Regression Calibration for Nonlinear Functions of Mismeasured Predictors

• Activity Number: 252
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 2:00 PM to 3:50 PM
• Sponsor: WNAR
• Author(s): David Yanez*+ and Quenna Wong and Jeffrey R. Wilson
• Companies: University of Washington and Collaborative Health Studies Coordinating Center and The University of Utah
• Keywords: errors in variables ; non-linear predictors ; calculated variables ; measurement errors ; Taylor series

Abstract

We investigate a problem in regression where interest is on the association between an outcome, Y, and a predictor, f(X), where f is a differentiable function, X is unobserved but imprecisely measured by W. If auxiliary data (e.g., replicates, validation data) are available and f is a linear function of X, regression calibration (RC) provides a convenient way to investigate the association between Y and f(X). The RC solution is exact for linear models and approximately correct for non-linear models. If f is a non-linear function, however, RC cannot be used in the usual fashion. In this paper, we employ a straight-forward approach that uses a Taylor Series approximation to obtain a RC-type solution to this problem. The solution can also be extended to scalar functions of multiple variables, provide replicates are available on each variable measured with error. An illustration is provided.