Statistical Inferences under Monotonic Hazard Trend in Survival Analysis

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.