A masked competing risks (MCR) model is a popular model for studying the lifetime (denoted by T) and the associated failure cause (denoted by C) of a J-component series system. The system fails if one of its components fails. The failure time might be censored and the failure cause might be masked. The investigator discovered that some of the assumptions used in the MCR modelare erroneous. In this project, the investigator proposes a new and a more realistic model, which is a significant improvement of the MCR model. Based on the new model, the PI proposes to study the parametric, non-parametric and semi-parametric estimation problems of the joint distribution of T and C.
The MCR data appear in numerous medical and industrial applications. For example, Dinse (1982) presents the MCR data of time until progression and the patient status at the time of progression for patients with glioblastoma (a cancer of the brain). The patient status may not be identified. Reiser et al.(1995) show that the MCR data arises from the testing of a particular type of IBM PS/2 computer. The cause of failure of a computer may only be narrowed down to a set of possible causes. The estimation of the joint distribution of T and C has a great impact in detecting the failure cause efficiently. The results of this research would provide a novel and realistic model for the MCR data and would provide statistical tools for analyzing the MCR data.
In the past three years, the PI, together with three of his Ph.D students, had made several accomplishments on the research project DMS- 0803456 sponsored by the NSF. As the outcomes of this project, the following seven papers have been accepted for publication in the peer-reviewed journals. In these papers, the PI considers the model for competing risks data with masked failure cause, called the masked competing risks (MCR) data hereafter. The MCR data are observations on the failure time T and failure cause C of a system. Examples of such MCR data include (1) failure time and cause of a broken TV, (2) death time and cause of a patient. The PI points out that some assumptions in the old MCR model are invalid, and the symmetry assumption in the old model can be improved. The PI has shown that some of the existing theoretic results are incorrect. Proper realistic models are proposed in PI's papers for the right-censored (RC) data or interval-censored (IC) data. Moreover, the PI proposes a new set-up to formulate the parametric families of distribution of (T,C). Notice that T is continuous but C is discrete. The existing parametric families are not suitable for parametric set-up. It is not a problem in the past, as in the old literature, people only consider the case that T and C are independent under the parametric approach. The PI proposes to consider the conditional distribution of T|C and the marginal distribution of C. Then one can make use the existing parametric families. If the joint cdf of (T,C) is of a parametric form, the MLE of the parameters can be obtained by numerical methods such as the Newton-Raphson method or the Monte-Carlo method. The PI also implement an algorithm for computing the MLE with right-censored MCR data. Under the new model the PI establishes the consistency and asymptotic normality of the parametric MLE under certain regularity conditions for finite dimensional parametric problems. The PI shows that the NPMLE of the joint cdf is not unique and there exists inconsistent NPMLE. Instead of constructing a consistent repaired NPMLE, as proposed in the proposal, the PI, together with his Ph.D student Jiahui Li, construct a consistent NPMLE. The consistency and asymptotic normality are established. The PI, together with his Ph.D student Dr. Jiaping Wang, have written a computer program for the NPMLE with IC MCR data (see [5]) and establish the consistency of the NPMLE with the IC MCR data. The PI is supervising his student to apply the proposed procedures for censored MCR data to the ``Long-term Prognostic Study of Breast Cancer Bone Marrow Micrometastases (BMM) on Relapse and Survival" conducted at Strang Cancer Prevention Center. A manuscript about the data analysis results is under preparing. Intellectual Merits. The new model proposed in this project meets the urgent need in the study of MCR data, because some major assumptions in the literature are invalid. The new model is quite similar to the mixed case interval censorship model (Schick and Yu (2000)) proposed by the PI for interval censoring data. The latter model has since been cited more than 20 times in the major statistical journals and a textbook (see Reference D2.), and has become the standard model for interval-censored data. The new model will play the same role for the MCR data as the mixed case model for interval-censored data. In fact, it lays a solid theoretic foundation for the study of MCR data and enables re-examination of all existing MCR studies in the literature. Broader Impact. The research topics proposed here are well suited for Ph.D student research projects. One Ph.D student of the PI, Dr. Jiaping Wang, got his Ph.D degree under the sponsorship of this award. Another two Ph.D students, Haoqing and Jiahui Li, are working on the projects of this proposal.
