Advancements in Cure Rate Modelling and Analysis of Multi-state Coherent Systems

多态相干系统治愈率建模和分析的进展

• 批准号: RGPIN-2020-06733
• 负责人: Balakrishnan, Narayanaswamy
• 金额: $ 3.13万
• 依托单位: McMaster University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=758902
• 关键词: Advancements; Cure; Rate; Modelling; Analysis

During the past six years, my research has primarily focused in the areas of Survival Analysis, Reliability Analysis,  Distribution Theory, Ordered Data Analysis and Stochastic Orderings. During  the next five years, I plan to pursue some outstanding problems in all these areas. SURVIVAL ANALYSIS: Due to the great advancements in the treatments of some diseases including  cancer and heart disease, a certain proportion of patients respond favourably to a treatment and may not show recurrence for a very long period of time.  They are referred to as "cured individuals" or "long-term survivors" meaning that they have reached a health stage wherein the disease is undetectable and would not recur  over a long  period.  For estimating this cure proportion, many flexible cure rate models and associated  inferential methods have been discussed in the literature.  In this project, I plan to develop a novel class of multi-stage destructive cure models to  model the possible destruction of cancerous cells that can happen at multiple times, for example, after the administration of each chemotherapy or radiation treatment.  I then plan to develop  inferential methods for such a multi-stage destructive cure model. RELIABILITY ANALYSIS:  Analysis of coherent system lifetime data has been studied extensively using the concept of "system signature". Efficient  inferential methods have  been developed for lifetime characteristics of systems and of components using signatures. But, most of these developments are on two-state systems (either up or down). Here, I plan to consider multi-state coherent systems with binary components and study the corresponding system signatures, ordered system signatures and their properties. I then plan to use them  to develop  inferential methods. DISTRIBUTION THEORY: Several bivariate and multivariate discrete distributions have been studied in the literature.   I plan to use the COM-Poisson model, general bivariate Poisson model and compounding to develop flexible  multivariate discrete distributions and also develop inferential methods for them. ORDERED DATA ANALYSIS AND STOCHASTIC ORDERINGS:  Recently various stochastic orderings have been discussed for minima and maxima from Proportional Hazards, Proportional Reversed Hazards and Scale families, and their application to claim amounts in Actuarial Science.  I plan to extend these results to general order statistics and also to generalize to dependent case. Anticipated Outcomes and Benefits to the Field and to Canada: Most post-docs and PhD students I supervised have taken up positions in many Universities, including Calgary, Manitoba, Waterloo, Ottawa and McMaster in Canada, and Purdue, Syracuse, Southern Methodist, Minnesota,  and Texas in USA.  Some others have joined Canadian companies such as Bombardier, BMO, Scotia Bank, CIBC, TD Bank, GE Capital, Rogers and Canadian Tire.  I anticipate the proposed research work to result in  similar outcomes and benefits.

在过去的六年中，我的研究主要集中在生存分析的领域，分布理论的生存：由于治疗方法的进步，包括癌症和心脏病，可能不会在很长的时间内表现出很长的时间时间。在您的文献中已经讨论了方法。或使用“系统签名”的概念，可以使用“系统签名”的概念，并使用二进制系统的系统来开发辐射治疗。系统系统系统签名和属性I然后计划开发推断分布理论：严重性双变量和多变量离散分布已在文献中死亡。开发灵活的多分布Andered数据分析和随机订单：最近从比例危害，比例的混响和规模家庭中为最小值和最大值提供了各种随机订单，以及他们要求扩展一般统计学的应用。我所监督的大多数案件。资本，罗杰斯和加拿大轮胎。