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.
