= Missingness overlap from marginal and complete-case counts
{title2=$m_{XY}=m_X+m_Y-(N-n_{XY})$}
= Two-variable missingness overlap
{synonym}
For $N$ observations, let $m_X$ and $m_Y$ count missing values of two <variables>, and let $n_{XY}$ count observations on which both are available. The number missing at least one variable is $N-n_{XY}$. Applying the <inclusion-exclusion principle> to the two missing-value <sets> gives the displayed number missing both. The disjoint counts are consequently $m_X-m_{XY}$ missing only $X$, $m_Y-m_{XY}$ missing only $Y$, $m_{XY}$ missing both, and $n_{XY}$ complete cases. Their nonnegativity is a necessary consistency check on the supplied totals.
This identifies an aggregate missingness pattern without reconstructing individual records. It does not identify a <missing-data mechanism>, establish <missing completely at random>, or justify treating a substantive response such as an explicit unknown category as a missing observation. Counts from different cohorts cannot be inserted into the identity without first establishing a common denominator.
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