A Bayesian approach to the g-formula

TL;DR

This paper introduces a Bayesian method for the g-formula in causal inference, enhancing estimation accuracy in small or sparse datasets, demonstrated through environmental tobacco smoke effects on children's BMI.

Contribution

It adapts the parametric g-formula to a Bayesian framework, providing algorithms and code for practical implementation in various data settings.

Findings

Bayesian g-formula improves causal effect estimates in small samples.

The approach is applicable to longitudinal and time-fixed data.

Demonstrated with real-world data on tobacco smoke and BMI.

Abstract

Epidemiologists often wish to estimate quantities that are easy to communicate and correspond to the results of realistic public health scenarios. Methods from causal inference can answer these questions. We adopt the language of potential outcomes under Rubin's original Bayesian framework and show that the parametric g-formula is easily amenable to a Bayesian approach. We show that the frequentist properties of the Bayesian g-formula suggest it improves the accuracy of estimates of causal effects in small samples or when data may be sparse. We demonstrate our approach to estimate the effect of environmental tobacco smoke on body mass index z-scores among children aged 4-9 years who were enrolled in a longitudinal birth cohort in New York, USA. We give a general algorithm and supply SAS and Stan code that can be adopted to implement our computational approach in both time-fixed and longitudinal data.