Optimal Configuration of a Square Array Group Testing Algorithm

• Published in: Communications in statistics. Theory and methods Vol. 40; no. 3; pp. 436 - 448
• Main Authors: Hudgens, Michael G., Kim, Hae-Young
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Taylor & Francis Group 01.01.2011; Taylor & Francis; Taylor & Francis Ltd
• Subjects: Algorithms; Arrays; Blood testing; Combinatorics; Combinatorics. Ordered structures; Composite sampling; Designs and configurations; Exact sciences and technology; Exact solutions; Experimental design; General topics; HIV; Mathematical analysis; Mathematics; Matrix; Optimization; Pooled testing; Primary 62K05; Probability and statistics; Sciences and techniques of general use; Screening; Secondary 62P10; Statistics; Upper bounds; Lower bound; Primary 62K05; Algorithm; Statistical method; Statistical test; Screening; Upper bound; Matrix; HIV; Experimental design; Blood testing; Pooled testing; Secondary 62P10; Composite sampling; Sampling
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610920903391303

We consider the optimal configuration of a square array group testing algorithm (denoted A2) to minimize the expected number of tests per specimen. For prevalence greater than 0.2498, individual testing is shown to be more efficient than A2. For prevalence less than 0.2498, closed form lower and upper bounds on the optimal group sizes for A2 are given. Arrays of dimension 2 × 2, 3 × 3, and 4 × 4 are shown to never be optimal. The results are illustrated by considering the design of a specimen pooling algorithm for detection of recent HIV infections in Malawi.