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

研究人员计划进一步发展不完整寿命数据分析的理论和统计方法，特别关注生存分析中的删失数据。拟议的研究由两个相互关联的研究主线组成：(A)基于经验似然(EL)的推理程序的发展。基于EL方法被证明的优势，提出了一种新的方法。PI和她的合作者计划开发在计算上可行和有效的渐近最优统计程序，以及(B)Fix-Neyman竞争风险模型的扩展，该模型侧重于模型中疾病恢复和复发的反复事件的特征。对于许多疾病，如乳腺癌和再生障碍性贫血(AA)，康复和复发是影响患者生存概率的重要事件。目前使用的大多数竞争风险模型都缺乏这一功能。研究小组计划在新的审查数据模型下开发统计推断程序。扩展的模型可以应用于其他类型的重复性事件，如流行病学调查(当前状态数据)和工程可靠性。在科学和工程中通常收集的终生或“事件发生时间”数据可能是免疫丧失的时间、癌症患者治疗后的存活时间、桥梁失败的时间等。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察到的寿命。不完整数据可能包括右删失或左删失、区间删失和截断数据。如果不对不完整性进行适当的纠正，数据分析和不确定性衡量将产生有偏见和不可靠的科学结论。因此，对于不完整数据的分析，制定合理的统计方法和理论至关重要。尽管在理论和应用方面取得了重大进展，但在不同的科学领域中蓬勃发展的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，拟议的扩展将扩展流行的Kaplan-Meier估计器，将康复和复发数据纳入患者生存概率的预测。人们希望，更好地利用现有数据将产生对某些疾病生存概率的更准确预测，并有助于确定影响患者生存的重要因素。开发数值解将是该项目不可或缺的一部分。将开发用于数据分析的算法。该项目的成功将推动不完全寿命数据统计理论及其应用的发展。经验似然方法的新颖使用将导致应用程序在计算上的高效算法。这个项目的研究和教育是密不可分的。计划对研究生进行培训，并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.