Group testing complexity

Laboratories use group testing to test high volumes of clinical specimens for pathogens, such as SARS-CoV-2, West Nile, and Chlamydia trachomatis. The process works by testing multiple specimens together as an amalgamation, rather than testing each specimen separately, to reduce the number of tests needed. There are many different algorithmic ways to apply group testing. The role of a statistician is to recommend an algorithm that will perform “best” relative to the information available, such as disease prevalence. Algorithms are most often compared by their expected number of tests needed for an application, where a lower value is preferred. Unfortunately, this measure alone does not account for some algorithms having a lower expected number of tests at the expense of being much more complex to implement. For this reason, we propose a new measure that we refer to as the complexity. In our paper, we present its definition and derive its expression for several common algorithms. We show that some algorithms may be too complex for implementation, while others should become more widely used. Our proposed measure is illustrated with a SARS-CoV-2 testing implementation. R functions and a Shiny app are provided to perform calculations.