The goal of this paper is to describe approaches for the joint analysis of repeatedly measured data with time-to-event end points, first separately and then in the framework of a single comprehensive model, emphasizing the efficiency of the latter approach. Data from the Johnston County Osteoarthritis (JoCo OA) Project will be used as an example to investigate the relationship between the change in repeatedly measured body mass index (BMI) and the time-to-event end point of incident worsening of radiographic knee OA that was defined as an increased Kellgren/Lawrence grade in at least 1 knee over time.
First, we provide an overview of the methods for analyzing repeated measurements and time-to-event end points separately. Then, we describe traditional (Cox proportional hazards model [CoxPH]) and emerging (joint model [JM]) approaches, both of which allow combined analysis of repeated measures with a time-to-event end point in the framework of a single statistical model. Finally, we apply the models to JoCo OA data and interpret and compare the results from the different approaches.
Applications of the JM (but not the CoxPH) showed that the risk of worsening radiographic OA is higher when BMI is higher or increasing, thus illustrating the advantages of the JM for analyzing such dynamic measures in a longitudinal study.
Joint models are preferable for simultaneous analyses of repeated measurement and time-to-event outcomes, particularly in the context of chronic disease, where dependency between the time-to-event end point and the longitudinal trajectory of repeated measurements is inherent.