A Hybrid Two-Stage Estimation Method for Jointly Modelling Longitudinal and Multi-State Processes: Application to Biomedical Data

Abstract

Joint modelling of longitudinal outcomes and a single survival event has been the focus of current research, although, data collected in practice may be more complicated most especially when multiple event outcomes occur. Consequently, an extension to a joint modelling approach to handle multi-states is needed to portray the interplay between a longitudinal observation and the multi- state outcome. In this thesis, a hybrid two-stage estimation method for jointly modelling longitudinal and survival, and a multi-state process is proposed. The proposed two-step modelling approach uses a Bayesian estimation for the submodel of the longitudinal process and then uses all the posterior predictive estimates from the first stage of the estimation process as inputs in stage two of the process. The proposed estimation method is first applied to time to a single survival outcome and extended to a multi-state process. These models are validated using a simulation study and empirical data from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) and Parkinson Progressive Marker Initiative (PPMI) studies. The approach was compared to Rizopollous joint, Bayesian joint, and Bayesian two-stage models. When applied to joint model with a single event time, it was evident from the simulation results that the proposed hybrid method performs effectively, both in estimating the fixed-effects and association parameters, especially with samples with larger sizes. When extended to the multi-state model, it was evident from the empirical results that the hybrid model with the last 100 posterior estimates, estimates both the fixed effects and association parameters precisely compared to the hybrid model with all 8000 posterior estimates and the frequentist model. To speed up the computational time and produce more precise estimates, the hybrid model with fewer posterior predictive estimates at the tail end of the converged Bayesian model from the longitudinal sub-model is recommended. Also, for samples with larger sizes, the hybrid model is a recommended approach as it yields less bias and precise estimates. An area of future work is to extend the hybrid models to multiple longitudinal and survival-type and multi-state outcomes.