Transformations of covariates for longitudinal data.
This paper develops a general approach for dealing with parametric transformations of covariates for longitudinal data, where the responses are modeled marginally and generalized estimating equations (GEEs) are used for estimation of regression parameters. We propose an iterative algorithm for obtaining regression and transformation parameters from estimating equations, utilizing existing software for GEE problems. The algorithmic technique is closely related to that used in the Box-Tidwell transformation in classical linear regression, but we develop it under the GEE setting and for more general transformation functions. We provide supporting theorems for consistency and asymptotic Normality of the estimates. Inference between two nested models is also considered. This methodology is applied to two data sets. One consists of pill dissolution data, the other is taken from the Pittsburgh Youth Study (PYS). The PYS is a prospective longitudinal study of the development of delinquency, substance use, and mental health in male youth. We use the model-based parametric approach to examine the association between alcohol use at an early stage of adolescent development and delinquency over the course of adolescence.
Thompson
Wesley K
WK
Department of Statistics, Rutgers University, Piscataway, NJ 08855, USA.
Xie
Minge
M
White
Helene R
HR
D000293:Adolescent; D000328:Adult; D000428:Alcohol Drinking / Q000453:epidemiology; D000465:Algorithms; D003415:Crime; D003627:Data Interpretation, Statistical; D006801:Humans; D007604:Juvenile Delinquency; D008137:Longitudinal Studies; D008297:Male; D015233:Models, Statistical; D012984:Software; D012995:Solubility; D013607:Tablets / Q000737:chemistry; D013997:Time Factors
D013607:Tablets