  Medical prediction applications often need to deal with small sample sizes
compared to the number of covariates. Such data pose problems for prediction
and variable selection, especially when the covariate-response relationship is
complicated. To address these challenges, we propose to incorporate co-data,
i.e. 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 co-data, an empirical Bayes
(EB) framework is developed that estimates, assisted by a co-data model, prior
covariate weights in the BART model. The proposed method can handle multiple
types of co-data simultaneously. Furthermore, the proposed EB framework enables
the estimation of the other hyperparameters of BART as well, rendering an
appealing 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 nonlinear, the method
benefits from the flexibility of BART to outperform regression-based co-data
learners. Finally, the use of co-data enhances prediction in an application to
diffuse large B-cell lymphoma prognosis based on clinical covariates, gene
mutations, DNA translocations, and DNA copy number data.
  Keywords: Bayesian additive regression trees; Empirical Bayes; Co-data;
High-dimensional data; Omics; Prediction
