  Joint modelling of longitudinal observations and event times continues to
remain a topic of considerable interest in biomedical research. For example, in
HIV studies, the longitudinal bio-marker such as CD4 cell count in a patient's
blood over follow up months is jointly modelled with the time to disease
progression, death or dropout via a random intercept term mostly assumed to be
Gaussian. However, longitudinal observations in these kinds of studies often
exhibit non-Gaussian behavior (due to high degree of skewness), and parameter
estimation is often compromised under violations of the Gaussian assumptions.
In linear mixed-effects model assumptions, the distributional assumption for
the subject-specific random-effects is taken as Gaussian which may not be true
in many situations. Further, this assumption makes the model extremely
sensitive to outlying observations. We address these issues in this work by
devising a joint model which uses a robust distribution in a parametric setup
along with a conditional distributional assumption that ensures dependency of
two processes in case the subject-specific random effects is given.
