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Biostatistics Advance Access originally published online on October 5, 2005
Biostatistics 2006 7(2):225-234; doi:10.1093/biostatistics/kxj003
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© The Author 2005. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Functional mixed-effects model for periodic data

Li Qin*

Statistical Center for HIV/AIDS Research and Prevention, Fred Hutchinson Cancer Research Center, Seattle, WA 98109, USA lqin{at}scharp.org

Wensheng Guo

Department of Biostatistics and Epidemiology University of Pennsylvania School of Medicine, Philadelphia, PA 19104, USA

* To whom correspondence should be addressed.

Periodic data are frequently collected in biomedical experiments. We consider the underlying periodic curves giving rise to these data, and account for the periodicity in their functional model to improve estimation and inference. We propose to incorporate the periodic constraint in the functional mixed-effects model setting. Both the fixed functional effects and random functional effects are modeled in the same periodic functional space, hence the population-average estimates and subject-specific predictions are all periodic. An efficient algorithm is given to estimate the proposed model by an O(N) modified Kalman filtering and smoothing algorithm. The proposed method is evaluated in different scenarios through simulations. Treatments to none-full period data and missing observations along the period are also given. Analysis of a cortisol data set obtained from a study on fibromyalgia is conducted as illustration.

Keywords: Functional data analysis; Kalman filter; Periodic constraint; Periodic spline; Smoothing spline; State space model


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