Joint Model for Longitudinal and Time-To-Event Data: a Two-Stage Approach

In clinical and epidemiological studies, very often, observations are collected on more than one correlated processes. For example, in AIDS related studies, along with a longitudinal biomarker like CD4 cell count, data on time-to-death is also recorded. Modelling them separately may give bias estimates. This necessitates the concept of joint modelling where two or more processes are modelled together. To link these processes, the usual technique is to use the same or highly correlated subject-specific random-effects for all the sub-models. In this work, structural correlation based on the conditional distribution of time-to-event given longitudinal response is used. A computationally efficient two-stage method is used to find the estimates. At the first stage, longitudinal submodel is fitted using nlme package in R. In the second stage, to avoid the complexity of second order differentiation, we have used an adaptive gradient descent algorithm. The simulation study shows that this structural correlation is good enough to take care of the correlation between these two simultaneous processes. A rapid convergence is also achieved. The proposed method is finally applied to a data set related to AIDS studies. Keywords