Optimal Group-testing Designs for Estimating Prevalence with Uncertain Testing Errors

Abstract

Optimal design problems for group-testing models are investigated, while the testing errors exist. Our goal is to find optimal designs to estimate the prevalence under 3 conditions respectively: (i) both error rates are known but may be less than 100%; (ii) both error rates are unknown and of interest as well; (iii) both error rates are nuisance parameters in the design problem. Under each condition, we determine the optimal number of distinct group sizes, the group sizes themselves, and the distribution of these group sizes. ?