Abstract:
Joint models for longitudinal and survival data have been widely discussed
in the literature. This thesis proposes a joint model using a stereotype
model for the longitudinal ordinal responses and a Cox proportional
hazards model for survival time. Our current joint model has a new feature
since no literature has examined the joint model under the stereotype
model. The stereotype model can improve the fit by adding extra score parameters,
but it still has the advantage of requiring only a single parameter
to describe the effect of a predictor on the item response levels. We give an
example to model longitudinal ordinal data and survival data for patients
being followed up after treatments. The main focus is on modeling both
the quality of life data and the survival data simultaneously with a goal
of understanding the association between the two processes over time.
These two models are linked through a latent variable that characterizes
the quality of life of an individual and is assumed to underlie the hazard
rate. In other words, the latent variable serves as a shared variable in the
joint model. We present the joint model in two different aspects: one based
on a Bayesian approach and the other one a semiparametric approach using
the EM algorithm. For the Bayesian approach, the latent variable is
treated as a continuous variable and is assumed to have a multivariate normal distribution. The partial survival likelihood function is used in the
survival component of the Bayesian joint model, while the full likelihood
function is considered in the semiparametric joint model. In the latter approach
the baseline hazard is assumed to be a step function and has no
parametric form. The latent variable in the semiparametric joint model
is then treated as a discrete variable. We illustrate our methodologies by
analyzing data from the Staccato study, a randomized trial to compare
two treatment methods, for Human Immunodeficiency Virus (HIV) infection
of Thai patients on Highly Active Antiretroviral Therapy (HAART), in
which the quality of life was assessed with a HIV Medical Outcome Study
(MOS-HIV) questionnaire. Furthermore, we extend the study further to
the case of multiple failure types in the survival component. Thus, the
extension of the joint model consists of the stereotype model and the competing
risks model. The Bayesian method is employed to estimate all unknown
parameters in this extended joint model. The results we obtained
are consistent for both the Bayesian joint model and the semiparametric
joint model. Both models show that patients who had a better quality of
life were associated with a lower hazard of HIV progression. Patients on
continuous treatment also had a lower hazard of HIV progression compared
with patients on CD4-guided interruption treatment.
