The parametric g-formula for time-to-event data: intuition and a worked example.

Abstract

The parametric g-formula can be used to estimate the effect of a policy, intervention, or treatment. Unlike standard regression approaches, the parametric g-formula can be used to adjust for time-varying confounders that are affected by prior exposures. To date, there are few published examples in which the method has been applied. We provide a simple introduction to the parametric g-formula and illustrate its application in an analysis of a small cohort study of bone marrow transplant patients in which the effect of treatment on mortality is subject to time-varying confounding. Standard regression adjustment yields a biased estimate of the effect of treatment on mortality relative to the estimate obtained by the g-formula. The g-formula allows estimation of a relevant parameter for public health officials: the change in the hazard of mortality under a hypothetical intervention, such as reduction of exposure to a harmful agent or introduction of a beneficial new treatment. We present a simple approach to implement the parametric g-formula that is sufficiently general to allow easy adaptation to many settings of public health relevance.