An Optimal Design for Hierarchical Generalized Group Testing

Abstract

Choosing an optimal strategy for hierarchical group testing is an important problem for practitioners who are interested in disease screening with limited resources. For example, when screening for infectious diseases in large populations, it is important to use algorithms that minimize the cost of potentially expensive assays. Black and co-workers described this as an intractable problem unless the number of individuals to screen is small. They proposed an approximation to an optimal strategy that is difficult to implement for large population sizes. We develop an optimal design with respect to the expected total number of tests that can be obtained by using a novel dynamic programming algorithm. We show that this algorithm is substantially more efficient than the approach that was proposed by Black and co-workers. In addition, we compare the two designs for imperfect tests. R code is provided for practitioners.

Nested Group Testing Procedures for Screening

“…All units have to be classified as either non-defective or defective by group testing. Since its introduction, GGTP has seen considerable theoretical investigation (Lee and Sobel (1972); Nebenzahl and Sobel (1973); Katona (1973); Hwang (1976a); Yao and Hwang (1988a,b); Kurtz and Sidi (1988); Kealy et al (2014); Malinovsky (2019bMalinovsky ( , 2020; Malinovsky et al (2020)).…”

“…. , p N an optimal nested and hierarchical procedures with respect to the expected total number of tests were developed as DP algorithms in Kurtz and Sidi (1988) and in Malinovsky et al (2020), respectively.…”

Network-Informed Constrained Divisive Pooled Testing Assignments

“…This is a simple approach where a certain number of samples are pooled and tested; should the resulting diagnostic test be negative, no more tests are conducted, whereas if positive, all individuals comprising the pool are subsequently tested. Other pooled testing strategies include the Sterrett Procedure (Sterrett, 1957) as well as hierarchical approaches (Black et al, 2015;Malinovsky et al, 2020). Work has also been done to generalize these procedures to the context where there are known heterogeneous probabilities of being infected (e.g., Hwang, 1975), including some of the previously mentioned studies.…”

Leveraging Network Structure to Improve Pooled Testing Efficiency

“…This approach to testing is referred to as a two‐stage Dorfman procedure, and, perhaps due to its simplicity, has seen widespread use (Hughes‐Oliver, 2006 ). There has since been numerous variations on this idea, including different strategies for following up a positive test result (e.g., Sterrett, 1957 ), and having more than two layers of the hierarchical testing strategy (e.g., Malinovsky et al, 2020 ) (non‐hierarchical strategies in which each sample may appear in multiple pools also has received much attention, but this paper will not focus on these approaches). See Hughes‐Oliver ( 2006 ) or Bilder ( 2022 ) for more information on pooled testing.…”

“…By using the network and how one individual may transmit the disease to another, we can construct pools of individuals which can reduce the total number of expected tests. There is a long history of optimising pooled testing strategies when there is available additional information on the heterogeneity of probabilities of being infected (Bilder et al, 2010 ; Black et al, 2015 ; Hwang, 1975 ; Malinovsky et al, 2020 ; Yao & Hwang, 1988 ). This paper also relates to obtaining an efficient pooling strategy, yet the direction is orthogonal to previous work.…”