Statistical Inferences under Monotonic Hazard Trend in Survival Analysis

正确评估在更危险的环境或恶劣条件下增加的危险率对于减少模态和故障率至关重要。然而，在许多应用中，风险率和环境之间的单调关系被错误指定或省略，并可能进一步导致偏差的风险评估。本计画将认真对待单调关系，以获得无偏且有效的统计推论。PI旨在利用有序风险率收集的数据进行分布比较、参数估计和假设检验。所提出的方法可以应用于广泛的领域，如生物医学，环境，社会和物理研究。该项目还将为更广泛的用户群开发开放源码软件。PI将为现代统计学的本科生和研究生提供研究机会。此外，研究生水平的课程将开发，以帮助学生探索和研究形状约束的统计模型和非参数回归。在这个项目中，PI侧重于非参数风险率排序和半参数Cox型比例风险模型在生存分析中的统计推断。当数据是在危险有序的环境或处理下收集时，PI的目的是通过非参数形状约束的有序优势曲线来检验分布的平等性，区分不平等的分布，并诊断危险率排序假设。如果收集了风险相关协变量，PI旨在研究具有等渗比例风险的部分线性Cox型模型。本计画亦将借由提供拟合优度测试来检视传统的Cox型回归模型。PI将在Cox型回归模型中探索所提出方法的理论和数值性能。该奖项反映了NSF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。

Correctly evaluating the increasing hazard rates under more risky environments or severe conditions is crucial for reducing modalities and failure rates. However, in many applications, the monotonic relationships between hazard rates and environments are misspecified or omitted and may further cause biased risk evaluation. This project will take the monotonic relationships seriously to obtain unbiased and efficient statistical inferences. The PI aims to develop distributional comparisons, parameter estimations, and hypothesis tests with data collected with ordered hazard rates. The proposed methods can be applied in broad areas such as biomedical, environmental, social, and physical studies. This project will also develop open-source software for a broader base of users. The PI will provide research opportunities for undergraduate and graduate students in modern statistics. In addition, graduate-level courses will be developed to help students explore and study shape-constrained statistical models and nonparametric regressions.In this project, the PI focuses on statistical inferences under nonparametric hazard rate orderings and semi-parametric Cox-type proportional hazard models in survival analysis. When data were collected under hazard-ordered environments or treatments, the PI aims to test the equality of distributions, distinguish unequal distributions, and diagnose the hazard rate ordering assumption through nonparametric shape-constrained ordinal dominance curves. If hazard-related covariates were collected, the PI aims to study the partial linear Cox-type model with isotonic proportional hazards. This project will also examine the traditional Cox-type regression model by providing a goodness-of-fit test. The PI will explore both the theoretical and numerical performances of the proposed methods in the Cox-type regression models.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.