Bayesian nonparametric inference for competing risks data

In the medical field, subjects may have several possible failure risks, but fail due to only one of them. In the lifetime of subjects, these failure risks compete together. Such a case is called a competing risks setting. Under the competing risks framework, regression on cause-specific hazards is a standard analysis to assess the covariates' effect. Instead of modeling the instantaneous hazard rate, investigators may also be interested in modeling the likelihood of a certain event. The cumulative incidence function is such a measurement and can be estimated from the cause-specific hazard and the overall survival function. However, coefficients from regression on the cause-specific hazards cannot be directly interpreted as those from regression on the cumulative incidence function. Fine and Gray (1999) developed a Cox type model directly on the cumulative incidence function of the cause of interest. Recently, Sun et al. (2006) generalized the work to the Cox-Aalen regression model. In this dissertation, we discuss a general method using Bayesian nonparametric techniques based on the full likelihood function.;The mixture of Polya trees process is one class of Bayesian nonparametric methods. It is assigned as a prior on the baseline (normalized) cumulative incidence function. Following the work of Hanson (2006), the Cox type model in Fine and Gray (1999) is implemented through Metropolis-Hastings chains using the full likelihood function. A simulation study is conducted to compare Bayesian and frequentist estimators. The robustness of the proposed method to the choice of model on the secondary event is addressed via extensive simulations. Model extensions to hierarchical structure (to incorporate center effects, for example) and time-dependent covariates/coefficients are discussed and implemented.;This general method can be used to analyze other regression models on cumulative incidence via appropriate changes in the likelihood. We also note that it can be easily adapted to models for cause-specific hazards. Proportional hazards models on cause-specific hazards and model extensions to hierarchical structure are also implemented in this dissertation.