# Revisiting the g-null paradox

arXiv: https://arxiv.org/abs/2103.03857 · HTML: https://mlsanity.com/paper/2103.03857/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Mar 2021.

## Built on by (most cited first, 3 of 3)

- [A Kernel Test for Causal Association via Noise Contrastive Backdoor Adjustment](https://mlsanity.com/paper/2111.13226/) (2021)
- [Deep Learning Methods for the Noniterative Conditional Expectation G-Formula for Causal Inference from Complex Observational Data](https://mlsanity.com/paper/2410.21531/) (2024)
- [A flexible Bayesian g-formula for causal survival analyses with time-dependent confounding](https://mlsanity.com/paper/2402.02306/) (2024)

## Abstract (arXiv)

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.