= Missing data
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<Missing data> are intended measurements that were not observed. Write $R=1$ when an outcome $Y$ is observed and let $X$ denote fully observed <covariate>[covariates]. The observation mechanism matters because observed cases can differ systematically from the target population.
<Missing completely at random> <mean>[means] $R$ is <independent random variables>[independent] of both $Y$ and $X$. <Missing at random> allows observation to depend on $X$, but requires $R$ and $Y$ to be conditionally <independent random variables>[independent] given $X$. <Missing not at random> permits additional dependence on the unobserved $Y$. For example, follow-up determined only by recorded age can be <missing at random> after conditioning on age; follow-up depending on unrecorded current symptoms can be <missing not at random>. The missing-at-random assumption generally cannot be established from the observed data alone.
An <observed-case analysis> need not estimate the population <mean> even under <missing at random>, because the <probability distribution>[distribution] of $X$ among observed cases can be different. Regression, <Inverse probability weighting> or <Multiple imputation> can address this under suitable assumptions, including a positive <probability> of observation throughout the target population. Stating those assumptions is part of the <statistical model> rather than a consequence of an imputation algorithm.
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