Cost considerations for efficient group testing studies

Abstract

A group testing study involves collecting samples from multiple individuals, pooling them, and testing them as a group. A realistic cost model for such a study should consider the costs both for collecting the samples, and for running the assays. Moreover, an efficient design should accommodate inaccuracies in any prespecified nominal test sensitivity and specificity values, and allow them to vary with group size. In this work, we derive locally optimal designs in this setting, and characterize their theoretical properties. We also provide a guaranteed algorithm for constructing the designs on discrete design spaces. Several simulated examples based on a real-world group testing study show that the proposed designs have high efficiency, and are not strongly sensitive to the working parameter specification that is used to obtain the locally optimal design.

Optimal group testing designs for prevalence estimation combining imperfect and gold standard assays

“…We state that the D s(i) -optimality is the D s -optimality among integer-supported designs, where "(i)" stands for integers. A D r s(i) -optimal design, denoted as ξ (i) r , can be obtained from Algorithm 1 in Huang et al (2020). Moreover, D g s(i) -and D b s(i)optimal designs, ξ Therefore, using similar arguments as above, Theorem 3.1 and Proposition 3.2 show that either ξ…”

“…Now we characterize D r s -, D g s -, and D b s -optimal designs, respectively. Theorem 2 in Huang et al (2020) provides the D r s -optimal design ξ * r which is a threepoint design involving the smallest allowable group size x L . Here we provide D g sand D b s -optimal designs using the complete class approach (Yang and Stufken, 2012).…”

“…For an approximate mixed design ξ and a given total budget C, the expected number of trials n 0 ip = Cw ip /c p (x ip ) with group size x ip under procedure p is not guaranteed to be an integer. For practical use, we obtain ξ with total budget C by implementing a two-step efficient rounding procedure for a budget-constrained design, introduced in Section 3.2 of Huang et al (2020). More explicitly, we first allocate the budget to have n 0 ip trials with group size x ip under procedure p, where x is the largest integer not greater than x.…”

“…Most theoretical studies on group testing only consider the setting where all tests are performed using the same assay. Some researchers make a simplified assumption that the test is perfect (Hughes-Oliver and Swallow, 1994;Hughes-Oliver and Rosenberger, 2000) or that the testing error rates are known values (Tu et al, 1995;Liu et al, 2012), while others allow the error rates to be estimated from the data (Huang et al, 2017(Huang et al, , 2020.…”

“…(ii) We consider mixed designs based on three testing procedures: each group sample is tested either by only one of the two assays, or by both assays. (iii) We utilize the cost considerations as in Huang et al (2020), that is, the relative costs for performing assays and for enrolling subjects, and then we fix the total budget and control the numbers of tests and subjects through their costs. In particular, according to (iii), when prevalence estimation is the only interest, only the gold standard is used when its cost is sufficiently low, and only the regular assay is used when the cost of the gold standard is sufficiently high; besides these two extreme conditions, a mixed design of the three procedures should be adopted.…”