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Semiparametric Regression for Periodic Longitudinal Hormone Data from Multiple Menstrual Cycles
Author(s) -
Zhang Daowen,
Lin Xihong,
Sowers MaryFran
Publication year - 2000
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2000.00031.x
Subject(s) - semiparametric regression , mathematics , smoothing spline , nonparametric regression , estimator , nonparametric statistics , variance function , covariate , statistics , smoothing , semiparametric model , parametric statistics , bilinear interpolation , spline interpolation
Summary. We consider Semiparametric regression for periodic longitudinal data. Parametric fixed effects are used to model the covariate effects and a periodic nonparametric smooth function is used to model the time effect. The within–subject correlation is modeled using subject‐specific random effects and a random stochastic process with a periodic variance function. We use maximum penalized likelihood to estimate the regression coefficients and the periodic nonparametric time function, whose estimator is shown to be a periodic cubic smoothing spline. We use restricted maximum likelihood to simultaneously estimate the smoothing parameter and the variance components. We show that all model parameters can be easily obtained by fitting a linear mixed model. A common problem in the analysis of longitudinal data is to compare the time profiles of two groups, e.g., between treatment and placebo. We develop a scaled chi‐squared test for the equality of two nonparametric time functions. The proposed model and the test are illustrated by analyzing hormone data collected during two consecutive menstrual cycles and their performance is evaluated through simulations.