title: A Note on the Minimax Solution for the Two-Stage Group Testing Problem.
abstract: Group testing is an active area of current research and has important applications in medicine, biotechnology, genetics, and product testing. There have been recent advances in design and estimation, but the simple Dorfman procedure introduced by R. Dorfman in 1943 is widely used in practice. In many practical situations, the exact value of the probabilitypof being affected is unknown. We present both minimax and Bayesian solutions for the group size problem whenpis unknown. For unboundedp, we show that the minimax solution for group size is 8, while using a Bayesian strategy with Jeffreys' prior results in a group size of 13. We also present solutions whenpis bounded from above. For the practitioner, we propose strong justification for using a group size of between 8 and 13 when a constraint onpis not incorporated and provide useable code for computing the minimax group size under a constrainedp.
authors.affiliation: Assistant Professor, Department of Mathematics and Statistics, University of Maryland, Baltimore, MD 21250.
authors.forename: Yaakov
authors.initials: Y
authors.lastname: Malinovsky
authors.affiliation: Chief and Senior Investigator, Biostatistics and Bioinformatics Branch, Division of Intramural Population Health Research, Eunice Kennedy Shriver National Institute of Child Health and Human Development, Bethesda, MD 20892.
authors.forename: Paul S
authors.initials: PS
authors.lastname: Albert
keywords: Loss function; Optimal design; Optimization problem