Adaptive Use of Co-Data Through Empirical Bayes for Bayesian Additive Regression Trees

For clinical prediction applications, we are often faced with small sample size data compared to the number of covariates. Such data pose problems for variable selection and prediction, especially when the covariate-response relationship is complicated. To address these challenges, we propose to incorporate external information on the covariates into Bayesian additive regression trees (BART), a sum-of-trees prediction model that utilizes priors on the tree parameters to prevent overfitting. To incorporate external information, an empirical Bayes (EB) framework is developed that estimates, assisted by a model, prior covariate weights in the BART model. The proposed EB framework enables the estimation of the other prior parameters of BART as well, rendering an appealing and computationally efficient alternative to cross-validation. We show that the method finds relevant covariates and that it improves prediction compared to default BART in simulations. If the covariate-response relationship is non-linear, the method benefits from the flexibility of BART to outperform regression-based learners. Finally, the benefit of incorporating external information is shown in an application to diffuse large B-cell lymphoma prognosis based on clinical covariates, gene mutations, DNA translocations, and DNA copy number data.