Regression Analysis on a Covariate with Heteroscedastic Measurement Error

• Activity Number: 437
• Type: Topic Contributed
• Date/Time: Wednesday, August 5, 2009 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Ying Guo*+ and Roderick J.A. Little
• Companies: University of Michigan and University of Michigan
• Keywords: measurement error ; heteroscedastic ; multiple imputation ; regression calibration

Abstract

We consider the estimation of the regression of an outcome D on a covariate X, where X is unobserved, but a variable Y which measures X with error is observed. A calibration sample that measures pairs of values of X and Y is also available. One common approach for measurement error correction is Regression Calibration (RC), which substitutes the unknown values of X by predictions from the calibration curve of X on Y. An alternative approach is to multiply impute the missing values of X given Y and D based on an imputation model. Freedman et al (2008) compares these two approaches. However, their work assumes the measurement error of Y has a constant variance, whereas in many situations, the variance varies as a function of X. We consider modifications of RC and MI that allow for heteroscedastic measurement error, and compare them by simulation. MI is shown to provide better inferences.