Seemingly unrelated Bayesian additive regression trees for cost-effectiveness analyses in healthcare

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 which is applicable in regression analyses with several dependent outcome variables. Our framework allows for continuous or binary outcomes and 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 simulation experiments 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.