Inference for multiple treatment effects using confounder importance learning

TL;DR

This paper introduces a Bayesian model averaging framework with data-driven priors to improve inference of multiple treatment effects amid many confounders, balancing confounder inclusion and variance inflation.

Contribution

It proposes a novel empirical Bayes approach that learns prior inclusion probabilities for covariates, with fast algorithms and implementation in the R package mombf.

Findings

Provides insights into salary variation and discriminatory factors.

Reassesses the link between abortion policies and crime.

Offers a scalable, data-adaptive confounder adjustment method.

Abstract

We address modelling and computational issues for multiple treatment effect inference under many potential confounders. Our main contribution is providing a trade-off between preventing the omission of relevant confounders, while not running into an over-selection of instruments that significantly inflates variance. We propose a novel empirical Bayes framework for Bayesian model averaging that learns from data the prior inclusion probabilities of key covariates. Our framework sets a data-dependent prior that asymptotically matches the true amount of confounding in the data, as measured by a novel confounding coefficient. A key challenge is computational. We develop fast algorithms, using an exact gradient of the marginal likelihood that has linear cost in the number of covariates, and a variational counterpart. Our framework uses widely-used ingredients and largely existing software, and it is implemented within the R package mombf. We illustrate our work with two applications. The first is the association between salary variation and discriminatory factors. The second, that has been debated in previous works, is the association between abortion policies and crime. Our approach provides insights that differ from previous analyses especially in situations with weaker treatment effects.