Thomas Klausch

Jeroen M. Goedhart, Thomas Klausch, Jurriaan Janssen et al.

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

Mingyang Cai, Thomas Klausch, Mark A. van de Wiel

Machine learning models used in medical applications often face challenges due to the covariate shift, which occurs when there are discrepancies between the distributions of training and target data. This can lead to decreased predictive accuracy, especially with unknown outcomes in the target data. This paper introduces a semi-supervised classification and regression tree (CART) that uses importance weighting to address these distribution discrepancies. Our method improves the predictive performance of the CART model by assigning greater weights to training samples that more accurately represent the target distribution, especially in cases of covariate shift without target outcomes. In addition to CART, we extend this weighted approach to generalized linear model trees and tree ensembles, creating a versatile framework for managing the covariate shift in complex datasets. Through simulation studies and applications to real-world medical data, we demonstrate significant improvements in predictive accuracy. These findings suggest that our weighted approach can enhance reliability in medical applications and other fields where the covariate shift poses challenges to model performance across various data distributions.

Thomas Klausch, Peter van de Ven, Tim van de Brug et al.

Optimal treatment regimes (OTR) are individualised treatment assignment strategies that identify a medical treatment as optimal given all background information available on the individual. We discuss Bayes optimal treatment regimes estimated using a loss function defined on the bivariate distribution of dichotomous potential outcomes. The proposed approach allows considering more general objectives for the OTR than maximization of an expected outcome (e.g., survival probability) by taking into account, for example, unnecessary treatment burden. As a motivating example we consider the case of oropharynx cancer treatment where unnecessary burden due to chemotherapy is to be avoided while maximizing survival chances. Assuming ignorable treatment assignment we describe Bayesian inference about the OTR including a sensitivity analysis on the unobserved partial association of the potential outcomes. We evaluate the methodology by simulations that apply Bayesian parametric and more flexible non-parametric outcome models. The proposed OTR for oropharynx cancer reduces the frequency of the more burdensome chemotherapy assignment by approximately 75% without reducing the average survival probability. This regime thus offers a strong increase in expected quality of life of patients.