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A Bayesian quantile joint modeling of multivariate longitudinal and time-to-event data

Author

Listed:
  • Damitri Kundu

    (Indian Statistical Institute)

  • Shekhar Krishnan

    (Tata Medical Center)

  • Manash Pratim Gogoi

    (Tata Medical Center)

  • Kiranmoy Das

    (Indian Statistical Institute
    Beijing Institute of Mathematical Sciences and Applications)

Abstract

Linear mixed models are traditionally used for jointly modeling (multivariate) longitudinal outcomes and event-time(s). However, when the outcomes are non-Gaussian a quantile regression model is more appropriate. In addition, in the presence of some time-varying covariates, it might be of interest to see how the effects of different covariates vary from one quantile level (of outcomes) to the other, and consequently how the event-time changes across different quantiles. For such analyses linear quantile mixed models can be used, and an efficient computational algorithm can be developed. We analyze a dataset from the Acute Lymphocytic Leukemia (ALL) maintenance study conducted by Tata Medical Center, Kolkata. In this study, the patients suffering from ALL were treated with two standard drugs (6MP and MTx) for the first two years, and three biomarkers (e.g. lymphocyte count, neutrophil count and platelet count) were longitudinally measured. After treatment the patients were followed nearly for the next three years, and the relapse-time (if any) for each patient was recorded. For this dataset we develop a Bayesian quantile joint model for the three longitudinal biomarkers and time-to-relapse. We consider an Asymmetric Laplace Distribution (ALD) for each outcome, and exploit the mixture representation of the ALD for developing a Gibbs sampler algorithm to estimate the regression coefficients. Our proposed model allows different quantile levels for different biomarkers, but still simultaneously estimates the regression coefficients corresponding to a particular quantile combination. We infer that a higher lymphocyte count accelerates the chance of a relapse while a higher neutrophil count and a higher platelet count (jointly) reduce it. Also, we infer that across (almost) all quantiles 6MP reduces the lymphocyte count, while MTx increases the neutrophil count. Simulation studies are performed to assess the effectiveness of the proposed approach.

Suggested Citation

  • Damitri Kundu & Shekhar Krishnan & Manash Pratim Gogoi & Kiranmoy Das, 2024. "A Bayesian quantile joint modeling of multivariate longitudinal and time-to-event data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 30(3), pages 680-699, July.
    • Handle: RePEc:spr:lifeda:v:30:y:2024:i:3:d:10.1007_s10985-024-09622-1
    DOI: 10.1007/s10985-024-09622-1
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    References listed on IDEAS

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    1. Hanze Zhang & Yangxin Huang, 2020. "Quantile regression-based Bayesian joint modeling analysis of longitudinal–survival data, with application to an AIDS cohort study," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(2), pages 339-368, April.
    2. Marco Alfò & Maria Francesca Marino & Maria Giovanna Ranalli & Nicola Salvati & Nikos Tzavidis, 2021. "M‐quantile regression for multivariate longitudinal data with an application to the Millennium Cohort Study," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(1), pages 122-146, January.
    3. Kiranmoy Das & Michael J. Daniels, 2014. "A semiparametric approach to simultaneous covariance estimation for bivariate sparse longitudinal data," Biometrics, The International Biometric Society, vol. 70(1), pages 33-43, March.
    4. Hemant Kulkarni & Jayabrata Biswas & Kiranmoy Das, 2019. "A joint quantile regression model for multiple longitudinal outcomes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(4), pages 453-473, December.
    5. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
    6. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    7. Jayabrata Biswas & Kiranmoy Das, 2021. "A Bayesian quantile regression approach to multivariate semi-continuous longitudinal data," Computational Statistics, Springer, vol. 36(1), pages 241-260, March.
    8. Kiranmoy Das, 2016. "A semiparametric Bayesian approach for joint modeling of longitudinal trait and event time," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(15), pages 2850-2865, November.
    9. Umberto Picchini & Andrea De Gaetano & Susanne Ditlevsen, 2010. "Stochastic Differential Mixed‐Effects Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(1), pages 67-90, March.
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