Statistical Analysis of a Joint Stochastic Model For Recurrent Competing Risks, Longitudinal Marker, and Health Status

Joint modeling approach has been applied in many applications in biomedical, reliability, and social-economic research. For example, in clinical trials and medical research, different kinds of patient information are gathered over time, such as recurrent competing risk events (e.g., relapses of different types of tumor), longitudinal marker (e.g., tumor size), and health status (e.g., if a patient is dead or not). These data are usually correlated, joint models enable the analysis of these correlated data. This dissertation proposes a class of joint dynamic models for simultaneously modeling the three types of processes: a recurrent competing risk (RCR) process, a health status (HS) process, and a discrete-valued longitudinal marker (LM) process. Experimental units or subjects are observed during a time period of possibly random duration. Consider a subject or unit being monitored over a period of random duration in a longitudinal time-to-event study, in a biomedical, public health, or engineering setting. As time moves forward, this unit experiences recurrent events of several types and a longitudinal marker transitions over a discrete state-space. In addition, its ``health\u27\u27 status also transitions over a discrete state-space containing at least one absorbing state. A vector of covariates will also be associated with this unit. Of major interest for this unit is the time-to-absorption of its health status process, which represents this unit\u27s lifetime. Aside from being affected by the covariate vector, there is a synergy among the recurrent competing risks processes, the longitudinal marker process, and the health status process in the sense that the time-evolution of each process is affected by the other processes. To exploit this synergy in order to obtain more realistic models and enhance inferential performance, a joint stochastic model for these components is proposed and the proper statistical inference methods for this model are developed. This joint model has the potential of facilitating precision interventions, thereby enhancing precision or personalized medicine. A stochastic process approach, using counting processes and continuous-time Markov chains, is utilized, which allows for modeling the dynamicity arising from the synergy among the model components and the impact of performed interventions after event occurrences and the increasing number of event occurrences. Likelihood-based inferential methods are developed based on observing a sample of these units. Properties of the inferential procedures are examined through simulations and illustrated using some real data sets. The asymptotic properties of the model parameters are also developed by using the Martingale Central Limit Theorem