In medical research, clinical events along with repeated measurements of a biological or medical outcome are often observed. When the clinical event is only observed in a time window (i.e. is interval censored) or the event only takes place at discrete time points, then the data are referred to as discrete time-to-event data or discrete survival data.
In this dissertation, approaches for modeling discrete time-to-event data and jointly modeling both discrete survival data and longitudinal data are reviewed. A predictive nonlinear shared parameter joint model is proposed for discrete time-to-event and longitudinal data. A discrete survival model with frailty and generalized linear mixed model for the longitudinal data are joined to predict the probability of events. This joint model focuses on analysis on discrete time-to-event outcome, taking advantage of repeated measurements, i.e. the probability of event in a time window can be more precisely predicted by incorporating longitudinal measurements. The area under the receive operating characteristic curve (ROC) and other measures, i.e. Brier score, discrimination slope, Gini index, Kolmogorov-Smirnov statistic and Hosmer-Lemeshow goodness of fit test are applied to compare the performance of the shared parameter joint model with a two-step model and a discrete survival model for discrete time.
Data from the Kawempe Community Healthy Study (KCHS) motivated this research. In the KCHS, time to tuberculin skin testing (TST) conversion from Tuberculosis (TB) negative to TB positive is the discrete event time and interest is in predicting TST conversion based on longitudinal measures of immunologic function. The tuberculosis (TB) immunology data are investigated using exploratory analyses. The shared parameter joint model, the two-step model and the discrete time survival model are fitted and compared using this TB immunology data. The characteristics of the shared parameter model, the two-step model and the discrete time survival model are studied using simulations based on the TB data. Results from both the TB data and simulated data show that the shared parameter joint model is superior to other two models according to the discrimination ability.