Revisiting nested group testing procedures: new results, comparisons, and robustness

TL;DR

This paper compares various nested group testing procedures, including Dorfman, Sterrett, and an optimal dynamic programming-based method, analyzing their efficiency, robustness, and providing new closed-form expressions for the Sterrett procedure.

Contribution

It introduces new closed-form expressions for the optimal Sterrett procedure and compares multiple nested group testing designs, including robustness analysis under incorrect prevalence assumptions.

Findings

Optimal Sterrett procedure derived in closed form

Nested designs compared in terms of efficiency and robustness

Robustness of procedures analyzed under prevalence mis-specification

Abstract

Group testing has its origin in the identification of syphilis in the US army during World War II. Much of the theoretical framework of group testing was developed starting in the late 1950s, with continued work into the 1990s. Recently, with the advent of new laboratory and genetic technologies, there has been an increasing interest in group testing designs for cost saving purposes. In this paper, we compare different nested designs, including Dorfman, Sterrett and an optimal nested procedure obtained through dynamic programming. To elucidate these comparisons, we develop closed-form expressions for the optimal Sterrett procedure and provide a concise review of the prior literature for other commonly used procedures. We consider designs where the prevalence of disease is known as well as investigate the robustness of these procedures when it is incorrectly assumed. This article provides a technical presentation that will be of interest to researchers as well as from a pedagogical perspective. Supplementary material for this article is available online.