Causal Inference
Bayesian g-formula and causal sensitivity analysis for survival outcomes Kevin Chen* Kevin Chen Sally Picciotto Ellen Eisen Patrick Bradshaw
Background. Parametric g-formula analyses are typically conducted from a frequentist point of view. However, a Bayesian approach can facilitate causal sensitivity analyses that account for systematic sources of error. We extend existing Bayesian formulations of the parametric g-formula to survival outcomes and settings where there may be unobserved time-varying confounding affected by past exposure. Throughout, we considered two types of hypothetical interventions: the first limits exposure to a hypothetical maximum but allows exposures below that limit to vary naturally; the second sets exposure to a hypothetical value.
Methods. We formulated and applied the Bayesian g-formula to simulated data to explore how conclusions might differ under three scenarios. We refer to the first scenario, where we utilized the full data including confounders, as ideal. In the second scenario (naive), we failed to account for unobserved time-varying confounders. In the final scenario (sensitivity), we conducted bias analyses using the Bayesian g-formula by including the unobserved time-varying confounders as latent variables governed by moderately informative priors in the parametric structural causal model.
Results. In our Bayesian g-formula analyses, the average difference between the posterior medians (triangles in the figure) and the true causal risk differences (orange lines) was similar in the sensitivity scenario to that in the ideal scenario. The average difference was several times larger in the naive scenario.
Conclusion. In contrast to the frequentist parametric g-formula, the Bayesian g-formula allows for coherent incorporation of suspected sources of bias to achieve bias-corrected point estimates that are close to the truth. The Bayesian g-formula may offer improved inferences in settings where accounting for an unobserved variable, such as a time-varying confounder, are desirable.
