Minimax Solution for the Two-Stage Group Testing Problem

• Activity Number: 456
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Yaakov Malinovsky*+ and Paul Albert
• Companies: University of Maryland Baltimore County and Eunice Kennedy Shriver National Institute of Child Health and Human Development
• Keywords: Group testing ; Minimax ; Loss function ; Optimal design ; Optimization 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 probability p of being affected is unknown. The interesting new practical question is how to find the group size which will protect against the ``worst value" of p (i.e., minimax solution) when the goal is the minimization of the expected number of tests. In the present work we present the optimal and minimax solutions. We also propose a Bayesian alternative to the minimax design, which we show performs well for this problem. We show that a constrained version of the minimax solution has substantial efficiency gain when the constraint is incorporated. For the practitioner we propose strong justification for using a group size of between five to eight when a constraint on p is not incorporated and provide useable code for computing the minimax group size under a constrained p.