This paper considers the problem of inferring the causal effect of a variable $Z$ on a survival time $T$. The error term of the model for $T$ is correlated with $Z$, which leads to a confounding issue. Additionally, $T$ is subject to dependent censoring, that is, $T$ is right censored by a censoring time $C$ which is dependent on $T$. In order to tackle the confounding issue, we leverage a control function approach relying on an instrumental variable. Further, it is assumed that $T$ and $C$ follow a joint regression model with bivariate Gaussian error terms and an unspecified covariance matrix, allowing us to handle dependent censoring in a flexible manner. We derive conditions under which the model is identifiable, a two-step estimation procedure is proposed and we show that the resulting estimator is consistent and asymptotically normal. Simulations are used to confirm the validity and finite-sample performance of the estimation procedure. Finally, the proposed method is used to estimate the effectiveness of the Job Training Partnership Act (JTPA) programs on unemployment duration.

中文翻译：

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受相关审查和混杂影响的生存数据的高斯模型

本文考虑推断变量 $Z$ 对生存时间 $T$ 的因果影响的问题。$T$ 模型的误差项与 $Z$ 相关，这导致了一个混淆问题。此外，$T$ 受到依赖审查，也就是说，$T$ 被审查时间 $C$ 正确审查，审查时间 $C$ 取决于 $T$。为了解决混杂问题，我们利用依赖于工具变量的控制函数方法。此外，假设 $T$ 和 $C$ 遵循具有双变量高斯误差项和未指定协方差矩阵的联合回归模型，允许我们以灵活的方式处理相关审查。我们推导出模型可识别的条件，提出了两步估计程序，并且我们证明了得到的估计量是一致的且渐近正态的。模拟用于确认估计过程的有效性和有限样本性能。最后，所提出的方法被用来估计就业培训合作法案（JTPA）计划对失业持续时间的有效性。