Revisiting the g-null Paradox

The (noniterative conditional expectation) 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 in some settings consistent with 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 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.

Automated summary

The noniterative conditional expectation parametric g-formula is an approach to estimating causal effects of sustained treatment strategies from observational data. However, it has a limitation known as the g-null paradox, where model misspecification is guaranteed in certain situations. This study aims to clarify the role of the g-null paradox in causal inference studies by presenting analytic examples and simulation-based illustrations of bias in parametric g-formula estimates under the conditions associated with this paradox. Our results emphasize the importance of avoiding overly parsimonious models when using this method.