A Gaussian model for survival data subject to dependent censoring and confounding

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.