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An instrumental variable approach under dependent censoring

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Abstract

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 dependent on 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.

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Acknowledgements

Financial support from the European Research Council (2016-2022, Horizon 2020 / ERC grant agreement No. 694409) is gratefully acknowledged. The authors are grateful for the valuable suggestions and feedback from the reviewers. Moreover, the authors would like to thank Sara Rutten and Ilias Willems for their useful comments and remarks.

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Authors and Affiliations

  1. ORSTAT, KU Leuven, Naamsestraat 69, 3000, Leuven, Belgium

    Gilles Crommen & Ingrid Van Keilegom

  2. Department of Economics, KU Leuven, Naamsestraat 69, 3000, Leuven, Belgium

    Jad Beyhum

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  1. Gilles Crommen
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  2. Jad Beyhum
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  3. Ingrid Van Keilegom
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Correspondence to Gilles Crommen.

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Crommen, G., Beyhum, J. & Van Keilegom, I. An instrumental variable approach under dependent censoring. TEST (2023). https://doi.org/10.1007/s11749-023-00903-9

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