Bivariate survival analysis with complete or censored data

测量两个变量之间的依赖程度在实践中是非常重要的。例如，假设收集了接受心脏移植的患者的数据。确定移植时的年龄与手术后的生存时间之间是否存在关系可能会引起人们的兴趣。在数据不完整的情况下，这种关联度量不容易估计。导致数据不完整的两种最常见的现象是删节和截断。例如，如果我们能得到的唯一信息是它的真实值大于某个数字c，那么一个观察结果就被称为“右截”。当只有X的值大于某个数字c的个体被包括在样本中时，变量X被称为“左截”（其他个体在数据收集过程中被完全遗漏）。还有其他几种数据不完全的方案。我打算开发在这种情况下估计两个变量之间相关性的方法。

Measuring the level of dependence between two variables is of great importance in practice. For example, suppose data are collected on patients receiving heart transplantation. It may be of interest to determine if there is a relationship between age at transplantation and the survival time following the operation. Such measures of association are not easy to estimate in presence of incomplete data. The two most common phenomenons causing incomplete data are censoring and truncation. For instance, an observation is said to be "right-censored" if the only information available to us is that its true value is greater than some number c. A variable X is said to be "left-truncated" when only individuals whose value of X is greater than some number c are included in the sample (other individuals are completely missed by the data collection process). There exist several other schemes of incomplete data. I intend to develop methods of estimating the dependence between two variables under such settings.