Strategies for variable selection in large-scale healthcare database studies with missing covariate and outcome data

Prior work has shown that combining bootstrap imputation with tree-based machine learning variable selection methods can recover the good performance achievable on fully observed data when covariate and outcome data are missing at random (MAR). This approach however is computationally expensive, especially on large-scale datasets. We propose an inference-based method RR-BART, that leverages the likelihood-based Bayesian machine learning technique, Bayesian Additive Regression Trees, and uses Rubin's rule to combine the estimates and variances of the variable importance measures on multiply imputed datasets for variable selection in the presence of missing data. A representative simulation study suggests that RR-BART performs at least as well as combining bootstrap with BART, BI-BART, but offers substantial computational savings, even in complex conditions of nonlinearity and nonadditivity with a large percentage of overall missingness under the MAR mechanism. RR-BART is also less sensitive to the end note prior via the hyperparameter $k$ than BI-BART, and does not depend on the selection threshold value $\pi$ as required by BI-BART. Our simulation studies also suggest that encoding the missing values of a binary predictor as a separate category significantly improves the power of selecting the binary predictor for BI-BART. We further demonstrate the methods via a case study of risk factors for 3-year incidence of metabolic syndrome with data from the Study of Women's Health Across the Nation.