Assessing Simultaneous Infection with Multiple Pathogens via Group Testing with Imperfect Multiplex Assays

Pooled testing procedures involve physically combining biomaterial from multiple individuals and testing the combined specimen for the presence of infection. Provided the prevalence of infection is relatively low, pooled testing allows one to screen many individuals at a fraction of the cost of traditional individual testing and has been widely used to screen both humans and animals for infection. Multiplex assays further increase efficiency by simultaneously screening for multiple pathogens. However, such assays are often imperfect, rendering both false-positive and false-negative results. In this work, we develop a means of estimating the prevalence of co-infections from imperfect multiplex pooled testing data for any pool size and any number of pathogens. Our approach uses an expectation-maximization (EM) algorithm to estimate the infection probabilities and uses Louis's method to estimate the associated variance-covariance matrix. We provide a means of determining which pool size which minimizes the variance of the estimated marginal or co-infection prevalence. We also present a hypothesis test for determining if infections are mutually independent. We validate our approach with an extensive simulation study and then apply it to a pooled testing data from a multiplex assay for four tick-borne pathogens.