Dorfman Testing with Correlated Responses

• Activity Number: 63
• Type: Topic Contributed
• Date/Time: Sunday, August 4, 2013 : 4:00 PM to 5:50 PM
• Sponsor: Biometrics Section
• Author(s): Elena Bordonali*+ and Michael G. Hudgens and Bahjat Qaqish
• Companies: and The University of North Carolina at Chapel Hill and UNCCH
• Keywords: Group Testing ; Pooled Testing ; Correlated Binary Data

Abstract

Group testing, a process in which units are pooled together and tested jointly for the presence of some trait, was first introduced by Dorfman. To date, the vast majority of group testing research assumes units are independent, however this assumption may be unrealistic in many settings. In this talk, we discuss the efficiency of Dorfman's procedure for a set of units having either exchangeable, first-order autoregressive or first-order moving average correlation. We present closed-form equations for the efficiency in each of these scenarios and derive a general relationship between the efficiencies under each of the correlation assumptions. In particular, the Dorfman efficiency is ordered by correlation structure as follows: independence (greatest), moving average, autoregressive and exchangeable (smallest). The differences in these efficiencies can be substantial such that efficiency can be substantially over- or underestimated by assuming the wrong correlation structure for a particular dataset. We illustrate these differences in efficiency with an example to highlight the importance of accurately characterizing the correlation structure when choosing a group testing algorithm.