Statistical Analysis of Incomplete lifetime Data: Theory, Stochastic Models and Empirical Likelihood

研究者计划进一步发展分析不完整寿命数据的理论和统计方法，特别关注生存分析中的删失数据。 本研究包含两个相互关联的研究主题：（一）发展以经验似然为基础的推论程序。 激发EL方法的优点，提出了一种新的方法。 主要研究者及其合作者计划开发计算上可行且有效的渐进最优统计程序，以及（B）Fix-Neyman竞争风险模型的扩展，重点关注模型中疾病恢复和复发的复发事件特征。 对于许多疾病，如乳腺癌和再生障碍性贫血（AA），恢复和复发是影响患者生存概率的重要事件。 目前大多数的竞争风险模型缺乏这一功能。 研究小组计划在新的删失数据模型下开发统计推断程序。 扩展模型可以应用于其他类型的复发事件，如流行病学调查（当前状态数据）和工程可靠性。 寿命或“时间到事件”数据，通常在科学和工程中收集，可以是免疫力丧失的时间，癌症患者治疗后的生存时间，桥梁故障的时间等。 由于采样方法、采样对象、实验方案和记录仪器的限制以及可能的其他原因，数据集往往包含大量未完全观测到的寿命。 不完全数据可能包括右或左删失数据、区间删失数据和截断数据。 如果不对不完整性进行适当纠正，数据分析和不确定性措施将产生有偏见和不可靠的科学结论。 因此，发展健全的统计方法和理论来分析不完整的数据至关重要。 尽管在理论和应用方面取得了重大进展，但在不同科学领域的新兴应用继续提出新的具有挑战性的数学问题和计算问题。 例如，拟议的扩展将通过在预测患者的生存概率中包括恢复和复发数据来扩展流行的Kaplan-Meier估计。 人们希望更好地利用现有数据将产生更准确的预测生存概率的一些疾病，并帮助确定影响患者生存的重要因素。 开发数值解决方案将是该项目的一个组成部分。 将为数据分析开发算法。 该项目的成功将推动不完全寿命数据的统计理论及其应用。 经验似然方法的新用途将导致计算效率高的算法的应用。 这个项目的研究和教育是分不开的。 计划培训研究生和从代表性不足的群体中招收学生。

The investigator plans to further the development of the theory and statistical methods for the analysis of incomplete lifetime data with special focus on censored data in survival analysis. The proposed research consists of two interrelated research thrusts: (A) The development of the empirical likelihood (EL)-based inference procedures. Motivated by the proven advantages of the EL method, a novel approach is proposed. The PI and her collaborator plan to develop asymptotically optimal statistical procedures that are computationally feasible and efficient, and (B) Extension of the Fix-Neyman competing risks model which focuses on a feature of recurrent events of recovery and relapse of a disease in the model. For many diseases, such as breast cancer and aplastic anemia (AA), recovery and relapse are important events affecting a patient's survival probability. Most of the currently employed competing risks models lack this feature. The research team plans to develop statistical inference procedures under the new model for censored data. The extended model can be applied to other types of recurrent events such as in epidemiology surveys (current status data) and engineering reliability. Lifetime or "time-to-event" data, commonly collected in science and engineering, could be time to loss of immunity, survival time of a cancer patient after a treatment, time to failure of a bridge and others. Due to sampling methods, sampling subjects, experimental protocols and limitations of recording instruments and possibly other reasons, data sets often contain a significant number of incompletely observed lifetimes. Incomplete data may include right or left censored, interval censored and truncation data. Without proper corrections for incompleteness, data analysis and uncertainty measures would produce biased and unreliable scientific findings. It is therefore of paramount importance to develop sound statistical methods and theory for the analyses of incomplete data. Despite significant advances in theory and applications, burgeoning applications in diverse science fields continues to present new challenging mathematical problems and computational issues. For example, the proposed extension would extend the popular Kaplan-Meier estimator by including recovery and relapse data in the prediction of a patient's survival probability. It is hoped that better utilization of available data would yield more accurate prediction of survival probability for some diseases and help to identify important factors affecting a patient's survival. Developing numerical solutions will be an integral part of the project. Algorithms will be developed for data analysis. The success of the project will advance the statistical theory of incomplete lifetime data and its applications. Novel use of the empirical likelihood method will result in computationally efficient algorithms for applications. Research and education for this project are inseparable. Training of graduate students and recruiting students from under represented group are planned.