  Missing covariate data commonly occur in epidemiological and clinical
research, and are often dealt with using multiple imputation (MI). 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 MI 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 MI, 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 to 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.

Methodology