Joint Modeling of Time-to-Event Data with Competing Risks

When analyzing time-to-event data, informative dropout due to competing risks is one prac- tical aspect that researchers should take into account. If we fail to account for the association between the event of interest and informative dropouts, unknown amplitude bias may be en- countered when identifying the effects of potential risk factors related to time to the main cause of failure. A joint modeling approach of time to the main event and time to the competing events is proposed, to capture the dependence between the main event and the informative dropout due to competing risks via a set of random terms. Two fundamental likelihood functions with different structures of the random terms are provided, which may be combined in practice. We used three methods to optimize the corresponding likelihood functions in order to estimate the unknown covariate effects: Gaussian quadrature method, Bayesian Markov Chain Monte Carlo method, and hierarchical likelihood method. Four bias reduction correction methods for the h-likelihood estimation approach are explored. These methods were aimed to improve the accuracy of parameter estimation. The performances of the three methods were compared via simulations. We applied proposed methods to identify risk factors for dementia.\ud \ud Time-to-event data have been widely investigated from clinical trials and from obser- vational studies. The proposed joint modeling method is significantly meaningful to public health research because informative dropout commonly exists for the time-to-event data. Methods that have been currently used either fail to adjust for the association between the main event and the informative dropout due to competing events or the methods used to adjust for the association are not easy to implement. In this dissertation, we showed that the proposed joint modeling approach provides less bias estimates on the effect of a risk factor and has fairly straightforward implementation, which will lead to benefits for medical research