A two-stage approach for joint modeling of longitudinal measurements and competing risks data

Joint modeling of longitudinal measurements and time-to-event data is used in many practical studies of medical sciences. Most of the time, particularly in clinical studies and health inquiry, there are more than one event and they compete for failing an individual. In this situation, assessing the competing risk failure time is important. In most cases, implementation of joint modeling involves complex calculations. Therefore, we propose a two-stage method for joint modeling of longitudinal measurements and competing risks (JMLC) data based on the full likelihood approach via the conditional EM (CEM) algorithm. In the first stage, a linear mixed effect model is used to estimate the parameters of the longitudinal sub-model. In the second stage, we consider a cause-specific sub-model to construct competing risks data and describe an approximation for the joint log-likelihood that uses the estimated parameters of the first stage. We express the results of a simulation study and perform this method on the "standard and new anti-epileptic drugs" trial to check the effect of drug assaying on the treatment effects of lamotrigine and carbamazepine through treatment failure.