Missing data imputation using utility-based regression and sampling approaches

Data are often missing not at random (MNAR) in scientific experiments. We treat the MNAR problem as an imbalanced learning task. Standard predictive error measures of regression (e.g., mean squared error) are not suitable for imbalanced learning problems, such as in clinical trials where extreme values tend to be MNAR. We investigate hybrid imbalanced learning approaches that combine utility-based regression (UBR) with synthetic minority oversampling technique for regression (SMOTER) in cross-sectional trial settings. UBR optimizes the product of the conditional probability density (estimated by quantile regression forests) and a utility function which takes the relevance of the target variable value and the prediction error into account. SMOTER oversamples the relevant rare cases. Simulations show that the proposed method provides plausible predictions and reduces the bias for realistic missing data scenarios when compared with standard approaches like random forests and multiple imputation (systematic bias is observed in those methods, i.e., a tendency to underestimate the mean and standard deviation given the presence of MNAR in the area of high values of the target variable). The proposed method is implemented in a real dataset from an antidepressant clinical trial, and similar pattern of the systematic bias from commonly used methods is observed in the real data compare to the proposed method. Therefore, we encourage the integration of utility-based learning strategies for handling of missing data in the analysis of clinical trials.