# Zero Inflation as a Missing Data Problem: a Proxy-based Approach

arXiv: https://arxiv.org/abs/2406.00549 · HTML: https://mlsanity.com/paper/2406.00549/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 27 references that are in the map.
- First posted on arXiv 1 Jun 2024.

## Builds on (most cited first, 7 of 7)

- [An Automated Approach to Causal Inference in Discrete Settings](https://mlsanity.com/paper/2109.13471/) (2021)
- [Full Law Identification In Graphical Models Of Missing Data: Completeness Results](https://mlsanity.com/paper/2004.04872/) (2020)
- [Identification In Missing Data Models Represented By Directed Acyclic Graphs](https://mlsanity.com/paper/1907.00241/) (2019)
- [Semiparametric Inference for Non-monotone Missing-Not-at-Random Data: the No Self-Censoring Model](https://mlsanity.com/paper/1909.01848/) (2019)
- [Gene Regulatory Network Inference in the Presence of Dropouts: a Causal View](https://mlsanity.com/paper/2403.15500/) (2024)
- [Markovian acyclic directed mixed graphs for discrete data](https://mlsanity.com/paper/1301.6624/) (2013)
- [Directed Graphical Models and Causal Discovery for Zero-Inflated Data](https://mlsanity.com/paper/2004.04150/) (2020)

## Abstract (arXiv)

A common type of zero-inflated data has certain true values incorrectly replaced by zeros due to data recording conventions (rare outcomes assumed to be absent) or details of data recording equipment (e.g. artificial zeros in gene expression data). Existing methods for zero-inflated data either fit the observed data likelihood via parametric mixture models that explicitly represent excess zeros, or aim to replace excess zeros by imputed values. If the goal of the analysis relies on knowing true data realizations, a particular challenge with zero-inflated data is identifiability, since it is difficult to correctly determine which observed zeros are real and which are inflated. This paper views zero-inflated data as a general type of missing data problem, where the observability indicator for a potentially censored variable is itself unobserved whenever a zero is recorded. We show that, without additional assumptions, target parameters involving a zero-inflated variable are not identified. However, if a proxy of the missingness indicator is observed, a modification of the effect restoration approach of Kuroki and Pearl allows identification and estimation, given the proxy-indicator relationship is known. If this relationship is unknown, our approach yields a partial identification strategy for sensitivity analysis. Specifically, we show that only certain proxy-indicator relationships are compatible with the observed data distribution. We give an analytic bound for this relationship in cases with a categorical outcome, which is sharp in certain models. For more complex cases, sharp numerical bounds may be computed using methods in Duarte et al.[2023]. We illustrate our method via simulation studies and a data application on central line-associated bloodstream infections (CLABSIs).