区间删失数据的半参数回归模型的有效估计方法

In this project, we propose several classes of novel semiparametric regression models for the analysis of interval-censored failure time data and develop corresponding efficient estimation procedures. Such data often occur in many areas such as medical studies, demographics, economics and social science. Most existing methods are designed for the analysis of right-censored data and no longer available for interval-censored data. Semiparmetric analysis of interval-censored data presents novel and challenging theoretical and computational problems in statistics. Some methods have been developed for regression analysis of interval-censored data, but most of them are ad-hoc and not efficient or only apply to limited situations. This project will study the theoretical properties of the proposed estimation methods in several classes of important survival analysis models, including the linear transformation and varying-coefficient partially linear transformation models, the additive hazards and varying-coefficient partially linear additive hazards models, and the linear transformed hazards and varying-coefficient partially linear transformed hazards models, in the cases of interval-censored data. These models are more general and flexible than the models that have been used for interval-censored data. The likelihood-based or sieve likelihood-based approaches will be used for estimation of model parameters. We will show that the resulting estimator of regression parameter is consistent, asymptotically normal, and achieves semiparametric efficiency bound for each model considered. The proposed methods are expected to be able to fill the gap in the literature on interval-censored data analysis. Simulation studies will be conducted to evaluate the proposed methods and compare them with the existing methods. Real data involving interval censoring will be analyzed to illustrate the applications of the proposed methods to important scientific problems.

区间删失数据在生物医学、人口学、经济学以及社会科学研究中大量存在，使得关于该类数据的统计分析成为近代统计学研究的热点问题之一。由于该类数据结构复杂，从而导致生存分析中大量关于右删失数据统计方法不再适用，也使得相应的统计推断的理论和计算都变得困难和有挑战性。目前已有的关于区间删失数据的统计推断方法或者不是有效的，或者只针对某些特定的模型，发展针对一般模型的有效的统计推断方法是目前该项研究的空白。本项目基于几类适用范围更广更灵活的半参数模型，研究区间删失数据下的有效的半参数统计推断方法，从而填补该项研究的部分空白。这些模型包括：线性转换模型和变系数部分线性转换模型、加危险率模型和变系数部分加危险率模型、转换风险模型和变系数部分转换风险模型。我们将利用似然和近似似然方法估计模型参数，并证明相应估计的相合性、渐近正态性和半参数有效性。通过模拟计算和实证分析评估我们方法在有限样本下的表现。

区间删失数据在生物医学、人口学、经济学以及社会科学研究中大量存在，使得关于该类数据的统计分析成为近代统计学研究的热点问题之一。由于该类数据结构复杂，从而导致生存分析中大量关于右删失数据统计方法不再适用，也使得相应的统计推断的理论和计算都变得困难和有挑战性。目前已有的关于区间删失数据的统计推断方法或者不是有效的，或者只针对某些特定的模型，发展针对一般模型的有效的统计推断方法是目前该项研究的空白。本项目基于几类适用范围更广更灵活的半参数模型，研究区间删失数据下的有效的半参数统计推断方法，从而填补该项研究的部分空白。我们分别利用似然和近似似然方法估计模型参数，研究了估计的渐近分布和半参数有效性，并设计了相应的计算方法，通过模拟计算和真实数据分析探索了我们提出的各种方法的实用性。由于实际问题中产生的数据结构更加复杂，比如存在数据缺失、有偏抽样数据和高维数据等，我们进一步研究了几类模型假设下，基于非随机缺失数据和有偏抽样删失数据的半参数统计推断问题，研究了基于高维删失数据的变量筛选方法。

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