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: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=741401
• 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.

在过去的六年里，我的研究主要集中在生存分析，可靠性分析，分布理论，有序数据分析和随机排序等领域。在今后五年中，我计划继续处理所有这些领域的一些悬而未决的问题。存活率分析：由于包括癌症和心脏病在内的一些疾病的治疗取得了巨大进步，有一定比例的病人对治疗反应良好，可能在很长一段时间内不会复发。他们被称为“治愈者”或“长期幸存者”这意味着他们已经达到了一个健康阶段，在这个阶段，疾病是无法检测到的，并且在很长一段时间内不会复发。为了估计这个治愈比例，在文献中已经讨论了许多灵活的治愈率模型和相关的推理方法。在这个项目中，我计划开发一类新的多阶段破坏性治愈模型来模拟可能在多个时间发生的癌细胞的可能破坏，例如，然后，我计划为这种多阶段破坏性治愈模型开发推理方法。可靠性分析：使用“系统特征”的概念，对相关系统寿命数据的分析进行了广泛的研究。有效的推理方法已经开发的寿命特性的系统和组件使用签名。但是，大多数这些发展都是在两个状态系统（向上或向下）。在这里，我计划考虑具有二元分量的多态相干系统，并研究相应的系统签名，有序系统签名及其性质。然后，我计划用它们来开发推理方法。分布理论：文献中已经研究了几个二元和多元离散分布。 我计划使用COM-Poisson模型，一般的二元Poisson模型和复合来开发灵活的多元离散分布，并开发它们的推理方法。有序数据分析和随机排序：最近，各种随机排序已经讨论了最小值和最大值的比例风险，比例反向风险和规模的家庭，以及他们的应用，索赔金额在精算科学。我计划将这些结果推广到一般的顺序统计量，也推广到相依的情况。外地和加拿大的预期成果和惠益：我所指导的博士后和博士生大多在加拿大的卡尔加里、马尼托巴、滑铁卢、渥太华和麦克马斯特等大学，美国的普渡、锡拉丘兹、南卫理公会、明尼苏达州和得克萨斯州等大学任职，还有一些人加入了加拿大的庞巴迪、BMO、斯科舍银行、加拿大帝国商业银行、道明银行、通用金融、罗杰斯和加拿大轮胎。我预计拟议的研究工作将导致类似的结果和好处。