A Bayesian joint model for multivariate longitudinal and time-to-event data with application to ALL maintenance studies

ABSTRACT

The most common type of cancer diagnosed among children is the Acute Lymphocytic Leukemia (ALL). A study was conducted by Tata Translational Cancer Research Center (TTCRC) Kolkata, in which 236 children (diagnosed as ALL patients) were treated for the first two years (approximately) with two standard drugs (6MP and MTx) and were then followed nearly for the next 3 years. The goal is to identify the longitudinal biomarkers that are associated with time-to-relapse, and also to assess the effectiveness of the drugs. We develop a Bayesian joint model in which a linear mixed model is used to jointly model three biomarkers (i.e. white blood cell count, neutrophil count, and platelet count) and a semi-parametric proportional hazards model is used to model the time-to-relapse. Our proposed joint model can assess the effects of different covariates on the progression of the biomarkers, and the effects of the biomarkers (and the covariates) on time-to-relapse. In addition, the proposed joint model can impute the missing longitudinal biomarkers efficiently. Our analysis shows that the white blood cell (WBC) count is not associated with time-to-relapse, but the neutrophil count and the platelet count are significantly associated with it. We also infer that a lower dose of 6MP and a higher dose of MTx jointly result in a lower relapse probability in the follow-up period. Interestingly, we find that relapse probability is the lowest for the patients classified into the “high-risk” group at presentation. The effectiveness of the proposed joint model is assessed through the extensive simulation studies.

KEYWORDS:

• Acute lymphocytic leukemia (ALL)
• joint model
• longitudinal outcomes
• posterior predictive distribution
• MCMC

Acknowledgements

The authors thank the editor, the associate editor, and two anonymous reviewers for their comments and suggestions. The pseudonymised clinical dataset used in this analysis included patients treated at the Tata Medical Center Kolkata on the ICiCLe-ALL-14 clinical trial (Clinical Trials Registry-India CTRI/2015/12/006434). Funding support for the clinical trial was provided by the National Cancer Grid (2016/001; 2016-) and the Indian Council of Medical Research (79/159/2015/NCD-III; 2017-19).

Data availability statement

The relevant datasets for this manuscript will be available on request. The dataset may not be publicly available for confidential issues.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Supplemental material

Supplemental data for this article can be accessed online at https://doi.org/10.1080/10543406.2023.2187413.

Supplemental online materials

Additional figures, tables and results, computational details, and details on the simulation studies are given in the Web-Appendix.

Additional information

Funding

The work was supported by the National Cancer Grid (2016/001; 2016-) and the Indian Council of Medical Research (79/159/2015/NCD-III; 2017-19). .