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MIBoost: A gradient boosting algorithm for variable selection after multiple imputation

Statistical learning methods for automated variable selection, such as the Least Absolute Shrinkage and Selection Operator (LASSO), elastic nets, and gradient boosting, have become increasingly popular tools for building powerful prediction models. Yet, in practice, analyses are often complicated by missing data. The most widely used approach to address missingness is multiple imputation, which involves creating several completed datasets. However, there is an ongoing debate about how to perform model selection in the presence of multiple imputed datasets. Simple strategies, such as pooling models across datasets, have been shown to have suboptimal properties. Although more sophisticated methods exist, they are often difficult to implement and therefore not widely applied. In contrast, two recent approaches extend the regularization methods LASSO and elastic nets to multiply imputed datasets by defining a single loss function, resulting in a unified set of coefficients across imputations. Our key contribution is to extend this principle to the framework of component-wise gradient boosting by proposing MIBoost, a novel algorithm that employs a uniform variable-selection mechanism across imputed datasets, together with its corresponding cross-validation routine MIBoostCV. In a simulation study, MIBoost yielded predictive performance comparable to that of other established methods, providing a practical boosting-based approach for variable selection with multiply imputed data. The proposed framework is implemented as the R package booami.

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