I review assumptions about the missing-data mechanism that underlie methods for the statistical analysis of data with missing values. I describe Rubin's original definition of missing at random, (MAR), its motivation and criticisms, and his sufficient conditions for ignoring the missingness mechanism for likelihood-based, Bayesian, and frequentist inference. Related definitions, including missing completely at random, always MAR, always missing completely at random, and partially MAR are also covered. I present a formal argument for weakening Rubin's sufficient conditions for frequentist maximum likelihood inference with precision based on the observed information. Some simple examples of MAR are described, together with an example where the missingness mechanism can be ignored even though MAR does not hold. Alternative approaches to statistical inference based on the likelihood function are reviewed, along with non-likelihood frequentist approaches, including weighted generalized estimating equations. Connections with the causal inference literature are also discussed. Finally, alternatives to Rubin's MAR definition are discussed, including informative missingness, informative censoring, and coarsening at random. The intent is to provide a relatively nontechnical discussion, although some of the underlying issues are challenging and touch on fundamental questions of statistical inference. Expected final online publication date for the Annual Review of Statistics, Volume 8 is March 7, 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
Statistical methods without estimating the missingness mechanism: a discussion of ‘statistical inference for nonignorable missing data problems: a selective review’ by Niansheng Tang and Yuanyuan Ju