Co-data Learning for Bayesian Additive Regression Trees
Jeroen M. Goedhart Thomas Klausch Jurriaan Janssen Mark A. van de Wiel
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