A robust pooled testing approach to expand COVID-19 screening capacity

Abstract

Limited testing capacity for COVID-19 has hampered the pandemic response. Pooling is a testing method wherein samples from specimens (e.g., swabs) from multiple subjects are combined into a pool and screened with a single test. If the pool tests positive, then new samples from the collected specimens are individually tested, while if the pool tests negative, the subjects are classified as negative for the disease. Pooling can substantially expand COVID-19 testing capacity and throughput, without requiring additional resources. We develop a mathematical model to determine the best pool size for different risk groups, based on each group's estimated COVID-19 prevalence. Our approach takes into consideration the sensitivity and specificity of the test, and a dynamic and uncertain prevalence, and provides a robust pool size for each group. For practical relevance, we also develop a companion COVID-19 pooling design tool (through a spread sheet). To demonstrate the potential value of pooling, we study COVID-19 screening using testing data from Iceland for the period, February-28-2020 to June-14-2020, for subjects stratified into high- and low-risk groups. We implement the robust pooling strategy within a sequential framework, which updates pool sizes each week, for each risk group, based on prior week's testing data. Robust pooling reduces the number of tests, over individual testing, by 88.5% to 90.2%, and 54.2% to 61.9%, respectively, for the low-risk and high-risk groups (based on test sensitivity values in the range [0.71, 0.98] as reported in the literature). This results in much shorter times, on average, to get the test results compared to individual testing (due to the higher testing throughput), and also allows for expanded screening to cover more individuals. Thus, robust pooling can potentially be a valuable strategy for COVID-19 screening.

Fig 1. Perfect information pool size and expected number of tests per subject versus prevalence rate for various test sensitivity values.

The perfect information pool size, n(p), and expected number of tests per subject, E[T(n(p),p)], for each prevalence scenario p between 0.01–0.292 for test sensitivity values, Se = 0.71, 0.98, 1.

Fig 2

Expected number of tests per subject versus pool size for various prevalence rates for test sensitivity values (a) Se = 0.98 and (b) Se = 0.71. The expected number of tests per subject, E[T(n(p),p)], for various prevalence scenarios p between 0.01–0.25 for test sensitivity values (a) Se = 0.98 and (b) Se = 0.71 for pool sizes from 2–32.

Fig 3

Weekly robust pool size and 95% confidence interval pool sizes for (a) High-risk and (b) Low-risk groups for two test sensitivity values, and actual weekly prevalence rates for (c) High-risk and (d) Low-risk groups. The robust pool size, n*, for each week along with pool sizes corresponding to the 95% confidence interval of the prevalence forecast for (a) high-risk and (b) low-risk groups for test sensitivity values, Se = 0.71 and 0.98, and the actual weekly prevalence rates for (c) high-risk and (d) low-risk groups.

Fig 4

Daily expected number of tests for the high-risk group for test sensitivity values of (a) 0.98 and (c) 0.71 and for the low-risk group for test sensitivity values of (b) 0.98 and (d) 0.71. The daily expected number of tests required for the (a) high-risk group with Se = 0.98, (b) low-risk group with Se = 0.98, (c) high-risk group with Se = 0.71, and (d) low-risk group with Se = 0.71 for the perfect information lower bound, robust pooling, and individual testing.

Fig 5

Expected number of low-risk subjects screened with 7,967 tests (a) under different strategies and (b) under different assumed test sensitivities, versus true test sensitivity, and the expected number of (c) False-negative cases and (d) Missed and False-negative Cases versus Test Sensitivity. The expected number of low-risk subjects screened with 7,967 tests (a) for the perfect information upper bound, robust pooling, n*, and individual testing versus test sensitivity, (b) assuming a prevalence rate, p, of 0.0065 and a test sensitivity, Se, of 0.70, 0.85, and 1 versus true test sensitivity, (c) FNs (out of the 7,967 low-risk subjects tested under both strategies), and (d) missed cases plus FNs for robust pooling and individual testing (out of 52,173 subjects, which corresponds to the expected number of low-risk subjects tested via robust pooling) versus test sensitivity.