Missing data

Missing data occur when some intended measurements are unobserved. Whether valid inference can ignore the missingness mechanism depends on how the probability of observation relates to observed and unobserved values.

Data are missing completely at random when the missingness indicator is independent of both observed and missing data.

Data are missing at random when the probability of missingness, conditional on observed data, does not depend further on the missing values.

Data are missing not at random when the probability of missingness still depends on an unobserved value after conditioning on the observed data.

Repeated measurements have a monotone missing-data pattern when every measurement after a subject's first missing value is also missing.

A complete-case analysis uses only observations for which every variable required by the analysis is observed. It can be biased when completeness selects observations according to their outcomes or other relevant variables.

Multiple imputation repeatedly draws missing values from fitted predictive distributions, analyzes each completed dataset, and combines the resulting estimates and uncertainty.