Multiple Imputation by Ordered Monotone Blocks With Application to the Anthrax Vaccine Research Program

Fan Li, Michela Baccini, Fabrizia Mealli, Elizabeth R. Zell, Constantine E. Frangakis, Donald B. Rubin

Research output: Contribution to journalArticlepeer-review


Multiple imputation (MI) has become a standard statistical technique for dealing with missing values. The CDC Anthrax Vaccine Research Program (AVRP) dataset created new challenges for MI due to the large number of variables of different types and the limited sample size. A common method for imputing missing data in such complex studies is to specify, for each of J variables with missing values, a univariate conditional distribution given all other variables, and then to draw imputations by iterating over the J conditional distributions. Such fully conditional imputation strategies have the theoretical drawback that the conditional distributions may be incompatible. When the missingness pattern is monotone, a theoretically valid approach is to specify, for each variable with missing values, a conditional distribution given the variables with fewer or the same number of missing values and sequentially draw from these distributions. In this article, we propose the “multiple imputation by ordered monotone blocks” approach, which combines these two basic approaches by decomposing any missingness pattern into a collection of smaller “constructed” monotone missingness patterns, and iterating. We apply this strategy to impute the missing data in the AVRP interim data. Supplemental materials, including all source code and a synthetic example dataset, are available online.

Original languageEnglish (US)
Pages (from-to)877-892
Number of pages16
JournalJournal of Computational and Graphical Statistics
Issue number3
StatePublished - Jul 3 2014


  • Bayesian
  • Conditional distribution
  • Incompatibility
  • Missing data
  • PIGS

ASJC Scopus subject areas

  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Statistics, Probability and Uncertainty

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