Flexible Instrumental Variable Models With Bayesian Additive Regression Trees

TL;DR

This paper introduces a flexible nonlinear instrumental variable regression model using Bayesian additive regression trees, enabling complex confounding control and interaction modeling in observational data, exemplified by genetic data analysis.

Contribution

It develops a novel Bayesian regression tree-based instrumental variable method that relaxes linearity assumptions, allowing for nonlinear and interactive confounding adjustment.

Findings

Successfully modeled nonlinear BMI-blood pressure relationship.

Demonstrated method's effectiveness with UK Biobank genetic data.

Enhanced ability to handle complex confounding in observational studies.

Abstract

Methods utilizing instrumental variables have been a fundamental statistical approach to estimation in the presence of unmeasured confounding, usually occurring in non-randomized observational data common to fields such as economics and public health. However, such methods usually make constricting linearity and additivity assumptions that are inapplicable to the complex modeling challenges of today. The growing body of observational data being collected will necessitate flexible regression modeling while also being able to control for confounding using instrumental variables. Therefore, this article presents a nonlinear instrumental variable regression model based on Bayesian regression tree ensembles to estimate such relationships, including interactions, in the presence of confounding. One exciting application of this method is to use genetic variants as instruments, known as Mendelian randomization. Body mass index is one factor that is hypothesized to have a nonlinear relationship with cardiovascular risk factors such as blood pressure while interacting with age. Heterogeneity in patient characteristics such as age could be clinically interesting from a precision medicine perspective where individualized treatment is emphasized. We present our flexible Bayesian instrumental variable regression tree method with an example from the UK Biobank where body mass index is related to blood pressure using genetic variants as the instruments.