Models and methods of statistical dependence with applications in clinical trials and risk management

为了开发对广泛的应用具有重大影响的创新统计理论，我们必须确定稳健和强大的统计方法的基本特征，以有效地解决重大的方法和实践挑战，包括复杂的数据结构(如相依观测)、特殊的(如重尾)分布，以及面对探索(即统计学习)和开发(即直接收益)之间的动态权衡时的知情决策的特殊任务。*我的长期研究计划的动机是开发统计模型和方法，以解决因重要的社会经济需求而产生的复杂的伦理、方法和实践问题，包括药品创新和保险实践。我的总体目标是为广泛的环境和广泛的应用建立一个统计探索和开发权衡的理论框架，并开发统计方法，将这些模型应用于统计不确定性和随机依赖下的序贯统计学习和知情决策的实际情况。*为了实现我的长期研究目标，NSERC的这项建议侧重于临床试验的风险管理和统计设计的具体目标。我们使用Copulas研究累积相依损失的风险价值，并将其扩展到动态风险度量。我们还研究了当索赔频率分布未知和/或索赔规模分布未知时，投资和/或再保险决策以最小化破产风险。我们使用Copulas通过在毒性和有效性之间进行最佳平衡来改进无缝的I/II期临床试验，并研究组合药物的I期临床试验和个性化药物的II和III期临床试验的最佳设计。*拟议的研究对保险业和公共卫生保健具有重要意义。风险措施被用来帮助保险公司防止破产。临床试验各阶段的优化设计有助于提高药物开发的伦理和效率，而不会破坏临床研究的有效性和完整性。*拟议的研究计划对于培训总部进行跨学科研究也很重要。我建议培养3名博士后研究员、4名博士生和3名硕士研究生。学生们，包括我现在的两名博士生。高素质的人员将参与拟议研究计划和目标的所有阶段。*我预计这项拟议的研究将发表10多篇论文和许多会议报告。我将培训HQP成为下一代研究人员，并为他们在加拿大学术界和工业界成功的职业生涯做好准备。

To develop innovative statistical theory with significant impact to a broad range of applications, we must identify essential characteristics of robust and powerful statistical methods that effectively address significant methodological and practical challenges, including complex data structures (such as dependent observations), special (such as heavy tailed) distributions, and peculiar tasks of informed decision making in the face of dynamic trade-off between exploration (i.e., statistical learning) and exploitation (i.e., immediate payoff). ******My long-term research program has been motivated by developing statistical models and methods that address complex ethical, methodological and practical issues arising from important socio-economic needs including pharmaceutical innovation and insurance practice. My overarching goal is to develop a theoretical framework of statistical exploration versus exploitation trade-off for a broad range of settings and a wide spectrum of applications, and develop statistical methods for applying such models to practical situations of sequential statistical learning and informed decision making under statistical uncertainty and stochastic dependence.******To achieve my long-term research goals, this NSERC proposal is focused on specific objectives of risk management and statistical design of clinical trials. We investigate value at risk for aggregated dependent losses using copulas and extend to dynamic risk measures. We also investigate investment and/or reinsurance decisions to minimize the risk of ruin when the claim frequency distribution is unknown and/or the claim size distribution is unknown. We use copulas to improve seamless Phase I/II clinical trials by optimally balancing the trade-off between toxicity and efficacy, and investigate the optimal design of Phase I clinical trials with combination drugs and Phases II and III clinical trials with personalized medicine. ******The proposed research is important to the insurance industry and public health care. Risk measures are used to assist insurance companies to prevent ruin. Optimal designs of various phases of clinical trials help improve the ethics and efficiency of drug development without undermining the validity and integrity of clinical research. ******The proposed research program is also important for training HQP on interdisciplinary research. I propose to train 3 post-doctoral fellows, 4 Ph.D. students, and 3 M.Sc. students, including my current 2 Ph.D. students. The highly qualified personnel will be involved in all stages of the proposed research program and objectives. ******I anticipate over 10 publications and many conference presentations from the proposed research. I will train HQPs to become the next generation of researchers and prepare them for successful careers in academia and industries in Canada.