Label Shift Estimators for Non-Ignorable Missing Data

• URL: http://arxiv.org/abs/2310.18261v1
• Date: Fri, 27 Oct 2023 16:50:13 GMT
• Title: Label Shift Estimators for Non-Ignorable Missing Data
• Authors: Andrew C. Miller and Joseph Futoma
• Abstract summary: We consider the problem of estimating the mean of a random variable Y subject to non-ignorable missingness, i.e., where the missingness mechanism depends on Y. We use our approach to estimate disease prevalence using a large health survey, comparing ignorable and non-ignorable approaches.
• Score: 2.605549784939959
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the problem of estimating the mean of a random variable Y subject to non-ignorable missingness, i.e., where the missingness mechanism depends on Y . We connect the auxiliary proxy variable framework for non-ignorable missingness (West and Little, 2013) to the label shift setting (Saerens et al., 2002). Exploiting this connection, we construct an estimator for non-ignorable missing data that uses high-dimensional covariates (or proxies) without the need for a generative model. In synthetic and semi-synthetic experiments, we study the behavior of the proposed estimator, comparing it to commonly used ignorable estimators in both well-specified and misspecified settings. Additionally, we develop a score to assess how consistent the data are with the label shift assumption. We use our approach to estimate disease prevalence using a large health survey, comparing ignorable and non-ignorable approaches. We show that failing to account for non-ignorable missingness can have profound consequences on conclusions drawn from non-representative samples.

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