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.