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非常重要。例如，假设收集关于接受心脏移植的患者的数据。确定移植时的年龄和手术后的生存时间之间是否存在关系可能是有意义的。在数据不完整的情况下，不容易估计这种关联性。导致不完整数据的两种最常见的现象是删失和截断。例如，一个观测值被称为“右删失”，如果我们唯一可用的信息是它的真值大于某个数c。当样本中只包括X值大于某个数字c的个体时（其他个体完全被数据收集过程遗漏），变量X被称为“左截断”。还有其他几种不完整数据的方案。我打算开发的方法，估计在这种情况下，两个变量之间的依赖关系。

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.