A joint model for longitudinal data profiles and associated event risks with application to a depression study

Summary.  In many longitudinal studies, a subject's response profile is closely associated with his or her risk of experiencing a related event. Examples of such event risks include recurrence of disease, relapse, drop-out and non-compliance. When evaluating the effect of a treatment, it is sometimes of interest to consider the joint process consisting of both the response and the risk of an associated event. Motivated by a prevention of depression study among patients with malignant melanoma, we examine a joint model that incorporates the risk of discontinuation into the analysis of serial depression measures. We present a maximum likelihood estimator for the mean response and event risk vectors. We test hypotheses about functions of mean depression and withdrawal risk profiles from our joint model, predict depression from updated patient histories, characterize associations between components of the joint process and estimate the probability that a patient's depression and risk of withdrawal exceed specified levels. We illustrate the application of our joint model by using the depression data.