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The Stata Journal
Volume 4 Number 4: pp. 402-420

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Controlling for time–dependent confounding using marginal structural models

Zoe Fewell
University of Bristol, UK
Zoe.Fewell@bristol.ac.uk
 Miguel A. Hernán
Harvard School of
Public Health, USA
mhernan@hsph.harvard.edu
Frederick Wolfe
National Data Bank for
Rheumatic Diseases, USA
fwolfe@arthritis-research.org
 Kate Tilling
University of Bristol, UK
Kate.Tilling@bristol.ac.uk
Hyon Choi
Harvard Medical School, USA
hchoi@partners.org
 Jonathan A. C. Sterne
University of Bristol, UK
Jonathan.Sterne@bristol.ac.uk
Abstract.   Longitudinal studies in which exposures, confounders, and outcomes are measured repeatedly over time have the potential to allow causal inferences about the effects of exposure on outcome. There is particular interest in estimating the causal effects of medical treatments (or other interventions) in circumstances in which a randomized controlled trial is difficult or impossible. However, standard methods for estimating exposure effects in longitudinal studies are biased in the presence of time-dependent confounders affected by prior treatment.

This article describes the use of marginal structural models (described by Robins, Hernán, and Brumback [2000]) to estimate exposure or treatment effects in the presence of time-dependent confounders affected by prior treatment. The method is based on deriving inverse-probability-of-treatment weights, which are then used in a pooled logistic regression model to estimate the causal effect of treatment on outcome. We demonstrate the use of marginal structural models to estimate the effect of methotrexate on mortality in persons suffering from rheumatoid arthritis.
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View all articles by these authors: Zoe Fewell, Miguel A. Hernán, Frederick Wolfe, Kate Tilling, Hyon Choi, Jonathan A. C. Sterne

View all articles with these keywords: marginal structural models, causal models, weighted regression, survival analysis, logistic regression, confounding

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