Revisiting the g-null paradox

TL;DR

This paper clarifies the g-null paradox in causal inference, illustrating how model misspecification can bias estimates when using the parametric g-formula, emphasizing the need for sufficiently flexible models.

Contribution

It provides a detailed analysis and simulation evidence explaining the g-null paradox, guiding practitioners to avoid overly simplistic models in causal effect estimation.

Findings

Model misspecification leads to bias under the g-null paradox.

Flexible models reduce bias in the parametric g-formula.

Analytic and simulation examples illustrate the paradox's implications.

Abstract

The parametric g-formula is an approach to estimating causal effects of sustained treatment strategies from observational data. An often cited limitation of the parametric g-formula is the g-null paradox: a phenomenon in which model misspecification in the parametric g-formula is guaranteed under the conditions that motivate its use (i.e., when identifiability conditions hold and measured time-varying confounders are affected by past treatment). Many users of the parametric g-formula know they must acknowledge the g-null paradox as a limitation when reporting results but still require clarity on its meaning and implications. Here we revisit the g-null paradox to clarify its role in causal inference studies. In doing so, we present analytic examples and a simulation-based illustration of the bias of parametric g-formula estimates under the conditions associated with this paradox. Our results highlight the importance of avoiding overly parsimonious models for the components of the g-formula when using this method.