Detecting Multiple Change Points In Piecewise Constant Hazard Function With Competing Risks

Cancer is a major public health problem in the world and is the second leading cause of death. With the improvement of living conditions and medical facilities the cancers which cannot be treated in the early stages already can be cured. With the progress of science, a growing number of statisticians and physicians work together on the clinical trials doing statistical analysis. Nowadays, there are many subjects which named professional medicine statistics, epidemiology statistics and so on. When combined medicine and statistics, we are more concerned about that can we use the analysis to judge the effectiveness of treatment programs. Now there are many scholars doing this aspect of data modeling. This article also focused on this aspect doing a simple modeling and statistical analysis.In this paper, the model is a combination of competition risks, survival analysis model and the likelihood function of type I censoring which is an improvement of piecewise constant hazard function model with competing risks, and then according to the discrete sequential boundaries to do the model selection which is equal to explore the change points of survival analysis. After the model simulation, we use the SEER website data which is the prostate cancer patients of 1973-2007 as an example to test our model.