Budget Constrained Group Testing Design for Prevalence Estimation with an Imperfect Assay and a Gold Standard

Abstract

In this work we focus on optimal group testing designs when a cheap imperfect assay and an expensive perfect assay (gold standard) for a target trait are both available. The primary goal is to accurately estimate the prevalence of the trait in a given population, where the sensitivity and specificity of the imperfect assay are treated as nuisance parameters. Budget constraints are used to reflect the costs of performing either of the two assays relative to the cost of collecting a subject’s data. A mixed design strategy can be adopted, where each sample is tested by either only the imperfect assay, only the perfect assay, or both assays. We characterize the optimal designs within the class via a tight upper bound on the number of distinct group sizes for each testing procedure. Based on this information, we provide an efficient algorithm to obtain an optimal budgeted design. (Jointly with Prof. Mong-Na Lo Huang and Prof. Kerby Shedden.) Key words and phrases: Cost function; Gold standard; Group testing; Mixed design strategy; Prevalence estimation; Testing error rates.