An instrumental variable approach under dependent censoring

TL;DR

This paper develops an instrumental variable method to estimate causal effects in survival analysis with dependent censoring and unobserved confounding, providing a consistent and asymptotically normal estimator validated through simulations and applied to job training impact.

Contribution

It introduces a novel control function approach using instrumental variables for dependent censoring in survival models with unobserved confounding.

Findings

Estimator is consistent and asymptotically normal.

Simulation studies confirm finite-sample validity.

Applied to assess job training effects on unemployment duration.

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 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.