Abstract: In regression analysis, covariate measurement error occurs in many applications. If a covariate variable of interest for a subject is the long-term average of some measurements, then in practice repeated measurements are considered surrogates for the true covariate. Surrogate variables, which are longitudinal, may be modeled as the sum of the unobserved true covariate and longitudinal errors, where the errors are dependent with a continuous correlation function of time. In this paper, we consider a flexible modeling of the correlation of the surrogate variable. This proposed polynomial correlation modeling is not as sensitive as an exponential type autocorrelation. A refined regression calibration estimator is studied for logistic regression. Simulation studies were conducted to examine the finite sample performance of a cubic correlation-based regression calibration estimator for exponential and piecewise-linear correlation models. The asymptotic covariance of the proposed estimator is given. The proposed method is applied to a study of adult obesity in relation to childhood body mass index.
Key words and phrases: Maximum likelihood, measurement error, polynomial regression, regression calibration.