| For competing risks data, two types of analysis are commonly used in testing the treatment effect on the cumulative incidence function. The first one is directly comparing the cumulative incidence function over time, and the second one is using regression techniques.;This dissertation consists of two parts. In the first part, we propose a class of weight functions for comparing two cumulative incidence functions. In many biomedical studies, researchers want to emphasize the comparison on a certain time period. The proposed weight functions allow users to focus their comparisons on either an early or a late time period. The performance of the new weight functions is evaluated by simulation studies and illustrated by a real data example. We develop the CIFsmry package for R to implement this new approach, which is available for public to use.;In the second part, we propose a diagnostic procedure for the widely used proportional subdistribution hazards model (Fine and Gray, 1999). The proposed procedure validates its subdistribution hazard function in three aspects: the proportionality, the linearity of the functional form, and the link function. For each test, we provide a p-value and a plot to check the corresponding model assumption visually. Simulation studies show that the new diagnostic procedure performs well. Two real data examples are included to illustrate the methodology. |
