title: Multiple Imputation to Account for Measurement Error in Marginal Structural Models.
abstract: 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.
authors.affiliation: 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.
authors.forename: Jessie K
authors.initials: JK
authors.lastname: Edwards
authors.forename: Stephen R
authors.initials: SR
authors.lastname: Cole
authors.forename: Daniel
authors.initials: D
authors.lastname: Westreich
authors.forename: Heidi
authors.initials: H
authors.lastname: Crane
authors.forename: Joseph J
authors.initials: JJ
authors.lastname: Eron
authors.forename: W Christopher
authors.initials: WC
authors.lastname: Mathews
authors.forename: Richard
authors.initials: R
authors.lastname: Moore
authors.forename: Stephen L
authors.initials: SL
authors.lastname: Boswell
authors.forename: Catherine R
authors.initials: CR
authors.lastname: Lesko
authors.forename: Michael J
authors.initials: MJ
authors.lastname: Mugavero
mesh_terms: D019380:Anti-HIV Agents / Q000627:therapeutic use*; D015982:Bias; D003627:Data Interpretation, Statistical; D015987:Effect Modifier, Epidemiologic; D005260:Female; D005500:Follow-Up Studies; D015658:HIV Infections / Q000188:drug therapy* / Q000401:mortality; D006801:Humans; D008297:Male; D015233:Models, Statistical; D009010:Monte Carlo Method; D064887:Observational Studies as Topic; D012907:Smoking / Q000009:adverse effects*; D014481:United States
chemical_list: D019380:Anti-HIV Agents