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

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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.