An instrumental variable approach under dependent censoring
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866917792365674496 |
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| author | Crommen, Gilles Beyhum, Jad Van Keilegom, Ingrid |
| author_facet | Crommen, Gilles Beyhum, Jad Van Keilegom, Ingrid |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_04184 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | An instrumental variable approach under dependent censoring Crommen, Gilles Beyhum, Jad Van Keilegom, Ingrid Statistics Theory 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. |
| title | An instrumental variable approach under dependent censoring |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2208.04184 |