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Penalized likelihood approach to estimate a smooth mean curve on longitudinal data
Author(s) -
JacqminGadda Hélène,
Joly Pierre,
Commenges Daniel,
Binquet Christine,
Chêne Geneviève
Publication year - 2002
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.1225
Subject(s) - akaike information criterion , mathematics , statistics , estimator , frequentist inference , bayes' theorem , bayesian probability , marginal likelihood , deviance information criterion , markov chain monte carlo , bayesian inference
Abstract This paper aims to propose a penalized likelihood approach to estimate a smooth mean curve for the evolution with time of a Gaussian variable taking into account the correlation structure of longitudinal data. The model is an extension of the mixed effects linear model including an unspecified function of time f ( t ). The estimator f̂ ( t ) is defined as the solution of the maximization of the penalized likelihood and is approximated on a basis of cubic M‐spline with a reduced number of knots. We present modifications of four criteria (cross‐validation, generalized cross‐validation, T of Rice, Akaike's criterion) to estimate the smoothing parameter when data are correlated; these four criteria gave very similar results in the simulation study. The simulation study showed also the superiority of the Bayesian confidence bands of the mean curve over the frequentist ones. We develop empirical Bayes estimates of subject‐specific deviations. This approach was applied to study the progression of CD4+ lymphocyte counts in a cohort of HIV patients treated with protease inhibitors. Copyright © 2002 John Wiley & Sons, Ltd.