Joint modelling of time-to-event and longitudinal response using robust skew normal-independent distributions

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.