High-Dimensional Confounding Adjustment Using Continuous Spike and Slab Priors

Abstract

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]

The How and Why of Bayesian Nonparametric Causal Inference

“…Similar priors that prioritize covariates associated with both the treatment and outcome have been developed in various contexts (see Wang et al, 2015;Antonelli et al, 2017;Wilson et al, 2018;Antonelli et al, 2019;Papadogeorgou and Dominici, 2020). While most of these approaches specifically focus on estimation using an outcome model, these ideas have also been extended to doubly robust estimators (Cefalu et al, 2017;Antonelli et al, 2020); see Section 7 for a discussion of double robustness.…”

Bayesian Approaches to Shrinkage and Sparse Estimation

“…post-double selection to overcome such bias. Hahn et al (2018) and Antonelli et al (2019) offer Bayesian counterparts in linear models, using shrinkage priors.…”

Comment: Regularization via Bayesian Penalty Mixing

“…In large part facilitated by further Bayesian considerations, the SSL has recently enjoyed a variety of elaborations and developments. These include variants of the SSL for high-dimensional confounding adjustment in causal analysis (Antonelli, Parmigiani, and Dominici (2019), for highdimensional Bayesian varying coefficient models , for grouped regression and sparse generalized additive models , for simultaneous variable and covariance selection in multivariate regression (Deshpande, Ročková, and George 2019), for graphical models with unequal shrinkage (Gan, Narisetty, and Liang (2019), for regression with unknown error variance (Moran, Ročková, and George 2019), for Bayesian biclustering (Moran, Ročková, and George 2020), for fast Bayesian factor analysis via automatic rotations to sparsity (Ročková and George 2016), for variable selection in time series (Ročková and McAlinn 2020), for generalized linear models (Tang, Shen, Zhang and Yi 2017a), and for the Cox survival model (Tang, Shen, Zhang and Yi 2017b).…”