Transformations of Covariates for Longitudinal Data

• Activity Number: 18
• Type: Contributed
• Date/Time: Sunday, August 11, 2002 : 2:00 PM to 3:50 PM
• Sponsor: General Methodology
• Author(s): Wesley Thompson*+
• Affiliation(s): Rutgers University
• Keywords: Longitudinal Data ; Box-Tidwell Transformation ; Fractional Polynomials ; Generalized Estimating Equations

Abstract

This paper develops a general approach for dealing with parameteric transformations of covariates for longitudinal data, where the responses are modelled marginally and the generalized estimating equations (GEE) (Liang and Zeger, 1986) are used for estimation of regression parameters. An iterative algorithm for obtaining regression and transformation parameters from estimating equations is proposed, where we utilize existing software for GEE problems. The technique used in the algorithm is closely related to that used in the Box-Tidwell transformation in the classical linear regressions, but we are developing it under the GEE setting and for more general transformation functions, including fractional polynomials, among others. Supporting theorems are provided, giving conditions for consistency and asymptotic normality of estimators. A score-based test and a "naive" likelihood ratio test for inference between two nested models are considered. The proposed parametric approach is a complement to the nonparametric regression approaches recently developed in longitudinal data settings.