Optimal group testing designs for estimating prevalence with uncertain testing errors

TL;DR

This paper develops optimal group testing designs to accurately estimate prevalence rates considering uncertain test sensitivity and specificity, providing strategies for different estimation goals and demonstrating robustness through a case study.

Contribution

It introduces optimal design strategies for group testing with uncertain test parameters, including both simultaneous and prevalence-focused approaches, and evaluates their robustness.

Findings

Optimal designs require three group sizes with equal frequencies for joint estimation.

Prevalence-only estimation favors unequal group size frequencies.

Proposed designs maintain high efficiency even with moderate parameter misspecification.

Abstract

We construct optimal designs for group testing experiments where the goal is to estimate the prevalence of a trait by using a test with uncertain sensitivity and specificity. Using optimal design theory for approximate designs, we show that the most efficient design for simultaneously estimating the prevalence, sensitivity and specificity requires three different group sizes with equal frequencies. However, if estimating prevalence as accurately as possible is the only focus, the optimal strategy is to have three group sizes with unequal frequencies. On the basis of a chlamydia study in the U.S.A., we compare performances of competing designs and provide insights into how the unknown sensitivity and specificity of the test affect the performance of the prevalence estimator. We demonstrate that the locally D- and Ds-optimal designs proposed have high efficiencies even when the prespecified values of the parameters are moderately misspecified.