  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 $\mathbf{X}$. As this is often unsuitable for
characterising SM in multivariate settings, we introduce a taxonomy for SM,
where each ${M}_j$ can depend on $\mathbf{M}_{-j}$ (i.e., all missingness
indicator vectors except ${M}_j$), in addition to $\mathbf{X}$. 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 $\mathbf{X}$ and
$\mathbf{M}_{-j}$ 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.
