Bayesian joint modeling of multivariate longitudinal and event-time outcomes with applications to ALL maintenance studies

Abstract

Joint analysis of longitudinal and event-time outcomes is a major research topic in the last two decades, mainly due to its successful applications in various disciplines including medical studies, biological studies, environmental studies, economics and many others. When a group of individuals are followed for a period of time points to study the progression of some event(s) of interest, some related variables (either time-varying or time-invariant) are also measured over time from the subjects. By jointly modeling the longitudinal outcomes and the time of occurrence of the event(s) of interest, one can (i) study the progression of the outcomes over time, (ii) assess the effects of the longitudinal outcomes on the event-time and (iii) assess the effects of the covariates on the evolution of the longitudinal outcomes and the event-time. In this thesis, we develop different Bayesian models and the computational algorithms for jointly analysing three longitudinal biomarkers and one event-time. Our work is motivated by a clinical experiment conducted by Tata Translational Cancer Research Center, Kolkata, where a group of 236 children, detected as leukemia patients, were treated with two standard drugs (6MP and MTx) nearly for the first two years, and then were followed for the next three years to see if there is a relapse. In our first work we develop a Bayesian joint model for simultaneously imputing the missing biomarker values and for dynamically predicting the non-relapse probability for each patient. In the second work, we develop a Bayesian quantile joint model to assess the effects of the biomarkers on the relapse-time at different quantile levels of the longitudinal biomarkers. Finally, in the third work, we develop a Bayesian latent class joint model for identifying the latent classes with respect to one of the biomarkers and to study the evolution of different biomarkers across different latent clusters. We also dynamically predict the median non-relapse probabilities for different latent classes based on the estimated model parameters. All our works are supported by extensive simulation studies and real applications to leukemia maintenance study.