Modelling Disease Trajectories in Colorectal Cancer with Longitudinal Carcinoembryonic Antigen (CEA) using Joint Multi-State Model

In colorectal cancer (CRC), Carcinoembryonic Antigen (CEA) is a widely recognized biomarker for monitoring disease progression. However, its dynamic nature is often neglected in conventional survival analyses. Patients with CRC may experience multiple time-to-event outcomes such as recurrence, metastasis, and death, which are typically analyzed independently using the Cox proportional hazards model. Since these outcomes are interdependent, the Cox model may provide incomplete risk estimates. Multi-state models (MSMs) offer an alternative framework by accounting for the dependence between multiple transitions. Extending this concept, Joint Multi-State Models (JMSMs) provide a flexible approach for simultaneously analyzing longitudinal biomarkers and survival processes. Unlike MSMs, where longitudinally measured CEA is treated as a static covariate, JMSMs explicitly model CEA trajectories using a linear mixed-effects model and link them with the multi-state process through shared random effects. This integration allows for a joint assessment of the longitudinal biomarker dynamics and disease progression. In this study, JMSM identified composite stage, age, and perineural invasion as significant predictors for the transition from diagnosis to metastasis. Longitudinal CEA levels were significantly associated with composite stage, age, and family history of cancer. The estimated association parameters revealed that higher CEA values accelerated transitions from diagnosis to recurrence, metastasis, and death. These findings demonstrate the critical role of longitudinally measured CEA in dynamically predicting survival outcomes in CRC patients. The JMSM framework provides deeper insight into disease progression and supports personalized risk assessment in clinical management.