Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2012 Aug 15;31(18):2000-9.
doi: 10.1002/sim.5316. Epub 2012 Apr 11.

The parametric g-formula to estimate the effect of highly active antiretroviral therapy on incident AIDS or death

Daniel Westreich  1 , Stephen R Cole, Jessica G Young, Frank Palella, Phyllis C Tien, Lawrence Kingsley, Stephen J Gange, Miguel A Hernán
Affiliations

The parametric g-formula to estimate the effect of highly active antiretroviral therapy on incident AIDS or death

Daniel Westreich et al. Stat Med. .

Abstract

The parametric g-formula can be used to contrast the distribution of potential outcomes under arbitrary treatment regimes. Like g-estimation of structural nested models and inverse probability weighting of marginal structural models, the parametric g-formula can appropriately adjust for measured time-varying confounders that are affected by prior treatment. However, there have been few implementations of the parametric g-formula to date. Here, we apply the parametric g-formula to assess the impact of highly active antiretroviral therapy on time to acquired immune deficiency syndrome (AIDS) or death in two US-based human immunodeficiency virus cohorts including 1498 participants. These participants contributed approximately 7300 person-years of follow-up (49% exposed to highly active antiretroviral therapy) during which 382 events occurred and 259 participants were censored because of dropout. Using the parametric g-formula, we estimated that antiretroviral therapy substantially reduces the hazard of AIDS or death (hazard ratio = 0.55; 95% confidence limits [CL]: 0.42, 0.71). This estimate was similar to one previously reported using a marginal structural model, 0.54 (95% CL: 0.38, 0.78). The 6.5-year difference in risk of AIDS or death was 13% (95% CL: 8%, 18%). Results were robust to assumptions about temporal ordering, and extent of history modeled, for time-varying covariates. The parametric g-formula is a viable alternative to inverse probability weighting of marginal structural models and g-estimation of structural nested models for the analysis of complex longitudinal data.

PubMed Disclaimer

Figures

FIGURE 1
FIGURE 1
Time-ordering of variables. For each visit j, we assume the order (Zij, Cij, Yij, Xij).
FIGURE 2
FIGURE 2
Number at risk, and number of endpoints, by length of study follow up for 1,498 participants.
FIGURE 3
FIGURE 3
Absolute risk of AIDS or death over follow-up in the never treated (solid black), observed (solid gray), natural course (dotted gray), and always treated (dotted black) g-formula scenarios.
See this image and copyright information in PMC

References

    1. Robins JM. A new approach to causal inference in mortality studies with sustained exposure periods – application to control of the healthy worker survivor effect. Mathe Model. 1986;7:1393–1512.
    1. Robins JM. Structural nested failure time models. In: Armitage P, Colton T, editors. Encyclopedia of Biostatistics. Chichester, UK: John Wiley & Sons; 1998. pp. 4372–4389.
    1. Robins JM, Hernán MA, Brumback B. Marginal structural models and causal inference in epidemiology. Epidemiology. 2000;11:550–560. - PubMed
    1. Hernán MA, Hernandez-Diaz S, Robins JM. A structural approach to selection bias. Epidemiology. 2004;15(5):615–625. - PubMed
    1. Cole SR, Platt RW, Schisterman EF, Chu H, Westreich D, Richardson D, Poole C. Illustrating bias due to conditioning on a collider. Int J Epidemiol. 2010;39(2):417–420. - PMC - PubMed

Publication types

Grants and funding

LinkOut - more resources