Abstract

Missing covariate data is a common issue in epidemiological and clinical research, and is often dealt with using multiple imputation (MI). When the analysis model is non-linear, or contains non-linear (e.g. squared) or interaction terms, this complicates the imputation of covariates. Standard software implementations of MI typically impute covariates from models that are uncongenial with such analysis models. We show how imputation by full conditional specification, a popular approach for performing MI, can be modified so that covariates are imputed from a model which is congenial with the analysis model. We investigate through simulation the performance of this proposal, and compare it to passive imputation of non-linear or interaction terms and the `just another variable’ approach. Our proposed approach provides consistent estimates provided the imputation models and analysis models are correctly specified and data are missing at random. In contrast, passive imputation of non-linear or interaction terms generally results in inconsistent estimates of the parameters of the model of interest, while the `just another variable’ approach gives consistent results only for linear models and only if data are missing completely at random. Furthermore, simulation results suggest that even under imputation model mis-specification our proposed approach gives estimates which are substantially less biased than estimates based on passive imputation. The proposed approach is illustrated using data from the National Child Development Survey in which the analysis model contains both non-linear and interaction terms.