Single and multi-objective optimal designs for group testing experiments with a focus on screening for an infectious disease

Group testing techniques are widely used in resource-constrained settings, such as infectious-disease screening, blood safety, DNA library screening, and industrial inspection, where the efficient use of limited testing resources depends critically on how the initial study is designed. This paper discusses various ways that group testing experiments can be designed more efficiently and flexibly, under a user-specified optimality criterion and cost structure. We construct optimal designs to estimate model parameters beyond the $D$-optimality criterion to include the $A$-, $c$-, $E$-optimality, and extend the framework for finding optimal designs with multiple objectives. For large studies, we use a general theory and obtain various types of optimal approximate designs. When sample sizes are small, we propose two algorithms to construct highly efficient exact designs under realistic budget constraints. Additionally, we investigate properties of the proposed designs under various operational uncertainties and create a Shiny app to facilitate implementation of the proposed designs. To fix ideas, we focus on finding highly efficient group testing designs for a Chlamydia screening trial with imperfect assays under budget constraints and show the advantages of our optimal designs over current methods.