  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.
