# Causal Inference With Outcome-Dependent Missingness And Self-Censoring

arXiv: https://arxiv.org/abs/2306.05511 · HTML: https://mlsanity.com/paper/2306.05511/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2023.

## Built on by (most cited first, 5 of 5)

- [End-To-End Causal Effect Estimation from Unstructured Natural Language Data](https://mlsanity.com/paper/2407.07018/) (2024)
- [Proximal Causal Inference With Text Data](https://mlsanity.com/paper/2401.06687/) (2024)
- [Recursive Equations For Imputation Of Missing Not At Random Data With Sparse Pattern Support](https://mlsanity.com/paper/2507.16107/) (2025)
- [FLOSS: Federated Learning with Opt-Out and Straggler Support](https://mlsanity.com/paper/2507.23115/) (2025)
- [Response to Discussions of "Causal and Counterfactual Views of Missing Data Models"](https://mlsanity.com/paper/2510.14694/) (2025)

## Abstract (arXiv)

We consider missingness in the context of causal inference when the outcome of interest may be missing. If the outcome directly affects its own missingness status, i.e., it is "self-censoring", this may lead to severely biased causal effect estimates. Miao et al. [2015] proposed the shadow variable method to correct for bias due to self-censoring; however, verifying the required model assumptions can be difficult. Here, we propose a test based on a randomized incentive variable offered to encourage reporting of the outcome that can be used to verify identification assumptions that are sufficient to correct for both self-censoring and confounding bias. Concretely, the test confirms whether a given set of pre-treatment covariates is sufficient to block all backdoor paths between the treatment and outcome as well as all paths between the treatment and missingness indicator after conditioning on the outcome. We show that under these conditions, the causal effect is identified by using the treatment as a shadow variable, and it leads to an intuitive inverse probability weighting estimator that uses a product of the treatment and response weights. We evaluate the efficacy of our test and downstream estimator via simulations.