Covariate-adjusted varying coefficient models

Covariate-adjusted regression was recently proposed for situations where both predictors and response in a regression model are not directly observed, but are observed after being contaminated by unknown functions of a common observable covariate. The method has been appealing because of its flexibility in targeting the regression coefficients under different forms of distortion. We extend this methodology proposed for regression into the framework of varying coefficient models, where the goal is to target the covariate-adjusted relationship between longitudinal variables. The proposed method of covariate-adjusted varying coefficient model (CAVCM) is illustrated with an analysis of a longitudinal data set containing calcium absorbtion and intake measurements on 188 subjects. We estimate the age-dependent relationship between these two variables adjusted for the covariate body surface area. Simulation studies demonstrate the flexibility of CAVCM in handling different forms of distortion in the longitudinal setting.