Joint Inference for Competing Risk Data

This dissertation develops joint inferential methods for the cause specific hazard function and the cumulative incidence function of a specific type of failure to assess the effects of a variable on the type of failure of interest in the presence of competing risks. Joint inference for the two functions are needed in practice because 1) they describe different characteristics of a particular type of failure, 2) they do not uniquely determine each other, and 3) the effects of a variable on the two functions can be different and one often does not know which effects are to be expected. We study both the group comparison problem and the Cox's regression problem. We also develop joint inference for other equivalent pairs of functions. Our simulation shows that the derived joint tests can be considerably more powerful than the Bonferroni method, which has important practical implications to the analysis and design of clinical studies with competing risks data. We illustrate our methods using a Hodgkin disease data and a lymphoma data. We also develop sample size calculation methods based on nonparametric two sample joint tests of the cause-specfic hazard and the all-cause hazard. A user friendly R-function is developed to implement the method. We illustrate the implementation of our method and the potential saving on the required sample size over the Bonferroni method through simulations and the 4-D (Die Deutsche Diabetes Dialyse Studie) clinical trial designed to compare a lipid lowering treatment with placebo in type 2 diabetic patients on hemodialysis