title: Appropriate inclusion of interactions was needed to avoid bias in multiple imputation.
abstract: Missing data are a pervasive problem, often leading to bias in complete records analysis (CRA). Multiple imputation (MI) via chained equations is one solution, but its use in the presence of interactions is not straightforward.
  
  
  
  We simulated data with outcome Y dependent on binary explanatory variables X and Z and their interaction XZ. Six scenarios were simulated (Y continuous and binary, each with no interaction, a weak and a strong interaction), under five missing data mechanisms. We use directed acyclic graphs to identify when CRA and MI would each be unbiased. We evaluate the performance of CRA, MI without interactions, MI including all interactions, and stratified imputation. We also illustrated these methods using a simple example from the National Child Development Study (NCDS).
  
  
  
  MI excluding interactions is invalid and resulted in biased estimates and low coverage. When XZ was zero, MI excluding interactions gave unbiased estimates but overcoverage. MI including interactions and stratified MI gave equivalent, valid inference in all cases. In the NCDS example, MI excluding interactions incorrectly concluded there was no evidence for an important interaction.
  
  
  
  Epidemiologists carrying out MI should ensure that their imputation model(s) are compatible with their analysis model.
authors.affiliation: School of Social and Community Medicine, University of Bristol, Canynge Hall, 39 Whatley Road, Bristol, BS8 2PS, UK. Electronic address: kate.tilling@bristol.ac.uk.
authors.forename: Kate
authors.initials: K
authors.lastname: Tilling
authors.affiliation: Department of Medical Statistics, London School of Hygiene and Tropical Medicine, University of London, Keppel Street, London WC1E 7HT, UK; Farr Institute of Health Informatics, London University College London, 222 Euston Road, London NW1 2DA, UK.
authors.forename: Elizabeth J
authors.initials: EJ
authors.lastname: Williamson
authors.affiliation: School of Social and Community Medicine, University of Bristol, Canynge Hall, 39 Whatley Road, Bristol, BS8 2PS, UK.
authors.forename: Michael
authors.initials: M
authors.lastname: Spratt
authors.affiliation: School of Social and Community Medicine, University of Bristol, Canynge Hall, 39 Whatley Road, Bristol, BS8 2PS, UK.
authors.forename: Jonathan A C
authors.initials: JA
authors.lastname: Sterne
authors.affiliation: Department of Medical Statistics, London School of Hygiene and Tropical Medicine, University of London, Keppel Street, London WC1E 7HT, UK; MRC Clinical Trials Unit, University College London, Aviation House 125 Kingsway, London WC2B 6NH, UK.
authors.forename: James R
authors.initials: JR
authors.lastname: Carpenter
mesh_terms: D015982:Bias; D003627:Data Interpretation, Statistical; D015340:Epidemiologic Research Design; D006801:Humans
keywords: Bias; Complete case analysis; Interaction; Missing data; Multiple imputation; Simulation