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: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=718453
• 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，可靠性分析，分布理论，有序数据分析和随机有序的领域。在接下来的五年中，我计划在所有这些领域中提出一些出色的问题。 生存分析：由于某些疾病（包括癌症和心脏病）的治疗方面取得了巨大进展，因此一定比例的患者对治疗有利，并且可能在很长一段时间内不会出现复发。 它们被称为“治愈的个体”或“长期幸存者”，这意味着他们已经达到了一个健康阶段，该疾病是无法检测到的，并且不会在很长一段时间内复发。 为了估算此治疗比例，文献中已经讨论了许多灵活的治疗速率模型和相关的推论方法。 在这个项目中，我计划开发一类新型的多阶段破坏性治疗模型，以模拟可能在每种化学疗法或放射治疗的给药后多次发生的癌细胞的破坏。 然后，我计划为这种多阶段破坏性治疗模型开发推论方法。 可靠性分析：使用“系统签名”的概念对相干系统寿命数据进行了广泛研究。已经为使用签名的系统和组件的寿命特征开发了有效的推论方法。但是，这些发展中的大多数都在两国系统（上或向下）上。在这里，我计划考虑具有二元组件的多状态相干系统，并研究相应的系统签名，有序的系统签名及其属性。然后，我计划使用它们来开发推论方法。 分布理论：文献中已经研究了几种双变量和多元离散分布。 我计划使用Com-Poisson模型，一般双变量泊松模型和复合来开发灵活的多元离散分布，并为其开发推论方法。 有序的数据分析和随机顺序：最近已经通过比例危害，比例逆转的危害和规模家庭以及其在精算科学中的索赔金额中讨论了各种随机顺序。 我计划将这些结果扩展到一般订单统计信息，并将其推广到依赖案例。 对该领域和加拿大的预期成果和利益：我所监督的大多数毕业后和博士学位学生都在加拿大的卡尔加里，曼尼托巴省，曼尼托巴省，滑铁卢，渥太华和麦克马斯特（包括卡尔加里，曼尼托巴省，渥太华和麦克马斯特）担任职务和德克萨斯州的德克萨斯州。 其他一些人也加入了加拿大公司，例如庞巴迪，BMO，Scotia Bank，CIBC，TD Bank，GE Capital，Rogers和Canadian Tire。 我预计拟议的研究工作会带来相似的结果和收益。