  Missing data are common in data analyses in biomedical fields, and imputation
methods based on random forests (RF) have become widely accepted, as the RF
algorithm can achieve high accuracy without the need for specification of data
distributions or relationships. However, the predictions from RF do not contain
information about prediction uncertainty, which was unacceptable for multiple
imputation. Available RF-based multiple imputation methods tried to do proper
multiple imputation either by sampling directly from observations under
predicting nodes without accounting for the prediction error or by making
normality assumption about the prediction error distribution. In this study, a
novel RF-based multiple imputation method was proposed by constructing
conditional distributions the empirical distribution of out-of-bag prediction
errors. The proposed method was compared with previous method with parametric
assumptions about RF's prediction errors and predictive mean matching based on
simulation studies on data with presence of interaction term. The proposed
non-parametric method can deliver valid multiple imputation results. The
accompanying R package for this study is publicly available.
