Estimating proportions by group retesting with unequal group sizes at each stage

Abstract

The group testing procedure divides sampled units into several groups, and then obtains an overall test result for each group. It is used to identify specific individuals who have a given attribute, or to estimate the overall prevalence of the attribute in the population. We here investigate how group retesting can improve precision of estimation and its cost-efficiency, which are important considerations for investigators. Retesting uses two or more group stages, with repeat testing of the original samples at each stage. Previous authors have proposed a procedure with two stages having equal group sizes, and where the number of groups tested at the second stage is based on the number of positive groups in the first stage. In this paper, our main focus is on estimating the prevalence of affected individuals in a population, and identifying cost-efficient experimental designs, when using two-stage testing with unequal group sizes at each stage. We use analytical solutions for the precision of estimation, together with simulations to evaluate various experimental designs. We consider the value of retesting at the second stage, and determine when using only one stage of testing might be sufficiently precise.