Statistical Inferences under Monotonic Hazard Trend in Survival Analysis

在更危险的环境或更恶劣的条件下，正确评估不断增加的风险比率，对于降低医疗模式和失败率至关重要。然而，在许多应用中，危险率和环境之间的单调关系被错误地指定或省略，可能进一步导致风险评估的偏见。本项目将认真对待单调关系，以获得公正和有效的统计推断。PI旨在开发分布比较、参数估计和假设检验，用有序的危险比率收集的数据进行检验。所提出的方法可广泛应用于生物医学、环境、社会和物理研究等领域。该项目还将为更广泛的用户群开发开放源码软件。PI将为本科生和研究生提供现代统计学的研究机会。此外，研究生课程将帮助学生探索和学习形状约束的统计模型和非参数回归。在这个项目中，PI侧重于生存分析中非参数危险率排序和半参数COX型比例风险模型下的统计推断。当在危险排序的环境或处理下收集数据时，PI的目的是通过非参数形状约束的顺序优势曲线来检验分布的相等性，区分不均匀的分布，并诊断危险率排序假设。如果收集了与风险相关的协变量，PI的目标是研究具有保序比例风险的部分线性COX模型。本项目还将通过提供拟合优度检验来检验传统的COX-型回归模型。PI将探索建议方法在COX-型回归模型中的理论和数字性能。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.