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Joint modelling of multivariate longitudinal outcomes and a time-to-event: A nonlinear latent class approach

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  • Proust-Lima, Cécile
  • Joly, Pierre
  • Dartigues, Jean-François
  • Jacqmin-Gadda, Hélène

Abstract

A joint model based on a latent class approach is proposed to explore the association between correlated longitudinal quantitative markers and a time-to-event. A longitudinal latent class model describes latent profiles of evolution of the latent process underlying the correlated markers. The latent process is linked to the markers by nonlinear transformations including parameters to be estimated. A proportional hazard model describes the joint risk of event according to the latent classes and two specifications of the risk function are considered: a parametric function and a semi-parametric function based on splines. Depending on the chosen risk function, estimation is performed by a maximum likelihood or a maximum penalized likelihood approach. A simulation study validates the estimation procedure. As a latent class model relies on the strong assumption that the markers and the time-to-event are independent conditionally on the latent classes, a test of conditional independence is proposed using the residuals conditional on time-to-event. The procedure does not require any posterior classification and can be conducted using standard statistical softwares. The methodology is applied to describe profiles of cognitive decline in the elderly and their associated risk of dementia.

Suggested Citation

  • Proust-Lima, Cécile & Joly, Pierre & Dartigues, Jean-François & Jacqmin-Gadda, Hélène, 2009. "Joint modelling of multivariate longitudinal outcomes and a time-to-event: A nonlinear latent class approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1142-1154, February.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:1142-1154
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    References listed on IDEAS

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    Cited by:

    1. Anaïs Rouanet & Pierre Joly & Jean‐François Dartigues & Cécile Proust‐Lima & Hélène Jacqmin‐Gadda, 2016. "Joint latent class model for longitudinal data and interval‐censored semi‐competing events: Application to dementia," Biometrics, The International Biometric Society, vol. 72(4), pages 1123-1135, December.
    2. Rizopoulos, Dimitris, 2012. "Fast fitting of joint models for longitudinal and event time data using a pseudo-adaptive Gaussian quadrature rule," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 491-501.
    3. Jesse D. Raffa & Joel A. Dubin, 2015. "Multivariate longitudinal data analysis with mixed effects hidden Markov models," Biometrics, The International Biometric Society, vol. 71(3), pages 821-831, September.
    4. Bernhardt, Paul W. & Zhang, Daowen & Wang, Huixia Judy, 2015. "A fast EM algorithm for fitting joint models of a binary response and multiple longitudinal covariates subject to detection limits," Computational Statistics & Data Analysis, Elsevier, vol. 85(C), pages 37-53.
    5. Brian Neelon & A. James O'Malley & Sharon-Lise T. Normand, 2011. "A Bayesian Two-Part Latent Class Model for Longitudinal Medical Expenditure Data: Assessing the Impact of Mental Health and Substance Abuse Parity," Biometrics, The International Biometric Society, vol. 67(1), pages 280-289, March.
    6. Alejandra Marroig & Graciela Muniz-Terrera, 2023. "Latent Class approach to analyze children’s nutritional trajectory and school dropout. A longitudinal population-based application," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(2), pages 1519-1531, April.
    7. Proust-Lima, Cécile & Philipps, Viviane & Liquet, Benoit, 2017. "Estimation of Extended Mixed Models Using Latent Classes and Latent Processes: The R Package lcmm," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 78(i02).
    8. Teng Fei & John Hanfelt & Limin Peng, 2023. "Evaluating the association between latent classes and competing risks outcomes with multiphenotype data," Biometrics, The International Biometric Society, vol. 79(1), pages 488-501, March.
    9. Hélène Jacqmin-Gadda & Cécile Proust-Lima & Jeremy M.G. Taylor & Daniel Commenges, 2010. "Score Test for Conditional Independence Between Longitudinal Outcome and Time to Event Given the Classes in the Joint Latent Class Model," Biometrics, The International Biometric Society, vol. 66(1), pages 11-19, March.
    10. Brisa N. Sánchez & Shan Kang & Bhramar Mukherjee, 2012. "A Latent Variable Approach to Study Gene–Environment Interactions in the Presence of Multiple Correlated Exposures," Biometrics, The International Biometric Society, vol. 68(2), pages 466-476, June.

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