Bayesian Additive Regression Trees for Group Testing Data.

When screening for low-prevalence diseases, pooling specimens (e.g., blood, urine, swabs, etc.) through group testing has the potential to substantially reduce costs when compared to testing specimens individually. A common goal in group testing applications is to estimate the relationship between an individual's true disease status and their individual-level covariate information. However, estimating such a relationship is a non-trivial problem because true individual disease statuses are unknown due to the group testing protocol and the possibility of imperfect testing. While several regression methods have been developed in recent years to accommodate the complexity of group testing data, the functional form of covariate effects is typically assumed to be known. To avoid model misspecification and to provide a more flexible approach, we propose a Bayesian additive regression trees framework to model the individual-level probability of disease with potentially misclassified group testing data. Our methods can be used to analyze data arising from any group testing protocol with the goal of estimating unknown functions of covariates and assay classification accuracy probabilities.