A Regularization/Extrapolation Corrected Score Method for Nonlinear Regression Models with Covariate Error

• Activity Number: 524
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: ENAR
• Author(s): David Zucker*+ and Malka Gorfine and Yi Li and Donna Spiegelman
• Companies: Hebrew University and Israel Institute of Technology and Dana-Farber Cancer Institute/Harvard School of Public Health and Harvard School of Public Health
• Keywords: Errors in variables ; nonlinear models ; logistic regression

Abstract

Many regression analyses involve explanatory variables that are measured with error, and ignoring this error leads to biased estimates for the regression coefficients. We present a new general method for adjusting for covariate error. Our method consists of an approximate version of the Stefanski-Nakamura corrected score approach, using the method of regularization for approximate solution of integral equations, along with an extrapolation device similar in spirit to that of the SIMEX method. Specifically, we compute estimates for various values of the regularization penalty parameter and extrapolate to a penalty parameter of zero. We develop the theory in the setting of classical likelihood models, covering nonlinear regression, logistic regression, and Poisson regression. The method is extremely general in terms of the types of measurement error models covered, and is a functional method in the sense of not requiring information on the distribution of the true covariate. We present a simulation study in the logistic regression setting, and provide an illustration on data from the Harvard Nurses' Health Study concerning the relationship between physical activity and breast cancer.