# Multiple imputation and test-wise deletion for causal discovery with incomplete cohort data

arXiv: https://arxiv.org/abs/2108.13331 · HTML: https://mlsanity.com/paper/2108.13331/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 76 references that are in the map.
- First posted on arXiv 30 Aug 2021.

## Builds on (most cited first, 6 of 6)

- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [Graphical Models for Processing Missing Data](https://mlsanity.com/paper/1801.03583/) (2018)
- [Causal Discovery in the Presence of Missing Data](https://mlsanity.com/paper/1807.04010/) (2018)
- [Fast Causal Inference with Non-Random Missingness by Test-Wise Deletion](https://mlsanity.com/paper/1705.09031/) (2017)
- [What Is Meant by "Missing at Random"?](https://mlsanity.com/paper/1306.2812/) (2013)
- [Missing at random: a stochastic process perspective](https://mlsanity.com/paper/1801.06739/) (2018)

## Built on by (most cited first, 2 of 2)

- [Constraint-based causal discovery with tiered background knowledge and latent variables in single or overlapping datasets](https://mlsanity.com/paper/2503.21526/) (2025)
- [PAIR-CI: Calibrated Conditional Independence Testing for Causal Discovery with Incomplete Data](https://mlsanity.com/paper/2605.04838/) (2026)

## Abstract (arXiv)

Causal discovery algorithms estimate causal graphs from observational data. This can provide a valuable complement to analyses focussing on the causal relation between individual treatment-outcome pairs. Constraint-based causal discovery algorithms rely on conditional independence testing when building the graph. Until recently, these algorithms have been unable to handle missing values. In this paper, we investigate two alternative solutions: Test-wise deletion and multiple imputation. We establish necessary and sufficient conditions for the recoverability of causal structures under test-wise deletion, and argue that multiple imputation is more challenging in the context of causal discovery than for estimation. We conduct an extensive comparison by simulating from benchmark causal graphs: As one might expect, we find that test-wise deletion and multiple imputation both clearly outperform list-wise deletion and single imputation. Crucially, our results further suggest that multiple imputation is especially useful in settings with a small number of either Gaussian or discrete variables, but when the dataset contains a mix of both neither method is uniformly best. The methods we compare include random forest imputation and a hybrid procedure combining test-wise deletion and multiple imputation. An application to data from the IDEFICS cohort study on diet- and lifestyle-related diseases in European children serves as an illustrating example.