Optimal group testing designs for prevalence estimation combining imperfect and gold standard assays

Abstract

We consider group testing studies where a relatively inexpensive but imperfect assay and a perfectly accurate but higher-priced assay are both available. The primary goal is to accurately estimate the prevalence of a trait of interest, with the error rates of the imperfect assay treated as nuisance parameters. Considering the costs for performing the two assays and enrolling subjects, we propose a $D_{s}$-optimal mixed design to provide maximal information about the prevalence. We show that extreme values for the cost of the perfect assay lead to designs in which only one of the two assays is used, but otherwise the optimal designs use both assays. We provide a guaranteed algorithm to efficiently build an optimal design on discrete design spaces. Our computational results also show the robustness of the proposed design.