# A Complete Characterisation of Structured Missingness

arXiv: https://arxiv.org/abs/2307.02650 · HTML: https://mlsanity.com/paper/2307.02650/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 41 references that are in the map.
- First posted on arXiv 5 Jul 2023.

## Builds on (most cited first, 5 of 5)

- [Graphical Models for Processing Missing Data](https://mlsanity.com/paper/1801.03583/) (2018)
- [Learning from data with structured missingness](https://mlsanity.com/paper/2304.01429/) (2023)
- [Multiple imputation for multilevel data with continuous and binary variables](https://mlsanity.com/paper/1702.00971/) (2017)
- [Model-assisted cohort selection with bias analysis for generating large-scale cohorts from the EHR for oncology research](https://mlsanity.com/paper/2001.09765/) (2020)
- [Prediction approaches for partly missing multi-omics covariate data: A literature review and an empirical comparison study](https://mlsanity.com/paper/2302.03991/) (2023)

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

- [CACTI: Leveraging Copy Masking and Contextual Information to Improve Tabular Data Imputation](https://mlsanity.com/paper/2506.02306/) (2025)
- [One Pipeline, Many Transformers: Pattern-Specific Imputation Specialists for Tabular Missing Data](https://mlsanity.com/paper/2510.02625/) (2025)

## Abstract (arXiv)

Our capacity to process large complex data sources is ever-increasing, providing us with new, important applied research questions to address, such as how to handle missing values in large-scale databases. Mitra et al. (2023) noted the phenomenon of Structured Missingness (SM), which is where missingness has an underlying structure. Existing taxonomies for defining missingness mechanisms typically assume that variables' missingness indicator vectors M1, M2, ..., Mp are independent after conditioning on the relevant portion of the data matrix X. As this is often unsuitable for characterising SM in multivariate settings, we introduce a taxonomy for SM, where each Mj can depend on M-j (i.e., all missingness indicator vectors except Mj), in addition to X. We embed this new framework within the well-established decomposition of mechanisms into MCAR, MAR, and MNAR (Rubin, 1976), allowing us to recast mechanisms into a broader setting, where we can consider the combined effect of X and M-j on Mj. We also demonstrate, via simulations, the impact of SM on inference and prediction, and consider contextual instances of SM arising in a de-identified nationwide (US-based) clinico-genomic database (CGDB). We hope to stimulate interest in SM, and encourage timely research into this phenomenon.