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Joint Modeling and Clustering Paired Generalized Longitudinal Trajectories With Application to Cocaine Abuse Treatment Data

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  • Hui Huang
  • Yehua Li
  • Yongtao Guan

Abstract

In a cocaine dependence treatment study, we have paired binary longitudinal trajectories that record the cocaine use patterns of each patient before and after a treatment. To better understand the drug-using behaviors among the patients, we propose a general framework based on functional data analysis to jointly model and cluster these paired non-Gaussian longitudinal trajectories. Our approach assumes that the response variables follow distributions from the exponential family, with the canonical parameters determined by some latent Gaussian processes. To reduce the dimensionality of the latent processes, we express them by a truncated Karhunen-Lóeve (KL) expansion allowing the mean and covariance functions to be different across clusters. We further represent the mean and eigenfunctions functions by flexible spline bases, and determine the orders of the truncated KL expansions using data-driven methods. By treating the cluster membership as a missing value, we cluster the cocaine use trajectories by a likelihood-based approach. The cluster membership and parameter estimates are jointly estimated by a Monte Carlo EM algorithm with Gibbs sampling steps. We discover subgroups of patients with distinct behaviors in terms of overall probability to use, binge verses periodic use pattern, etc. The joint modeling approach also sheds new lights on relating relapse behavior to baseline pattern in each subgroup. Supplementary materials for this article are available online.

Suggested Citation

  • Hui Huang & Yehua Li & Yongtao Guan, 2014. "Joint Modeling and Clustering Paired Generalized Longitudinal Trajectories With Application to Cocaine Abuse Treatment Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1412-1424, December.
  • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:508:p:1412-1424
    DOI: 10.1080/01621459.2014.957286
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    Cited by:

    1. Tengteng Xu & Riquan Zhang & Xiuzhen Zhang, 2023. "Estimation of spatial-functional based-line logit model for multivariate longitudinal data," Computational Statistics, Springer, vol. 38(1), pages 79-99, March.
    2. Yifan Zhu & Chongzhi Di & Ying Qing Chen, 2019. "Clustering Functional Data with Application to Electronic Medication Adherence Monitoring in HIV Prevention Trials," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(2), pages 238-261, July.
    3. Cai Li & Luo Xiao & Sheng Luo, 2022. "Joint model for survival and multivariate sparse functional data with application to a study of Alzheimer's Disease," Biometrics, The International Biometric Society, vol. 78(2), pages 435-447, June.
    4. Gertheiss, Jan & Goldsmith, Jeff & Staicu, Ana-Maria, 2017. "A note on modeling sparse exponential-family functional response curves," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 46-52.
    5. Li, Yehua & Qiu, Yumou & Xu, Yuhang, 2022. "From multivariate to functional data analysis: Fundamentals, recent developments, and emerging areas," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    6. Julia Wrobel & Vadim Zipunnikov & Jennifer Schrack & Jeff Goldsmith, 2019. "Registration for exponential family functional data," Biometrics, The International Biometric Society, vol. 75(1), pages 48-57, March.
    7. Pan, Lanfeng & Li, Yehua & He, Kevin & Li, Yanming & Li, Yi, 2020. "Generalized linear mixed models with Gaussian mixture random effects: Inference and application," Journal of Multivariate Analysis, Elsevier, vol. 175(C).

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