区间删失数据下几类半参数回归模型的统计推断

Interval censoring is an important censoring mechanism in survival analysis. Interval-censored data has enjoys strong applicability in epidemiological, medical, financial, sociological studies and so on， there is great theoretical significance to research interval-censored data. Compared with right-censored data in survival analysis, interval-censored data is a more general and more complex data. Because of the complexity of interval censoring mechanism and the special structure of interval-censored data, most of the inference approaches for right-censored data are not appropriate for interval-censored data due to the fundamental differences between right censoring and interval censoring, and some theories for right-censored data are not applicable to interval-censored data. The goal of this proposal is to develop some statistical inference methods for several semiparametric models with interval-censored data, which will study the following problems: Statistical inference problems under the proportional hazards model with interval-censored data. Statistical inference problems under the the additive hazards model with auxiliary covariates with interval-censored data. Statistical inference problems for linar transformation model and the varying-coefficient partial linear proportional hazards model with interval-censored data. The estimate problems of hazards ratio. Regression analysis problems for clustered interval-censored data under the frailty model. The research of this proposal will improve the theories of regression analysis with interval-censored data, which will improve the research level of survival analysis in China.

区间删失是生存分析中一种重要的删失方式. 区间删失数据在流行病学、医学、金融学﹑社会学等领域有很强的应用背景，对其进行研究有重大的理论意义.相比较生存分析中常见的右删失数据，区间删失数据是一类更一般也更复杂的数据，由于区间删失机制的复杂性和区间删失数据结构的特殊性，绝大多数用于右删失数据的统计推断方法和一些基础理论工具不再适用于区间删失数据.本项目的目的是为区间删失数据下几类典型的半参数模型给出行之有效的统计推断方法. 本项目的研究内容涉及：区间删失数据下，基于比例风险率模型的统计推断问题；基于加法风险率模型且带辅助协变量的统计推断问题；基于线性变换模型的统计推断问题；基于变系数部分线性比例风险率模型的统计推断问题；两个风险率函数比的估计问题；基于脆性风险率模型对聚类的区间删失数据做回归分析的问题.本项目的研究将进一步完善区间删失数据下回归分析的理论，进一步提高我国生存分析的研究水平.

区间删失是生存分析中一种重要的删失方式. 区间删失数据在流行病学、医学、金融学﹑社会学等领域有很强的应用背景，对其进行研究有重大的理论意义.相比较生存分析中常见的右删失数据，区间删失数据是一类更一般也更复杂的数据，由于区间删失机制的复杂性和区间删失数据结构的特殊性，绝大多数用于右删失数据的统计推断方法和一些基础理论工具不再适用于区间删失数据. 通过开展本项目的研究工作，申请人及其研究团队以区间删失数据为研究对象，研究了基于加法风险率模型下带辅助协变量的回归分析问题；研究了基于函数系数的风险率模型的回归分析问题；研究了两个生存函数是否相等的假设检验问题；研究了基于脆性风险率模型的回归分析的问题等. 通过四年的努力，申请人及其研究团队完成了本项目的研究内容相关的14篇学术论文，其中9篇论文已经被国外SCI期刊正式发表，有5篇论文正在评审过程中(已提交修改稿)，另外还有三篇论文已经完成理论推导。本项目的顺利实施将进一步完善区间删失数据下回归分析的理论，进一步提高我国生存分析的研究水平。