Estimating the prevalence rate of a disease is crucial for controlling its spread, and for planning of healthcare services. Due to limited testing budgets and resources, prevalence estimation typically entails pooled, or group, testing where specimens (e.g., blood, urine, tissue swabs) from a number of subjects are combined into a testing pool, which is then tested via a single test. Testing outcomes from multiple pools are analyzed so as to assess the prevalence of the disease. The accuracy of prevalence estimation relies on the testing pool design, i.e., the number of pools to test and the pool sizes (the number of specimens to combine in a pool). Determining an optimal pool design for prevalence estimation can be challenging, as it requires prior information on the current status of the disease, which can be highly unreliable, or simply unavailable, especially for emerging and/or seasonal diseases.

We develop and study frameworks for prevalence estimation, under highly unreliable prior information on the disease and limited testing budgets. Embedded into each estimation framework is an optimization model that determines the optimal testing pool design, considering the trade-off between testing cost and estimation accuracy. We establish important structural properties of optimal testing pool designs in various settings, and develop efficient and exact algorithms. Our numerous case studies, ranging from prevalence estimation of the human immunodeficiency virus (HIV) in various parts of Africa, to prevalence estimation of diseases in plants and insects, including the Tomato Spotted Wilt virus in thrips and West Nile virus in mosquitoes, indicate that the proposed estimation methods substantially outperform current approaches developed in the literature, and produce robust testing pool designs that can hedge against the uncertainty in model inputs.Our research findings indicate that the proposed prevalence estimation frameworks are capable of producing accurate prevalence estimates, and are highly desirable, especially for emerging and/or seasonal diseases under limited testing budgets.