have two notable weaknesses when used to estimate heterogeneous treatment effects. First, they can yield badly biased estimates of treatment effects when fit to data with strong confounding. The Bayesian causal forest model presented in this paper avoids this problem by directly incorporating an estimate of the propensity function in the specification of the response model, implicitly inducing a covariatedependent prior on the regression function. Second, standard approaches to response surface modeling do not provide adequate control over the strength of regularization over effect heterogeneity. The Bayesian causal forest model permits treatment effect heterogeneity to be regularized separately from the prognostic effect of control variables, making it possible to informatively "shrink to homogeneity". While we focus on observational data, our methods are equally useful for inferring heterogeneous treatment effects from randomized controlled experiments where careful regularization is somewhat less complicated but no less important. We illustrate these benefits via the reanalysis of an observational study assessing the causal effects of smoking on medical expenditures as well as extensive simulation studies.

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Section: Relationship To Previous Literaturementioning

confidence: 99%

Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects (with Discussion)

2020

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“…Other notable work on Bayesian treatment effect estimation includes Gustafson and Greenland (2006), Zigler and Dominici (2014), Heckman, Lopes and Piatek (2014), Li and Tobias (2014), ?…”

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confidence: 99%

Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects

2017

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This paper develops a semi-parametric Bayesian regression model for estimating heterogeneous treatment effects from observational data. Standard nonlinear regression models, which may work quite well for prediction, can yield badly biased estimates of treatment effects when fit to data with strong confounding. Our Bayesian causal forest model avoids this problem by directly incorporating an estimate of the propensity function in the specification of the response model, implicitly inducing a covariate-dependent prior on the regression function. This new parametrization also allows treatment heterogeneity to be regularized separately from the prognostic effect of control variables, making it possible to informatively "shrink to homogeneity", in contrast to existing Bayesian non-and semi-parametric approaches. We illustrate the benefits of this approach via the reanalysis of an observational study assessing the causal effects of smoking on medical expenditures as well as extensive simulation studies.

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“…Treatment effect estimation is an important topic with a long and varied literature; a comprehensive review is beyond the scope of this paper. For review articles from an expressly Bayesian perspective, see Li and Tobias (2014) or Heckman et al (2014). This paper focuses more narrowly on the impact of regularization or "shrinkage" priors on the estimation of treatment effects from observational studies.…”

Section: Variablementioning

confidence: 99%

Regularization and Confounding in Linear Regression for Treatment Effect Estimation

et al. 2018

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IN LINEAR REGRESSION FOR TREATMENT EFFECT ESTIMATIONThis paper investigates the use of regularization priors in the context of treatment effect estimation using observational data where the number of control variables is large relative to the number of observations. First, the phenomenon of "regularization-induced confounding" is introduced, which refers to the tendency of regularization priors to adversely bias treatment effect estimates by over-shrinking control variable regression coefficients. Then, a simultaneous regression model is presented which permits regularization priors to be specified in a way that avoids this unintentional "re-confounding".The new model is illustrated on synthetic and empirical data.1. Introduction. This paper considers the use of Bayesian regularized linear regression models for the purpose of estimating a treatment effect from observational data. Treatment effects -the amount some response variable would change if the value of the treatment variable were changed by a given amount -can only be properly estimated from observational data by taking into account all of the various explanatory factors that may otherwise account for the observed correlation between the treatment and response variables. In the case of a linear regression model (assuming it to be correct) this "adjustment for confounding" means that the model includes a sufficient set of control variables as regressors in addition to the treatment

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Bayesian Analysis of Treatment Effect Models

Cited by 10 publications

References 47 publications

Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects (with Discussion)

Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects (with Discussion)

Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects

Regularization and Confounding in Linear Regression for Treatment Effect Estimation

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