Semiparametric Joint Dynamic Modeling of a Longitudinal Marker, Recurrent Competing Risks, and a Terminal Event

The joint modeling framework has found extensive applications in cancer and other biomedical research. For example, recent initiatives and developments in precision medicine call for appropriate prognostic tools to assist individualized or personalized approaches in cancer diagnosis and treatment. Data generated by clinical trials and medical research often include correlated longitudinal marker measurements and time- to-event information, which are possibly a recurrent event, competing risks, and a survival outcome. Primary interests of joint modeling include the association between the longitudinal marker measurements and time-to-event data, as well as predictions of survival probabilities of new observational units from the same population. The dissertation deals with joint dynamic modeling of a longitudinal marker, recurrent competing risks, and a terminal event. To tackle the problem of simulta- neously modeling three types of data processes, we begin by proposing joint dynamic models of recurrent competing risks (RCR) and a terminal event (TE). We adopt the counting process approach of survival analysis to specify the joint models, where history of data, or filtration is considered. Intensity processes of the recurrent com- peting risks (RCR) and the terminal event (TE) also includes fixed covariates, past event occurrences as well as impact of possible interventions. Impact of past event occurrences is important to be accounted for in the intensity processes because it is reasonable to assume that if a unit has experienced a certain type of recurrent event many times up to time t, the probability of a new event occurrence of this unit could either increase or decrease compared to those who have experienced fewer event occurrences, depending on the context of the data. Consequently, as the different aspects of the intensity processes change over time, the intensity processes evolve dynamically. A frailty variable, or latent variable, which is unobserved, is often used to in- duce association in survival analysis. We introduce a frailty variable Z into the joint dynamic model proposed previously. For parameter estimation, we propose semi- parametric inference procedures for the joint models with no-frailty and with frailty cases. Nelson-Aalen type of estimators are derived for baseline hazards, and partial likelihoods are obtained to estimate the unknown finite-dimensional parameters in the joint models. We illustrate the inference procedures on simulated datasets. Sim- ulation studies with moderate sample sizes are performed to understand large/finite- sample properties of the proposed estimators. We also address the issue of predicting terminal event (TE) probabilities of a new unit from the same population, and provide an example for the simulated population. When correlated longitudinal marker measurements, recurrent competing risks event occurrences, and status of a terminal event are the data of interest, we propose a joint dynamic model that link the three data processes together. The joint dynamic model consists of the longitudinal marker (LM) submodel, the recurrent competing risks (RCR) submodal, and the terminal event (TE) submodel. For each observa- tional unit, the marker is measured at irregularly spaced times within the monitoring period or until the terminal event happens. The longitudinal marker submodel is a mixed model with a fixed linear time trend. A frailty variable, or the random effect in the submodel induces both within-subject correlation as well as the association between the longitudinal marker process and the recurrent competing events. Ad- ditionally, this random variable induces correlation between the longitudinal marker values and the terminal event. The joint models capture dependence structure of the data from the following two aspects: firstly, past longitudinal marker history affect the intensity process of the recurrent competing events, including that of the terminal event; at the same time, past event occurrences of RCR also affect the mean process of the longitudinal marker. Secondly, the frailty variable represents all other unob- served variables that induce associations between the different processes (LM, RCR, and TE). Built upon the aforementioned joint dynamic model of RCR and TE, the proposed joint dynamic models (of LM, RCR and TE) possess similar dynamic na- ture. A semiparametric inference procedure involving an EM algorithm is proposed. Future research activities for this joint model are indicated