ABSTRACT
It has been seen in Chapters 1 and 3 how, given an MAR missing data mechanism, a valid analysis that ignores the missing value mechanism can be obtained within a likelihood or Bayesian framework, provided that mild regularity conditions hold. For simple nonlikelihood-based frequentist inferences, the more stringent MCAR assumption is required. An important class of modified frequentist methods are also valid under MAR however; these include inverse probability weighted and doubly robust semi-parametric approaches (Robins, Rotnitzky, and Zhao 1994, Bang and Robins 2005) (see Chapters 8 and 9). Further, semiparametric and other frequentist approaches can be combined with multiple imputation to yield inferences that hold under MAR (see Part IV of this volume). An increasing number of software implementations of these methods are now appearing in standard software.
