Parametric g-Formula

Both are g-methods that target the same kind of causal effect under the same assumptions, but they estimate it differently. The g-formula models the outcome and the full time-varying confounder process and simulates counterfactual worlds, whereas a marginal structural model reweights subjects by inverse probability of treatment so the confounder–exposure association is broken, then fits a simple outcome model on the pseudo-population. The g-formula is generally more efficient and handles dynamic regimes naturally, but it requires modeling the whole covariate process and is sensitive to its misspecification; weighting requires only treatment models but can be unstable under near-positivity violations. They are complementary and often reported together.

When a time-varying confounder is affected by prior exposure, it is simultaneously a confounder of later exposure and a mediator of earlier exposure. Conditioning on it in a single regression blocks the indirect pathway you want to estimate (over-adjustment) and can open a collider bias path, so the estimate is biased in a direction you cannot sign. The g-formula avoids conditioning entirely: it integrates over the confounder distribution under the intervened exposure history, which keeps the mediating role intact while still controlling confounding. This is the central reason g-methods exist.

The g-null paradox is the observation that, under the sharp causal null where exposure has no effect at any time on the outcome or on the covariates, it is generally impossible for all the parametric submodels in the g-formula to be simultaneously correctly specified. As a consequence a misspecified g-formula can reject a true null even in large samples. In practice it means you should fit flexible covariate and outcome models, check the natural-course simulation against observed data, and interpret a 'significant' effect cautiously when it is small. It is a real concern but manageable with careful modeling and diagnostics.