Multiple imputation of covariates by fully conditional specification: Accommodating the substantive model

Jonathan W Bartlett, Shaun R Seaman, Ian R White, James R Carpenter

Research output: Contribution to journalArticlepeer-review

307 Citations (SciVal)


Missing covariate data commonly occur in epidemiological and clinical research, and are often dealt with using multiple imputation. Imputation of partially observed covariates is complicated if the substantive model is non-linear (e.g. Cox proportional hazards model), or contains non-linear (e.g. squared) or interaction terms, and standard software implementations of multiple imputation may impute covariates from models that are incompatible with such substantive models. We show how imputation by fully conditional specification, a popular approach for performing multiple imputation, can be modified so that covariates are imputed from models which are compatible with the substantive model. We investigate through simulation the performance of this proposal, and compare it with existing approaches. Simulation results suggest our proposal gives consistent estimates for a range of common substantive models, including models which contain non-linear covariate effects or interactions, provided data are missing at random and the assumed imputation models are correctly specified and mutually compatible. Stata software implementing the approach is freely available.

Original languageEnglish
Pages (from-to)462-487
Number of pages26
JournalStatistical Methods in Medical Research
Issue number4
Early online date12 Feb 2014
Publication statusPublished - 1 Aug 2015


  • Models, Statistical
  • Journal Article
  • Research Support, N.I.H., Extramural
  • Research Support, Non-U.S. Gov't


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