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An Analysis of Paediatric Cd4 Counts for Acquired Immune Deficiency Syndrome Using Flexible Random Curves

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  • Minggao Shi
  • Robert E. Weiss
  • Jeremy M. G. Taylor

Abstract

In this paper we analyse CD4 counts from infants born to mothers who are infected with the human immunodeficiency virus. A random effects model with linear or low order polynomials in time is unsatisfactory for these longitudinal data We develop an alternative approach based on a flexible family of models for which both the fixed and the random effects are linear combinations of β‐splines. The fixed and random parts are smooth functions of time and the covariance structure is parsimonious. The procedure allows estimates of each individual's smooth trajectory over time to be exhibited. Model selection, estimation and computation are discussed. Centile curves are presented that take into account the longitudinal nature of the data We emphasize a graphical approach to the presentation of results.

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  • Minggao Shi & Robert E. Weiss & Jeremy M. G. Taylor, 1996. "An Analysis of Paediatric Cd4 Counts for Acquired Immune Deficiency Syndrome Using Flexible Random Curves," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 45(2), pages 151-163, June.
    • Handle: RePEc:bla:jorssc:v:45:y:1996:i:2:p:151-163
    DOI: 10.2307/2986151
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    Cited by:

    1. Ming Xiong & Ao Yuan & Hong-Bin Fang & Colin O. Wu & Ming T. Tan, 2022. "Estimation and Hypothesis Test for Mean Curve with Functional Data by Reproducing Kernel Hilbert Space Methods, with Applications in Biostatistics," Mathematics, MDPI, vol. 10(23), pages 1-17, December.
    2. Boland, Joanna & Telesca, Donatello & Sugar, Catherine & Jeste, Shafali & Goldbeck, Cameron & Senturk, Damla, 2022. "A study of longitudinal trends in time-frequency transformations of EEG data during a learning experiment," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    3. Justin Petrovich & Matthew Reimherr & Carrie Daymont, 2022. "Highly irregular functional generalized linear regression with electronic health records," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(4), pages 806-833, August.
    4. Peihua Qiu & Lu You, 2022. "Dynamic disease screening by joint modelling of survival and longitudinal data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1158-1180, November.
    5. Mengfei Ran & Yihe Yang, 2022. "Optimal Estimation of Large Functional and Longitudinal Data by Using Functional Linear Mixed Model," Mathematics, MDPI, vol. 10(22), pages 1-28, November.
    6. Park, Yeonjoo & Simpson, Douglas G., 2019. "Robust probabilistic classification applicable to irregularly sampled functional data," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 37-49.
    7. Mingfei Dong & Donatello Telesca & Catherine Sugar & Frederick Shic & Adam Naples & Scott P. Johnson & Beibin Li & Adham Atyabi & Minhang Xie & Sara J. Webb & Shafali Jeste & Susan Faja & April R. Lev, 2023. "A Functional Model for Studying Common Trends Across Trial Time in Eye Tracking Experiments," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(1), pages 261-287, April.

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