A Complete Characterisation of Structured Missingness
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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 M_1, M_2, ..., M_p are independent after conditioning on the relevant portion of the data matrix π. As this is often unsuitable for characterising SM in multivariate settings, we introduce a taxonomy for SM, where each M_j can depend on π_-j (i.e., all missingness indicator vectors except M_j), in addition to π. 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 π and π_-j on M_j. 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.
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