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. 2014 Nov;25(6):889-97.
doi: 10.1097/EDE.0000000000000160.

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

Alexander P Keil  1 , Jessie K Edwards, David B Richardson, Ashley I Naimi, Stephen R Cole
Affiliations

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

Alexander P Keil et al. Epidemiology. 2014 Nov.

Abstract

Background: 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.

Methods: 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.

Results: Standard regression adjustment yields a biased estimate of the effect of treatment on mortality relative to the estimate obtained by the g-formula.

Conclusions: 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.

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Figures

Figure 1
Figure 1
Directed acyclic graph showing hypothesized causal relationships among study variables for days k − 1 and k. This graph demonstrates bias in regression stratification methods in estimating the effect of exposure over time (GνHDk−1, GνHDk) on subsequent death when time-varying factors on confounding pathways (Relapsek) may be affected by prior exposure.
Figure 2
Figure 2
Parametric g-formula algorithm for bone marrow transplant data.
Figure 3
Figure 3
Incidence curves for (A.) death. (B.) return to normal platelet levels, (C.) relapse and (D.) graft-versus-host-disease (GvHD) from both observed (gray line) and g-formula natural course Monte Carlo (black line) data.
Figure 3
Figure 3
Incidence curves for (A.) death. (B.) return to normal platelet levels, (C.) relapse and (D.) graft-versus-host-disease (GvHD) from both observed (gray line) and g-formula natural course Monte Carlo (black line) data.
Figure 3
Figure 3
Incidence curves for (A.) death. (B.) return to normal platelet levels, (C.) relapse and (D.) graft-versus-host-disease (GvHD) from both observed (gray line) and g-formula natural course Monte Carlo (black line) data.
Figure 3
Figure 3
Incidence curves for (A.) death. (B.) return to normal platelet levels, (C.) relapse and (D.) graft-versus-host-disease (GvHD) from both observed (gray line) and g-formula natural course Monte Carlo (black line) data.
Figure 4
Figure 4
Survival functions: observed from the bone marrow transplant data; from the natural-course intervention in the g-formula; and from the hypothetical intervention “prevented” graft-versus-host disease (top line) after bone marrow transplants using the g-formula. The gray line indicates the observed survival curve, while the solid black lines indicate the survival curves from the Monte Carlo data for the g-formula interventions.
See this image and copyright information in PMC

Comment in

References

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