STATISTICAL INFERENCE FOR INCOMPLETE SURVIVAL DATA

这项研究的第一个目标是制定统计程序， 协助规划和分析不完全生存时间。第二个是 开发一个统一的诊断程序，折叠刀和 Cox模型的Bootstrap和偏似然估计。这项研究 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的生存数据。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)、 截断数据和截尾数据(目标3)和二元截尾数据(目标4)。 目标1-4不仅本身很重要，它们还可以应用于 艾滋病数据。长期存活者的统计推断和 亨廷顿氏病将会发生。在许多情况下，在实验中， 相当大比例的动物在某些醉人水平上不会 在实验结束时死亡。同样的情况也会发生在艾滋病身上 发病率。部分感染者永远不会患上艾滋病(或 会在很晚的时候患上艾滋病)。我们通过使用混合物对这些数据进行建模 有两个种群。对于具有协变量的动物，我们将使用Logistic 长期存活者比例模型和长期存活者的Cox模型 短期存活者的失效时间。一种半非参数技术将 用来提出统计分析。 将发展双删失数据的线性秩统计量。这些 统计学可以应用于动物致瘤性实验。它 预计这一过程将是统计和计算的 比目前使用的更有效。它们的扩展 对间隔删失数据的统计也将进行调查。这个 间隔审查的数据将符合好时血友病患者与艾滋病的队列 自然地学习。因为血清转换的数据可能只有 被确定为发生在上一次血清阴性之间的时间间隔内 和第一个血清阳性的血清样本。在以下情况下自然会出现截断 只有在时间过后的某个已知时间，个人才会受到观察 起源。例如，在对感染艾滋病儿童的儿科研究中 只有在当前日历之前患上艾滋病的人才能被确认为艾滋病 时间到了。针对这类数据提出的主要研究领域是：(I) 时间截断与失效之间独立性假设的检验 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。 生存的广义自洽估计的性质 我们将研究二元删失数据的函数。这是意料之中的 估计将是一个真正的生存函数，并且更有效 而不是目前使用的那些。Bootstrap方法是公认的 统计工具即使在非统计学家中也是如此，但自助法 考克斯模型并不是很成功。在最后一个目标中，我们提出了一个 COX模型重抽样方案的统一和有前途的程序 和最大偏似然估计。同样的想法也可以 用于诊断和折刀。最重要的功能是 计算效率高，因为该过程仅形成风险集合 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.