Optimal retesting configurations for hierarchical group testing

Hierarchical group testing is widely used to test individuals for diseases. This testing procedure works by first amalgamating individual specimens into groups for testing. Groups testing negatively have their members declared negative. Groups testing positively are subsequently divided into smaller subgroups and are then retested to search for positive individuals. We propose a new class of informative retesting procedures for hierarchical group testing that acknowledges heterogeneity among individuals. These procedures identify the optimal number of groups and their sizes at each testing stage to minimize the expected number of tests. We apply our proposals in two settings: human immunodeficiency virus testing programmes that currently use three-stage hierarchical testing and chlamydia and gonorrhoea screening practices that currently use individual testing. For both applications, we show that substantial savings can be realized by our new procedures.