Variable selection and prediction of clinical outcome with multiply-imputed data via Bayesian model averaging

Multiple imputation (MI) is increasingly used to deal with missing data in medical studies, whilst variable selection and prediction on multiply-imputed data is an area under intense research in statistics. A commonly used strategy is to select a single top model based on the Rubin's rules (RR). However, such approaches do not take the model uncertainty into consideration, which might lead to over-confident inferences. In this paper, we extended the Bayesian model averaging method to perform variable selection and prediction under multiple imputation (MI-BMA), which takes into account the uncertainties originated from both the missing data and the model selection. We applied the MI-BMA method to simulated datasets as well as a real data set from a prospective cohort, and demonstrated the advantage of our method as compared with the classical RR stepwise method.