Collaborative Proposal: Novel Semiparametric Two-part Models: New Theories and Applications

这项研究的长期目标是开发新的半参数分析工具，用于生物学、经济学、人口学和医学研究。在这项研究中，研究人员提出了新的半参数两部分模型来分析(1)情形I和(2)情形k区间截尾数据和(3)左截尾数据。与已有的模型相比，该模型考虑了半参数变换函数和部分线性协变量效应，具有更大的灵活性。本文首次系统地研究了区间截尾数据下的半参数两部分治愈率模型和左截尾数据下的两部分线性变换模型。研究人员使用先进的经验过程技术严格地建立了拟议估计的渐近性质，并展示了未来此类数据的半参数分析的系统框架。深入的数值研究被用来证明所提出的方法的优越性，并为实际数据分析提供指导。(1)从建模的角度来看，它从总体上丰富了半参数方法。所提出的模型与现有的参数或半参数模型有很大的不同，是半参数模型家族中有价值的补充。(2)从方法论的角度，研究人员利用先进的经验过程技术建立了半参数模型惩罚估计和基于重抽样的推断的一般框架。这一框架对其他许多研究也很有用。(3)从统计实践的角度来看，拟议的研究为分析正在进行的研究提供了强大的工具，并产生了直接的影响。(4)大量的数值研究表明，所提出的方法更高效、更灵活，且对模型误指定的敏感性较低。在大规模研究中，变量可能具有复杂的、非线性的关联，而收集观测数据可能非常昂贵。拟议的模型与严格的分析技术一起，提供了对这些数据的更有效的利用，揭示了更微妙的结构，并从长远来看有利于整个科学社会。这项拟议的研究具有以下有益的教育和社会影响。(1)它促进了来自不同机构和背景的研究人员之间更紧密的合作。(2)它促进了耶鲁大学和华盛顿大学的教学、培训和学习。(3)研究人员出席统计和科学会议并介绍他们的研究，这可能会促进其他科学家之间的跨学科研究。

The long term goal of this study is to develop novel semiparametric analysis tools for biological, economical, demographical, and medical studies. In this study, the investigators propose novel semiparametric two-part models for analysis of (1) case I and (2) case k interval censored data with a cured subgroup, and (3) left censored data. Compared with existing ones, the proposed models have greater flexibility by allowing for semiparametric transformation functions and partially linear covariate effects. This study is the first to systematically investigate semiparametric two-part cure rate models with interval censored data, and two-part partially linear transformation models with left censored data. The investigators rigorously establish asymptotic properties of the proposed estimates using advanced empirical process techniques, and demonstrate a systematic framework for future semiparametric analysis of such data. Intensive numerical studies are employed to demonstrate superiority of proposed methods and provide guidelines for practical data analysis.This study has the following scientific merits. (1) From a modeling point of view, it enriches semiparametric methodologies in general. The proposed models differ significantly from existing parametric or semiparametric alternatives, and are valuable additions to the family of semiparametric models. (2) From a methodology point of view, the investigators establish a general framework of penalized estimation and resampling-based inference for semiparametric models using advanced empirical process techniques. This framework is useful for many other studies. (3) From a statistical practice point of view, the proposed study provides powerful tools for analyzing ongoing studies and has a direct impact. (4) In addition, extensive numerical studies show that the proposed methods are more efficient, more flexible, and less sensitive to model mis-specification. In large scale studies, variables can have complex, nonlinear associations, and observations may be extremely expensive to collect. The proposed models, along with rigorous analysis techniques, provide more efficient usage of such data, reveal more subtle structures, and benefit the whole scientific society in the long run. The proposed study has the following beneficial, educational and social impacts. (1) It fosters more intensive collaborations among investigators from different institutes and background.(2) It promotes teaching, training and learning at Yale University and University of Washington. (3) The investigators attend statistical and scientific meetings and present their research, which may promote interdisciplinary research among other scientists.