Causal Effect Estimation under Informative Censoring: A Multiple-Imputation Approach with Shadow Calibration

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Abstract
In many data-driven decision-making scenarios, it is crucial to accurately estimate causal effects on time-to-event outcomes, e.g., time-to-purchase. However, these outcomes are often right-censored: due to events occurring beyond the observation period or loss to follow-up, the observed durations for censored samples are the last follow-up times rather than the actual event times. Critically, this censoring is usually informative : the censoring mechanism is intrinsically linked to the event time, which may be partially missing. This dependency violates the non-informative censoring assumption in conventional survival analysis. Consequently, the latent information in censored data is non-ignorable for causal effect estimation, inducing a censoring bias that remains unresolved by current methodologies. To overcome these challenges, we establish a theoretical framework for identifying causal effects on time-to-event outcomes under informative censoring. Based on this, we propose Multiple Imputation with Shadow Calibration (MISC), a principled framework leveraging shadow variables --- fully observed covariates correlated with event time but conditionally independent of the censoring mechanism --- to enable unbiased estimation. Specifically, MISC (1) automatically learns valid shadow representations from observed covariates, (2) utilizes these representations to identify the conditional distribution of event times to impute censored units, and (3) estimates causal effects using the imputed data. Experimental results on semi-synthetic benchmarks and real-world datasets from medical scenarios and a large-scale e-commerce platform show that MISC achieves state-of-the-art performance in causal effect estimation and counterfactual prediction. Codes are available at: https://github.com/suikateiou/MISC.

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