A joint latent-class Bayesian model with application to ALL maintenance studies

Acute Lymphocytic Leukemia (ALL) is globally the main cause of death from blood cancer among children. While the survival rate of ALL has increased significantly in the first-world countries (e.g. in the United States) over the last 50 years the same is not the case for the developing countries. In this article, we develop a joint latent-class Bayesian model for analysing a dataset from a clinical trial conducted by the Tata Translational Cancer Research Center (TTCRC), Kolkata. The trial considers a group of children who were identified as ALL patients, and were treated with two standard drugs (i.e. 6MP and MTx) over a period of time. Three longitudinal biomarkers (i.e. lymphocyte count, neutrophil count and platelet count) were collected from the patients whenever they visited the clinic (weekly/bi-weekly). We consider a latent-class model for the lymphocyte count which is the main biomarker associated with ALL, and the other two biomarkers, i.e. the neutrophil count and the platelet count are modeled using linear mixed models. The time-to-event is modeled by a semi-parametric proportional hazards model, and is linked to the longitudinal submodels by sharing the Gaussian random effects. The proposed model detects two latent classes for the lymphocyte count, and we estimate the class-specific (average) non-relapse probability at different time points of the study period. We notice a significant difference in the estimated non-relapse probabilities between the two latent classes. Through simulation study we illustrate the accuracy and practical usefulness of the proposed joint latent-class model over the traditional models.