Variable selection with missing data in both covariates and outcomes: Imputation and machine learning

Variable selection in the presence of both missing covariates and outcomes is an important statistical research topic. Parametric regression are susceptible to misspecification, and as a result are sub-optimal for variable selection. Flexible machine learning methods mitigate the reliance on the parametric assumptions, but do not provide as naturally defined variable importance measure as the covariate effect native to parametric models. We investigate a general variable selection approach when both the covariates and outcomes can be missing at random and have general missing data patterns. This approach exploits the flexibility of machine learning models and bootstrap imputation, which is amenable to nonparametric methods in which the covariate effects are not directly available. We conduct expansive simulations investigating the practical operating characteristics of the proposed variable selection approach, when combined with four tree-based machine learning methods, extreme gradient boosting, random forests, Bayesian additive regression trees, and conditional random forests, and two commonly used parametric methods, lasso and backward stepwise selection. Numeric results suggest that, extreme gradient boosting and Bayesian additive regression trees have the overall best variable selection performance with respect to the $$ score and Type I error, while the lasso and backward stepwise selection have subpar performance across various settings. There is no significant difference in the variable selection performance due to imputation methods. 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.