This paper considers the problem of inferring the causal effect of a variable $Z$ on a dependently censored survival time $T$. We allow for unobserved confounding variables, such that the error term of the regression model for $T$ is correlated with the confounded variable $Z$. Moreover, $T$ is subject to dependent censoring. This means that $T$ is right censored by a censoring time $C$, which is dependent on $T$ (even after conditioning out the effects of the measured covariates). A control function approach, relying on an instrumental variable, is leveraged to tackle the confounding issue. Further, it is assumed that $T$ and $C$ follow a joint regression model with bivariate Gaussian error terms and an unspecified covariance matrix such that the dependent censoring can be handled in a flexible manner. Conditions under which the model is identifiable are given, a two-step estimation procedure is proposed, and it is shown 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 causal effect of job training programs on unemployment duration.

翻译：本文审议了一个变量Z$对受审查的生存时间的因果关系的推断问题。 我们允许出现未观察到的令人费解的变量,因此,美元回归模型的错误术语与混结变量Z美元相关。 此外,美元T美元受独立审查。这意味着,美元T$由审查时间C美元进行右审查,这取决于美元T美元(即便在限定了所测量的共变项的影响之后)。 一种依赖工具变量的控制功能方法被杠杆化,用于解决相互交织的问题。 此外,还假设美元T$和美元C$遵循一个联合回归模式,使用双变量Gausian错误术语和一个未具体说明的共变差矩阵,以便可以灵活地处理独立审查。 给出了模型可识别的条件,提出了两步估算程序,并表明由此得出的估算值是一致的,且是正常的。 模拟用于证实工作周期有效性和定数性估算程序所使用的工作周期是所使用的方法。