Evaluation of Four Multiple Imputation Methods for Handling Missing Binary Outcome Data in the Presence of an Interaction between a Dummy and a Continuous Variable

Multiple imputation by chained equations (MICE) is the most common method for imputing missing data. In the MICE algorithm, imputation can be performed using a variety of parametric and nonparametric methods. The default setting in the implementation of MICE is for imputation models to include variables as linear terms only with no interactions, but omission of interaction terms may lead to biased results. It is investigated, using simulated and real datasets, whether recursive partitioning creates appropriate variability between imputations and unbiased parameter estimates with appropriate confidence intervals. We compared four multiple imputation (MI) methods on a real and a simulated dataset. MI methods included using predictive mean matching with an interaction term in the imputation model in MICE (MICE-interaction), classification and regression tree (CART) for specifying the imputation model in MICE (MICE-CART), the implementation of random forest (RF) in MICE (MICE-RF), and MICE-Stratified method. We first selected secondary data and devised an experimental design that consisted of 40 scenarios (2 x 5 x 4), which differed by the rate of simulated missing data (10%, 20%, 30%, 40%, and 50%), the missing mechanism (MAR and MCAR), and imputation method (MICE-Interaction, MICE-CART, MICE-RF, and MICE-Stratified). First, we randomly drew 700 observations with replacement 300 times, and then the missing data were created. The evaluation was based on raw bias (RB) as well as five other measurements that were averaged over the repetitions. Next, in a simulation study, we generated data 1000 times with a sample size of 700. Then, we created missing data for each dataset once. For all scenarios, the same criteria were used as for real data to evaluate the performance of methods in the simulation study. It is concluded that, when there is an interaction effect between a dummy and a continuous predictor, substantial gains are possible by using recursive partitioning for imputation compared to parametric methods, and also, the MICE-Interaction method is always more efficient and convenient to preserve interaction effects than the other methods.