带终止事件的聚类复发事件的统计推断问题

In survival analysis , recurrent event data is frequently encountered. Examples include the repeated to hospital, tumer recurrences. In biometric medical, the clustered data arise frequently. For example, the offsprings from the same mother share common characteristics. The recurrent event is relative to treatment, the subject’s body indications, and the cluster the subject belongs to. Therefore, It is important and significant to study the clustered recurrent event. Because of the existence of the terminal event, it becomes more difficult to study the clustered recurrent event with the terminal event.. The project studies the statistical inference for the semiparametric model of the clustered recurrent event with a terminal event. The semiparametric models include additive rates function model, additive-multiplicative rates function model, accelerated means function model, additive hazards model for gap times, transformed hazards model for gap times and some time-varying coefficients effect models. The research includes constructing an estimating equation to obtain the estimator, deriving the asymptotic distributions of the estimator, numerical simulation for verifying the proposed procedure, applying the method for a real data. When analyzing the real data, we will select an appropriate model from many models through model checking. The project has an important theory significance and practical application value.

在生存分析中，复发事件数据是常见的一种数据类型。比如：在医院里，病人会重复就诊，癌症患者的肿瘤会复发。在生物医学中，聚类数据也是比较常见的。比如，同一个母亲的后代有一些共同的特征。个体的复发情况不仅与治疗，以及本身的体征有关，还与他所在的聚类有关系。所以，研究聚类复发事件是有意义的。同时由于终止事件的存在使得带终止事件的聚类复发事件的研究更困难。.本项目主要研究带终止事件的聚类复发事件的半参数建模与统计推断，其中包括复发事件的加性比率模型，加性-乘积比率模型，加速均值模型，复发事件间隔时间的加性风险函数模型和转移风险函数模型，以及一些变系数效应模型。对提出的模型建立估计方程；推导估计量的方差估计和大样本性质；并进行数值模拟，同时，将提出的方法用来分析实际数据。对于实际数据会进行模型的检验，及各个模型之间的比较，最终找到一个最适合的模型。本项目的研究是有着重要的理论意义和实际应用价值的。