区间删失数据下竞争风险模型研究

项目名称： 区间删失数据下竞争风险模型研究

项目编号： No.10801003

项目类型： 青年科学基金项目

立项/批准年度： 2009

项目学科： 金属学与金属工艺

项目作者： 沈俊山

作者单位： 北京大学

项目金额： 15万元

中文摘要： 在基金的资助下, 项目组完成了以下课题的研究: (1). 缺失数据下单指标模型相关参数的统计推断， 得到了相应统计量的相合性和中心极限定理, 给出了如何选择光滑参数 (带宽)的方法； (2).研究了带有协变量的区间删失数据下竞争风险模型的参数推断问题，得到了最大似然估计的大样本性质以及有限样本性质，证明了估计量的有效性； (3).利用筛法研究了缺失删失信息时, Cox 模型的统计推断问题； (4) 在不完全数据的非参数模型研究中，利用经验似然的思想， 结合EM算法, 研究了复杂数据下似然比统计量的计算以及大样本性质.

中文关键词： 缺失数据; 竞争风险模型; 经验似然;EM 算法;区间删失数据.

英文摘要： (1). Under missing at random, we estimate the unknown link function and the direction parameter in a single index model. The central limit theory and the convergence rate of the law of the iterated logarithm for the estimator of the direction parameter are derived, the optimal convergence rate for the estimator of the link function is obtained (2). The proportional hazards model is the most commonly used model in regression analysis of failure time data. we study proportional hazards model to current status data when there exist competing risks. The maximum likelihood estimates of the unknown parameters are derived and their consistency and convergence rate are established. Also we show that the estimates of regression coefficients are efficient and have asymptotically normal distributions. (3).We analyze right-censored failure time data when censoring indicators are missing for some subjects. We present an efficient estimation procedure for regression parameters that does not require the proportionality assumption. An EM algorithm is developed and the method is evaluated by a simulation study, which indicates that the proposed methodology performs well for practical situations. An illustrative example is provided. (4).In recent years, empirical likelihood method has been employed to deal with incomplete data. One way to do it is to construct synthetic complete data from incomplete sample. Unfortunately, since the synthetic data are not independent and identically distributed, the corresponding empirical likelihood ratio no longer converges to a standard chi-square distribution. We propose a new self-consistent EM algorithm with constraint to deal with the likelihood ratio for incomplete data and study some properties of the algorithm.

英文关键词： Missing data; Competing risks model; Empirical likelihood; EM algorithm; Interval censored data.