MNAR

Missing Not At Random (MNAR) describes a missing data mechanism in which the probability of a data value being missing depends on the value itself or on unobserved factors related to the missing data. This contrasts with Missing Completely At Random (MCAR), where missingness is independent of all data, and Missing At Random (MAR), where missingness depends only on observed information. MNAR often occurs when nonresponse is related to the outcome of interest or to unmeasured characteristics.

Because MNAR involves unobserved information, it is not identifiable from the observed data alone. Analysts commonly use models that jointly describe the data and the missingness process, such as selection models, pattern-mixture models, or shared-parameter models. All approaches require strong, sometimes unverifiable assumptions about the missing data and the mechanism causing missingness.

Handling MNAR typically relies on sensitivity analyses to assess how results change under different MNAR assumptions, since no single model can be proven correct from the data alone. When possible, researchers use external data, auxiliary variables, or study designs that reduce nonresponse. Standard methods that assume MAR or MCAR may yield biased estimates if the true mechanism is MNAR; hence careful consideration of missingness is essential in analysis and interpretation.