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