A mixed-effects Bayesian regression model for multivariate group testing data

Laboratories use group (pooled) testing with multiplex assays to reduce the time and cost associated with screening large populations for infectious diseases. Multiplex assays test for multiple diseases simultaneously, and combining their use with group testing can lead to highly efficient screening protocols. However, these benefits come at the expense of a more complex data structure which can hinder surveillance efforts. To overcome this challenge, we develop a general Bayesian framework to estimate a mixed multivariate probit model with data arising from any group testing protocol that uses multiplex assays. In the formulation of this model, we account for the correlation between true disease statuses and heterogeneity across population subgroups, and we provide for automated variable selection through the adoption of spike and slab priors. To perform model fitting, we develop an attractive posterior sampling algorithm which is straightforward to implement. We illustrate our methodology through numerical studies and analyze chlamydia and gonorrhea group testing data collected by the State Hygienic Laboratory at the University of Iowa.