  In recent years, theoretical results and simulation evidence have shown
Bayesian additive regression trees to be a highly-effective method for
nonparametric regression. Motivated by cost-effectiveness analyses in health
economics, where interest lies in jointly modelling the costs of healthcare
treatments and the associated health-related quality of life experienced by a
patient, we propose a multivariate extension of BART applicable in regression
and classification analyses with several correlated outcome variables. Our
framework overcomes some key limitations of existing multivariate BART models
by allowing each individual response to be associated with different ensembles
of trees, while still handling dependencies between the outcomes. In the case
of continuous outcomes, our model is essentially a nonparametric version of
seemingly unrelated regression. Likewise, our proposal for binary outcomes is a
nonparametric generalisation of the multivariate probit model. We give
suggestions for easily interpretable prior distributions, which allow
specification of both informative and uninformative priors. We provide detailed
discussions of MCMC sampling methods to conduct posterior inference. Our
methods are implemented in the R package `suBART'. We showcase their
performance through extensive simulations and an application to an empirical
case study from health economics. By also accommodating propensity scores in a
manner befitting a causal analysis, we find substantial evidence for a novel
trauma care intervention's cost-effectiveness.
