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

为了发展对广泛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，这些方法有效地解决了重大的方法和实践挑战，包括复杂的数据结构（如依赖观测），特殊的（如重尾）分布，以及面对探索之间动态权衡的特殊决策任务(即，统计学习)和利用（即，即时回报）。******我的长期研究计划的动机是开发统计模型和方法，解决复杂的伦理、方法和实践问题，这些问题来自重要的社会经济需求，包括制药创新和保险实践。我的总体目标是为广泛的设置和广泛的应用开发一个统计探索与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顺序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，这个NSERC提案的重点是临床试验的风险管理和统计设计的具体目标。我们研究在风险价值的累积依赖损失使用copula和扩展到动态风险措施。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，如何将破产风险最小化的投资和/或再保险决策。我们利用copulas优化毒性和疗效之间的平衡，以改善I/II期临床试验的无缝衔接，并研究联合药物的I期临床试验和个性化药物的II和III期临床试验的优化设计。******建议的研究对保险业和公共卫生保健很重要。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，同时又不损害临床研究的有效性和完整性。******建议的研究计划对于培训HQP进行跨学科研究也很重要。我计划培养3名博士后，4名博士，3名硕士，其中包括我现在的2名博士研究生。高素质的人员将参与拟议的研究计划和目标的各个阶段。******我预计将有超过10篇出版物和许多会议报告来自拟议的研究。我将培养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的成功职业生涯做好准备。

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.