Assumptions and analysis planning in studies with missing data in multiple variables: moving beyond the MCAR/MAR/MNAR classification

Abstract

Researchers faced with incomplete data are encouraged to consider whether their data are ‘missing completely at random’ (MCAR), ‘missing at random’ (MAR) or ‘missing not at random’ (MNAR) when planning their analysis. However, there are two major problems with this classification as originally defined by Rubin in the 1970s. First, when there are missing data in multiple variables, the plausibility of the MAR assumption is difficult to assess using substantive knowledge and is more stringent than is generally appreciated. Second, although MCAR and MAR are sufficient conditions for consistent estimation with specific methods, they are not necessary conditions and therefore this categorization does not directly determine the best approach for handling the missing data in an analysis. How best to handle missing data depends on the assumed causal relationships between variables and their missingness, and what these relationships imply in terms of the ‘recoverability’ of the target estimand (the population parameter that encodes the answer to the underlying research question). Recoverability is defined as whether the estimand can be consistently estimated from the patterns and associations in the observed data without needing to invoke external information on the extent to which the distribution of missing values might differ from that of observed values. In this manuscript we outline an approach for deciding which method to use to handle multivariable missing data in an analysis, using directed acyclic graphs to depict missingness assumptions and determining the implications in terms of recoverability of the target estimand.