The main objective of this research is to use Archimedean copula models to analyze survival data. The proposed strategies are useful in medical research and financial data analysis. The investigator will address three different problems. The first problem is to solve the identifiability problem for Archimedean copula models for dependent censored data. The second problem concerns left truncated bivariate data. The investigator will explore ways to best estimate the unknown parameters in Archimedean copula models using truncated bivariate data. A model selection procedure for Archimedean copula models will also be investigated. The last problem is to establish guidelines for selecting models belonging to Archimedean copula family based on survival data. Research will be conducted to demonstrate the performance of the proposed strategies.
The proposed methods and strategies are motivated by clinical trials involving dependent censoring problem and the study of the correlated bivariate survival data in AIDS research. The results of this project will be helpful for determining the underlying relationship between random variables when they are subject to different censoring patterns. The theoretic results will contribute to the advancement of the statistical theory on correlation studies and deepen the understanding of the dependence structure of Archimedean copula models.