STATISTICAL INFERENCE FOR INCOMPLETE SURVIVAL DATA

这项研究的第一个目标是制定统计程序， 帮助计划和分析不完整的生存时间。 二是 制定一个统一的诊断程序， 考克斯模型和偏似然估计的bootstrap。 研究 包含五个目标。 前四个主题考虑统计推断 关于不同种类的不完整生存数据。 这些是混合物 生存时间和其他变量（目标1），双删失数据（目标2）， 截尾截尾数据（目标3）和双变量截尾数据（目标4）。 目标1 - 4不仅本身很重要，而且可以应用于 艾滋病数据。 长期存活者的统计推断， 就会患上亨廷顿舞蹈症。 在许多情况下，在实验中， 相当大比例的动物在某些中毒水平下不 在实验结束时死去。 同样的情况也会发生在艾滋病身上 发病率。 一部分受感染的人永远不会发展成艾滋病（或 很晚才会患上艾滋病）。 我们通过将混合物 两个人口。 对于具有协变量的动物，我们将使用logistic 长期存活者比例的模型和长期存活者比例的考克斯模型。 短期幸存者的失败时间。 半非参数技术将 用于统计分析。 将开发双删失数据的线性秩统计量。 这些 统计学可应用于动物致瘤性实验。 它 预计该程序将在统计和计算上 比目前使用的更有效。 这些延伸 还将研究区间删失数据的统计量。 的 区间删失数据将拟合患有艾滋病的好时血友病患者队列 自然学习。 因为血清阳转的数据只能是 确定发生在末次血清阴性 和第一个血清阳性血清样本。 截断自然出现， 只有在某个已知的时间之后， 起源 例如，在对患有艾滋病的儿童的研究中， 只有在当前日历之前患上艾滋病才能被识别 时间 针对这类数据提出的主要研究领域是： 检验时间截断与失效之间的独立性假设 时间，以及（ii）提供基于线性回归的统计推断 模型以及考克斯模型。 生存广义自洽估计的性质 将研究双变量删失数据的函数。 预计 估计量将是一个真正的生存函数， 比目前使用的。 Bootstrap方法是一种公认的 统计工具，即使在非统计学家，但自助法 对考克斯模型来说并不成功。 在最后一个目标中，我们提出了一个 考克斯模型的一个统一的有希望的恢复格式 最大偏似然估计 同样的想法也可以 用于诊断和折叠。 最重要的特征是 计算效率高，因为该过程只形成风险集 一次

The first objective of the study is to develop statistical procedures that aid the planning and analysis of incomplete survival time. The second is to develop a unified procedure of diagnostics, the jackknife and the bootstrap for the Cox model and partial likelihood estimators. The study contains five aims. The first four topics consider statistical inference about different kinds of incomplete survival data. These are the mixture of survival time and other variables (aim 1), doubly-censored data (aim 2), truncated data with censoring (aim 3) and bivariate censored data (aim 4). Aims 1-4 are not only important in their own right, they can be applied to the AIDS data. Statistical inference for the long-term survivors and Huntington's disease will be developed. In many cases, in the experiments, a substantial proportion of the animals at some intoxicant levels do not die by the end of the experiment. The same situation will happen in AIDS incidence. A portion of infected individuals will never develop AIDS (or will develop AIDS very late). We model these data by involving the mixture of two populations. For an animal with covariate, we will use the logistic model for the proportion of long-term survivors and Cox model for the failure time of short-term survivors. A semi-nonparametric technique will be employed to propose statistical analyses. Linear rank statistic for doubly-censored data will be developed. These statistics can be applied to tumorigenicity experiments with animals. It is anticipated that the procedure will be statistically and computationally more efficient than those in current use. The extension of these statistics to the interval censored data will be investigated as well. The interval censored data will fit the Hershey hemophiliacs cohort with AIDS study naturally. Because the data of seroconversion could be only determined to have occurred in the interval between the last seronegative and the first seropositive serum sample. Truncation arises naturally when individuals come under observation only some known time after the time origin. For example, in the study of pediatric AIDS children who contract AIDS can only be identified if they develop AIDS before current calendar time. The major areas of research proposed for these kind of data are (i) testing the independency assumption between truncation of time and failure time, and (ii) providing statistical inference based on linear regression model as well as the Cox model. The properties of generalized self-consistent estimator of the survival function for bivariate censored data will be studied. It is anticipated that the estimator will be a genuine survival function and more efficient than those in current use. Bootstrap method is a well-recognized statistical tool even among the non-statisticians, but the bootstrap method is not very successful for the Cox model. In the last aim, we propose a unified and promising procedure of the resampling scheme for the Cox model and the maximum partial likelihood estimators. The same idea can also be used for diagnostic and jackknife. The most important feature is the computationally efficient, because the procedure only form the risk set once.