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Epidemiology. 2015 Sep;26(5):645-52. doi: 10.1097/EDE.0000000000000330.

Multiple Imputation to Account for Measurement Error in Marginal Structural Models.

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From the aDepartment of Epidemiology, University of North Carolina at Chapel Hill, Chapel Hill, NC; bDivision of Allergy and Infectious Diseases, Department of Medicine, University of Washington, Seattle, WA; cDivision of Infectious Diseases, Department of Medicine, University of North Carolina at Chapel Hill, Chapel Hill, NC; dSchool of Medicine, University of California, San Diego, San Diego, CA; eSchool of Medicine, Johns Hopkins University, Baltimore, MD; fFenway Health, Boston, MA; and gDivision of Infectious Diseases, Department of Medicine, University of Alabama at Birmingham, Birmingham, AL.



Marginal structural models are an important tool for observational studies. These models typically assume that variables are measured without error. We describe a method to account for differential and nondifferential measurement error in a marginal structural model.


We illustrate the method estimating the joint effects of antiretroviral therapy initiation and current smoking on all-cause mortality in a United States cohort of 12,290 patients with HIV followed for up to 5 years between 1998 and 2011. Smoking status was likely measured with error, but a subset of 3,686 patients who reported smoking status on separate questionnaires composed an internal validation subgroup. We compared a standard joint marginal structural model fit using inverse probability weights to a model that also accounted for misclassification of smoking status using multiple imputation.


In the standard analysis, current smoking was not associated with increased risk of mortality. After accounting for misclassification, current smoking without therapy was associated with increased mortality (hazard ratio [HR]: 1.2 [95% confidence interval [CI] = 0.6, 2.3]). The HR for current smoking and therapy [0.4 (95% CI = 0.2, 0.7)] was similar to the HR for no smoking and therapy (0.4; 95% CI = 0.2, 0.6).


Multiple imputation can be used to account for measurement error in concert with methods for causal inference to strengthen results from observational studies.

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