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

为了开发对广泛应用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，这些方法可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（如相关观测），特殊（如重尾）分布，以及在探索（即，统计学习）和利用（即，立即支付）。我的长期研究计划一直受到开发统计模型和方法的激励，这些模型和方法解决了重要社会经济需求（包括制药创新和保险实践）所产生的复杂伦理，方法和实际问题。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，并开发将此类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明智决策的实际情况的统计方法。该NSERC提案集中于临床试验风险管理和统计设计的特定目标。我们研究的风险价值的累计相关损失使用copula和扩展到动态风险措施。我们还研究了投资和/或再保险决策，以尽量减少破产的风险时，索赔频率分布是未知的和/或索赔规模分布是未知的。我们使用copula来改善无缝I/II期临床试验，通过最佳平衡毒性和疗效之间的权衡，并研究I期临床试验的最佳设计与组合药物和II期和III期临床试验与个性化药物。这项研究对保险业和公共卫生保健很重要。风险度量用于帮助保险公司防止破产。临床试验各个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。 拟议的研究计划也是重要的培训HQP跨学科研究。拟培养博士后3名，博士4名。学生和3名硕士生，包括我目前的2名博士生。学生高素质的人员将参与拟议研究计划和目标的所有阶段。我预计超过10个出版物和许多会议介绍从拟议的研究。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.