Multiple Imputation to Account for Measurement Error in Marginal Structural Models

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


Background: 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.

Methods: 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.

Results: 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).

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

Publication types

  • Research Support, N.I.H., Extramural

MeSH terms

  • Anti-HIV Agents / therapeutic use*
  • Bias*
  • Data Interpretation, Statistical*
  • Effect Modifier, Epidemiologic
  • Female
  • Follow-Up Studies
  • HIV Infections / drug therapy*
  • HIV Infections / mortality
  • Humans
  • Male
  • Models, Statistical*
  • Monte Carlo Method
  • Observational Studies as Topic
  • Smoking / adverse effects*
  • United States


  • Anti-HIV Agents