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

Damitri Kundu1, Shekhar Krishnan2, Manash Pratim Gogoi2

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Summary

This study introduces a Bayesian quantile joint model to analyze longitudinal biomarkers and relapse time in Acute Lymphocytic Leukemia (ALL) patients. The model reveals that higher lymphocyte counts increase relapse risk, while higher neutrophil and platelet counts decrease it, with specific drug effects observed.

Keywords:
Acute lymphocytic leukemia (ALL)Asymmetric laplace distribution (ALD)Joint modelMCMCQuantile regression

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Area of Science:

  • Biostatistics
  • Clinical Research
  • Computational Biology

Background:

  • Traditional linear mixed models struggle with non-Gaussian longitudinal data and event-time outcomes.
  • Quantile regression offers a more appropriate approach for non-Gaussian data, allowing analysis across different outcome levels.
  • Understanding how time-varying covariates influence event-time across various outcome quantiles is crucial for complex diseases.

Purpose of the Study:

  • To develop and apply a Bayesian quantile joint model for simultaneously analyzing longitudinal biomarkers and time-to-relapse in Acute Lymphocytic Leukemia (ALL) patients.
  • To investigate the impact of longitudinal biomarker levels on relapse risk across different quantiles.
  • To assess the effects of treatments (6MP and MTx) on biomarkers and their relationship with relapse time.

Main Methods:

  • A Bayesian quantile joint model was developed for three longitudinal biomarkers (lymphocyte, neutrophil, platelet counts) and time-to-relapse.
  • The Asymmetric Laplace Distribution (ALD) was used for outcomes, with its mixture representation enabling a Gibbs sampler algorithm for parameter estimation.
  • The model allows for different quantile levels for each biomarker while simultaneously estimating regression coefficients for specific quantile combinations.

Main Results:

  • Higher lymphocyte counts were found to accelerate relapse risk, whereas higher neutrophil and platelet counts jointly reduce relapse risk.
  • The drug 6-mercaptopurine (6MP) was inferred to reduce lymphocyte counts across most quantiles.
  • The drug methotrexate (MTx) was inferred to increase neutrophil counts across most quantiles.

Conclusions:

  • The proposed Bayesian quantile joint model effectively analyzes complex longitudinal data and event-time outcomes in cancer research.
  • Biomarker levels have a significant, quantile-dependent impact on relapse risk in ALL patients.
  • Specific chemotherapy drugs exhibit distinct effects on biomarker trajectories and, consequently, on relapse risk.