Joint analysis of longitudinal measurements and survival data has received much attention in recent years. However, previous work has primarily focused on a single failure type for the event time. In this paper we consider joint modeling of repeated measurements and competing risks failure time data to allow for more than one distinct failure type in the survival endpoint which occurs frequently in clinical trials. Our model uses latent random variables and common covariates to link together the sub-models for the longitudinal measurements and competing risks failure time data, respectively. An EM-based algorithm is derived to obtain the parameter estimates, and a profie likelihood method is proposed to estimate their standard errors. Our method enables one to make joint inference on the multiple outcomes which is often necessary in analyses of clinical trials. Furthermore, joint analysis has several advantages compared with separate analysis of either the longitudinal data or competing risks survival data. By modeling the event time, the analysis of longitudinal measurements is adjusted to allow for non-ignorable missing data due to informative dropout, which cannot be appropriately handled by the standard linear mixed effcts models alone. In addition, the joint model utilizes information from both outcomes, and could be substantially more efficient than the separate analysis of the competing risk survival data as shown in our simulation study. The performance of our method is evaluated and compared with separate analyses using both simulated data and a clinical trial for the scleroderma lung disease.
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