Michael Stutz

Date of Award

Summer 2021

Document Type

Open Access Dissertation



First Advisor

Joshua M. Tebbs


Group testing is an efficient method of disease screening, whereby individual specimens (e.g., blood, urine, etc.) are pooled together and tested as a whole for the presence of disease. A common goal is to use data arising from these testing protocols to better understand the relationship between disease status and potential risk factors (e.g., age, symptom status, etc.). Numerous statistical methodologies have been developed for this purpose, most of which are built within the framework of a generalized linear model. Recent authors have suggested the inadequacy of such regression methods to capture the true functional relationships when nonlinear effects are present. In this dissertation, we develop new parametric and nonparametric regression methods for group testing data using the expectation-maximization algorithm. Our methods can be implemented with any group testing algorithm and have the flexibility to seamlessly account for both linear and nonlinear covariate effects. In addition, our methods are the first within the group testing literature to integrate machine learning techniques. A growing number of assays have the ability to detect multiple diseases simultaneously. One such assay is the Aptima Combo 2 Assay (AC2A), which is able to simultaneously test for the presence of chlamydia and gonorrhea. With this as our motivating example, we generalize our regression methods to allow for a bivariate response. We use simulation to demonstrate the estimation performance of our algorithms and provide a real data application of our methods using disease screening data obtained from the University of Iowa.