Multiple imputation with non-additively related variables: Joint-modeling and approximations

This paper investigates multiple imputation methods for regression models with interacting continuous and binary predictors when continuous variable may be missing. Usual implementations for parametric multiple imputation assume a multivariate normal structure for the variables, which is not satisfied for a binary variable nor its interaction with a continuous variable. To accommodate interactions, missing covariates are multiply imputed from conditional distribution in a manner consistent with the joint model. Alternative imputation methods under multivariate normal assumptions are also considered as candidate approximations and evaluated in a simulation study. The results suggest that the joint modeling procedure performs generally well across a wide range of scenarios and so do the approximation methods that incorporate interactions in the model appropriately by stratification. It is critical to include interactions in the imputation model as failure to do so may result in low coverage and bias. We apply the joint modeling approach and approximation methods in the study of childhood trauma with gender × trauma interaction.