title: On using summary statistics from an external calibration sample to correct for covariate measurement error.
abstract: BACKGROUND
  Covariate measurement error is common in epidemiologic studies. Current methods for correcting measurement error with information from external calibration samples are insufficient to provide valid adjusted inferences. We consider the problem of estimating the regression of an outcome Y on covariates X and Z, where Y and Z are observed, X is unobserved, but a variable W that measures X with error is observed. Information about measurement error is provided in an external calibration sample where data on X and W (but not Y and Z) are recorded.
  
  
  METHODS
  We describe a method that uses summary statistics from the calibration sample to create multiple imputations of the missing values of X in the regression sample, so that the regression coefficients of Y on X and Z and associated standard errors can be estimated using simple multiple imputation combining rules, yielding valid statistical inferences under the assumption of a multivariate normal distribution.
  
  
  RESULTS
  The proposed method is shown by simulation to provide better inferences than existing methods, namely the naive method, classical calibration, and regression calibration, particularly for correction for bias and achieving nominal confidence levels. We also illustrate our method with an example using linear regression to examine the relation between serum reproductive hormone concentrations and bone mineral density loss in midlife women in the Michigan Bone Health and Metabolism Study.
  
  
  CONCLUSIONS
  Existing methods fail to adjust appropriately for bias due to measurement error in the regression setting, particularly when measurement error is substantial. The proposed method corrects this deficiency.
authors.affiliation: Merck & Co, Inc, Rahway, NJ , USA. ying.guo2@merck.com
authors.forename: Ying
authors.initials: Y
authors.lastname: Guo
authors.forename: Roderick J
authors.initials: RJ
authors.lastname: Little
authors.forename: Daniel S
authors.initials: DS
authors.lastname: McConnell
mesh_terms: D000704:Analysis of Variance; D015519:Bone Density; D001842:Bone and Bones / Q000378:metabolism; D016001:Confidence Intervals; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D016014:Linear Models; D008824:Michigan / Q000453:epidemiology; D008875:Middle Aged; D015999:Multivariate Analysis; D012044:Regression Analysis; D012107:Research Design / Q000706:statistics & numerical data; D012738:Sex Hormone-Binding Globulin / Q000032:analysis
chemical_list: D012738:Sex Hormone-Binding Globulin