| Competing risks data are often observed in medical research, industrial life testing, economics and sociology. In the competing risks framework, each subject may fail from one of several distinct types or causes. Analysis of such data is complicated by dependent censoring of an event of interest by other failure types. This thesis focuses on the analysis of competing risks data through the cause-specific hazard function and cumulative incidence function. The work is motivated by studies of breast cancer and studies of contraceptive use. We first study parametric quantile inferences using the cumulative incidence function. Two types of parametric quantile inferences are proposed. We also propose a simplified procedure for nonparametric quantile inference. Extending the parametric quantile inferences for one sample, we propose covariate adjusted quantile inferences. The methods are applied to the analysis of breast cancer data. Next, we study the semiparametric and parametric regression model of the cumulative incidence function on discrete failure times with competing risks. The inferences are developed based on maximum likelihood estimation. Extending the semiparametric inference on discrete failure times with competing risks, we propose the semiparametric regression model of the cumulative incidence function on discrete failure times with recurrent competing risks. The methods are illustrated with the analysis of contraceptive use data in Indonesia. |
