Abstract: In a group testing study, the researcher collects samples from multiple individuals, pools the results, and tests them as a group. A realistic cost model for such a study should consider both the costs of collecting the samples and those of running the assays. Moreover, an efficient design should accommodate inaccuracies in any prespecified nominal test sensitivity and specificity values, allowing them to vary with the group size. We derive locally optimal designs in this setting, and characterize their theoretical properties. We also provide a guaranteed algorithm for constructing designs on discrete design spaces. Several simulated examples based on a real-world group testing study show that the proposed designs have high efficiency. In addition, the designs are not strongly sensitive to the working parameter specification used to obtain the locally optimal design.

Key words and phrases: Budget-constrained design, dilution effect, group testing.