Background Prior work has shown that combining bootstrap imputation with tree-based machine learning variable selection methods can provide good performances 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. Methods We propose an inference-based method, called RR-BART, which 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 MAR data. We conduct a representative simulation study to investigate the practical operating characteristics of RR-BART, and compare it with the bootstrap imputation based methods. We further demonstrate the methods via a case study of risk factors for 3-year incidence of metabolic syndrome among middle-aged women using data from the Study of Women’s Health Across the Nation (SWAN). Results The simulation study suggests that even in complex conditions of nonlinearity and nonadditivity with a large percentage of missingness, RR-BART can reasonably recover both prediction and variable selection performances, achievable on the fully observed data. RR-BART provides the best performance that the bootstrap imputation based methods can achieve with the optimal selection threshold value. In addition, RR-BART demonstrates a substantially stronger ability of detecting discrete predictors. Furthermore, RR-BART offers substantial computational savings. When implemented on the SWAN data, RR-BART adds to the literature by selecting a set of predictors that had been less commonly identified as risk factors but had substantial biological justifications. Conclusion The proposed variable selection method for MAR data, RR-BART, offers both computational efficiency and good operating characteristics and is utilitarian in large-scale healthcare database studies.

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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 likelihoodbased 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 π 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.