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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 covariates. The observation mechanism matters because observed cases can differ systematically from the target population.

Missing completely at random means $R$ is independent of both $Y$ and $X$. Missing at random allows observation to depend on $X$, but requires $R$ and $Y$ to be conditionally 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 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.