Semiparametric joint models for semi-competing risks data with missing cause of informative terminal event

Understanding disease process on cancer-related health outcomes has attracted intense clinical, epidemiologic and translational research interest. Despite a high level of research activity on cancel-related outcomes, several critical questions remain unresolved, partly due to lack of appropriate statistical analysis methods addressing data structure and study design. One challenge in analyzing such data is that death dependently censors cancer progression (e.g., recurrence), whereas progression does not censor death. We dealt with the dependent censoring by first selecting a suitable copula model through an exploratory diagnostic approach and then developing an inference procedure to simultaneously estimate the marginal survival function of cancer relapse and an association parameter in the copula model. The additional challenge is missing cause of death and unreliable cause of death information. Therefore, an immediate question is how to analyze the semi-competing risks data in presence of uncertain type of censoring due to missing causes of death. We adopted a novel Expectation-Maximization (EM) algorithm to account for such uncertainty. We showed that the proposed estimators possess consistency and weak convergence, and use simulation studies to evaluate their finite sample performance. The proposed methods were applied to a retrospective cohort study of women diagnosed with American Joint Committee on Cancer pathologic stage I or II breast cancer who were treated at The University of Texas MD Anderson Cancer Center between January 1, 1985 and December 31, 2000.