Co-data Learning for Bayesian Additive Regression Trees

• URL: http://arxiv.org/abs/2311.09997v2
• Date: Sun, 03 Nov 2024 14:03:49 GMT
• Title: Co-data Learning for Bayesian Additive Regression Trees
• Authors: Jeroen M. Goedhart, Thomas Klausch, Jurriaan Janssen, Mark A. van de Wiel,
• Abstract summary: We propose to incorporate co-data into a sum-of-trees prediction model. The proposed method can handle multiple types of co-data simultaneously. Co-data enhances prediction in an application to diffuse large B-cell lymphoma prognosis.
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• Abstract: 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

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