LEAPS-MPS: Flexible Semiparametric Transformation Models with Applications to Personalized Medicine

当感兴趣的故障时间只被部分观察到时，就会出现截尾数据。该项目将开发新颖而强大的半参数转换模型，以更有效地分析这些数据。此外，该项目旨在促进对个性化医疗的理解和进步，这是一个专注于为个体患者量身定制医疗决策和干预措施的领域。虽然主要是出于生物医学应用的动机，如艾滋病毒疫苗和艾滋病治疗，但这项研究的成果将广泛应用于各种学科，包括工程、经济、金融和社会科学。PI将设立新的夏季研究项目，旨在增加代表性不足的群体在统计学本科研究中的参与，并为他们在高等学位课程和学术界和工业界的职业生涯中取得成功做好准备。此外，该项目将提供研究生水平的研究培训机会。本研究提出的新模型在重要方向上扩展了传统的转换模型，有效地弥补了生存分析中最突出的两种模型——加性-乘法模型和转换模型之间的差距。无限维参数的存在带来了相当大的计算和理论挑战。为了应对这些挑战，该项目将开发健壮且可扩展的期望求解算法，用于在各种审查机制下估计模型参数，包括右审查、区间审查和部分区间审查。此外，将提出一类新的半参数转换模型来估计最优治疗方案，这是个性化医疗的一个重要课题。本研究将利用现代经验过程理论，为调查提出的估计器发展新的理论论据。将对艾滋病毒疫苗和艾滋病临床试验进行模拟研究和真实数据分析，以演示这些方法。PI还将为该领域的研究人员和从业人员创建和分发用户友好的开源软件。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Censored data arise when the failure time of interest is only partially observed. This project will develop novel and powerful semiparametric transformation models to more effectively analyze such data. Furthermore, this project aims to contribute to the understanding and advancement of personalized medicine, a field focused on tailoring medical decisions and interventions to individual patients. Although primarily motivated by biomedical applications, such as HIV vaccine and AIDS treatment, the outcomes of this research will have broad applications in diverse disciplines, including engineering, economics, finance, and social sciences. The PI will establish new summer research programs designed to increase the participation of underrepresented groups in undergraduate research in statistics and prepare them for success in advanced degree programs and careers in academia and industry. Additionally, the project will offer research training opportunities at the graduate level. The new models proposed in this research extend the traditional transformation models in important directions and effectively bridge the gap between additive-multiplicative and transformation models, two of the most prominent models in survival analysis. The presence of infinite dimensional parameters poses considerable computational and theoretical challenges. To address these challenges, this project will develop robust and scalable Expectation-Solving algorithms for estimating model parameters under various censoring mechanisms, including right-censored, interval-censored, and partly interval-censored. Moreover, a new class of semiparametric transformation models will be proposed for estimating optimal treatment regimes, an important topic in personalized medicine. This research will leverage modern empirical process theory to develop new theoretical arguments for investigating the proposed estimators. Simulation studies and real data analysis on HIV vaccine and AIDS clinical trials will be performed to demonstrate the methods. The PI will also create and distribute user-friendly open-source software to researchers and practitioners in the field.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.