Adaptation of joint latent class trees to multivariate longitudinal outcomes

Joint Latent Class Trees (JLCT) is a tree-based method that allows for the joint modeling of longitudinal and time-to-event data using time-varying covariates, thereby overcoming the limitations of traditional methods that require time invariant covariates. However, the original JLCT method can only accommodate a single longitudinal outcome, which is a significant limitation in many clinical studies where multiple longitudinal biomarkers are monitored simultaneously. To address this constraint, the JLCT framework has been extended in this thesis to support multiple longitudinal outcomes, resulting in a new method called Multivariate Joint Latent Class Trees (MJLCT). This approach enables the simultaneous modeling of multiple longitudinal variables along with survival data. The MJLCT method was applied to the PAQUID dataset, which includes MMSE, BVRT, and IST biomarkers, using single, dual, and triple response configurations. The results showed that multi-response models produced lower IBS and RMSE values than single-response models, confirming MJLCT's effectiveness in handling complex data structures. Simulation studies demonstrated that increasing sample size improves model performance, and scenarios with survival outcome generated from Weibull distribution yielded the lowest prediction errors. On the other hand, stopping criteria had no significant effect on performance measures. Comparisons with JLCT revealed that although both methods yielded similar results in many scenarios, MJLCT showed stronger generalization performance. Overall, this thesis has demonstrated that MJLCT not only provides structural flexibility over JLCT, but also enhances its generalization capacity, resulting in more reliable predictions. Therefore, it has been concluded that MJLCT is a more suitable modeling approach for studies involving multiple longitudinal outcomes.