Bivariate survival analysis with complete or censored data

衡量两个变量之间的依赖程度在实践中具有重要意义。例如，假设收集了接受心脏移植的患者的数据。确定移植时的年龄和手术后的存活时间之间是否有关系可能是有意义的。在数据不完整的情况下，这种关联性的衡量标准并不容易估计。导致数据不完整的两个最常见的现象是删减和截断。例如，如果我们所能获得的唯一信息是一个观测的真值大于某个数字c，则该观测被称为“右删减”。当样本中只包括其值大于某个数字c的个人时，变量X被称为“左截断”(其他个人在数据收集过程中完全遗漏)。还有其他几种不完整数据的方案。我打算开发在这样的环境下估计两个变量之间的相关性的方法。

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.