Statistics, Department of


First Advisor

Professor Christopher R. Bilder

Date of this Version



Hitt, B.D. (2020). Group testing identification: Objective functions, implementation, and multiplex assays [Doctoral dissertation, University of Nebraska-Lincoln]. UNL Digital Commons.


A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Doctor of Philosophy, Major: Statistics, Under the Supervision of Professor Christopher R. Bilder. Lincoln, Nebraska: April, 2020

Copyright 2020 Brianna D. Hitt

Chapter 2 (and the corresponding appendix) of this dissertation is published: Hitt, B., Bilder, C., Tebbs, J., and McMahan, C. (2019). The objective function controversy for group testing: Much ado about nothing? Statistics in Medicine 38(24), 4912-4923. Used with permission.


Group testing is the process of combining items into groups to test for a binary characteristic. One of its most widely used applications is infectious disease testing. In this context, specimens (e.g., blood, urine) are amalgamated into groups and tested. For groups that test positive, there are many algorithmic retesting procedures available to identify positive individuals. The appeal of group testing is that the overall number of tests needed is significantly less than for individual testing when disease prevalence is small and an appropriate algorithm is chosen. Group testing has a number of applications beyond infectious disease testing, such as drug discovery, food contamination detection, and diagnosis of faulty network sensors.

An important decision that needs to be made prior to implementation is the group sizes to use. In best practice, an objective function is minimized to determine the optimal set of group sizes, known as the optimal testing configuration (OTC). We examine several different objective functions and show that the OTCs and corresponding results (e.g., number of tests, accuracy) are largely the same for these functions when using standard group testing algorithms.

Both estimating the probability of disease and identifying positive individuals are goals of group testing. We present the first general R functions for identification and make these available in the new binGroup2 package. We also include in this package estimation functions from the binGroup package by creating a unified framework for them.

We developed a web-based Shiny application to assist laboratory personnel in determining how well a group testing algorithm is expected to perform before implementation. The app utilizes binGroup2 functions to calculate the expected number of tests and diagnostic accuracy measures for a wide variety of algorithms using one- and two-disease assays. The OTC can be found with the app as well.

Most group testing research using one-disease assays makes the assumption of equal sensitivity and equal specificity values across all stages of testing. We present derivations of operating characteristics for group testing algorithms that allow the diagnostic test accuracy to differ across stages of testing. These resulting expressions are incorporated into the binGroup2 package.

Adviser: Christopher R. Bilder