key: cord-0703160-7ssn44q3
authors: Nianogo, Roch A.; Emeruwa, I. Obi; Gounder, Prabhu; Manuel, Vladimir; Anderson, Nathaniel W.; Kuo, Tony; Inkelas, Moira; Arah, Onyebuchi A.
title: Optimal uses of pooled testing for COVID‐19 incorporating imperfect test performance and pool dilution effect: An application to congregate settings in Los Angeles County
date: 2021-05-27
journal: J Med Virol
DOI: 10.1002/jmv.27054
sha: 24fbb2bbd94ee2529ead3ca5f2650b245fb8bbaf
doc_id: 703160
cord_uid: 7ssn44q3

INTRODUCTION: Pooled testing is a potentially efficient alternative strategy for COVID‐19 testing in congregate settings. We evaluated the utility and cost‐savings of pooled testing based on imperfect test performance and potential dilution effect due to pooling and created a practical calculator for online use. METHODS: We developed a 2‐stage pooled testing model accounting for dilution. The model was applied to hypothetical scenarios of 100 specimens collected during a one‐week time‐horizon cycle for varying levels of COVID‐19 prevalence and test sensitivity and specificity, and to 338 skilled nursing facilities (SNFs) in Los Angeles County (Los Angeles) (data collected and analyzed in 2020). RESULTS: Optimal pool sizes ranged from 1 to 12 in instances where there is a least one case in the batch of specimens. 40% of Los Angeles SNFs had more than one case triggering a response‐testing strategy. The median number (minimum; maximum) of tests performed per facility were 56 (14; 356) for a pool size of 4, 64 (13; 429) for a pool size of 10, and 52 (11; 352) for an optimal pool size strategy among response‐testing facilities. The median costs of tests in response‐testing facilities were $8250 ($1100; $46,100), $6000 ($1340; $37,700), $6820 ($1260; $43,540), and $5960 ($1100; $37,380) when adopting individual testing, a pooled testing strategy using pool sizes of 4, 10, and optimal pool size, respectively. CONCLUSIONS: Pooled testing is an efficient strategy for congregate settings with a low prevalence of COVID‐19. Dilution as a result of pooling can lead to erroneous false‐negative results.

Testing is essential for monitoring and mitigating the spread of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the virus that causes coronavirus disease 2019 . 1, 2 Due to nationwide shortages in testing reagents and supplies, testing capacity in the United States and worldwide has been constrained.

These constraints lengthened the turnaround time for receiving the diagnostic result as demand for testing increased. Public health guidance for congregate settings such as skilled nursing facilities (SNFs) required a volume of testing that is expensive and that could worsen the turnaround time for SARS-CoV-2 test results for residents of these facilities and the general public. 3, 4 Delayed results can slow the identification of outbreaks in these facilities and limit the effect of other mitigation efforts. [5] [6] [7] Therefore, cost-effective methods to reduce turnaround time for obtaining test results and for maintaining appropriate testing frequency are urgently needed.

Pooled testing is one such method that has been used to optimize limited testing resources and has been approved by the US Food and Drug Administration (FDA). [8] [9] [10] [11] Pooled testing, or group testing, was first proposed in 1943 by Robert Dorfman as a solution to the aforementioned problem that would require fewer chemical analyses than would individual testing for testing a large population. 9 Briefly, pooled testing involves grouping individual test specimens into pools which are then processed. If a pool is negative, then there is no further testing of the individual specimens in that pool. If a pool is positive, then all individual specimens in that pool are processed. 9 Research is ongoing to perfect this method. [12] [13] [14] The demand for testing in the COVID-19 pandemic has rekindled the need to revisit this strategy. In their recent study, Cherif et al. 15 described an epidemiologic model that simulated the impact of pooled testing based on regional disease prevalence and SARS-CoV-2 real-time reverse transcription-polymerase chain reaction (PCR) testing characteristics. The authors concluded that a pooled testing strategy is an improvement over individual testing in settings where there is a COVID-19 prevalence of less than 30 percent and a pool size that varies with the inverse of the square root of the prevalence and test sensitivity. Although this study shed some light on pooled testing for COVID-19, it did not thoroughly address the potential impact of the dilution effect due to pooling, that is, the decrease in test sensitivity as a result of pooled testing. 16 We designed the current study to address this additional question by evaluating the impact of imperfect testing performance and pooling dilution on the number of tests needed as well as on the potential resulting cost savings, first in a hypothetical scenario and second using actual prevalence data from Los Angeles SNFs. In addition, we developed an analytic 'calculator' with an accompanying online tool to estimate pool sizes that may be needed at these settings, comparing the potential tradeoffs in terms of test swabs, reagents, supplies and performance, and cost savings. This study can advance our understanding of how pooled testing could be used to monitor and manage SARS-CoV-2 infection in congregate settings, especially for SNFs in Los Angeles and throughout the U.S. 4, 17 The study focuses on SNFs because these patients are among the most vulnerable at-risk populations in the U.S. and worldwideaccounting for approximately one-third to one-half of COVID-19 deaths. 17 The Centers for Disease Control and Prevention (CDC) recently issued guidance that encourages use of pooled testing in such facilities. 3 

We searched the literature for the existing dilution model for pooled testing for COVID-19 to inform our pooled testing strategy. In the absence of current dilution models for COVID-19, we developed a preliminary prediction model of decreased sensitivity as a function of pool size. Several studies have suggested that test sensitivity decreases with increasing pool sizes, but few have developed an easy-to-implement prediction dilution model as a function of pool sizes for SARS-CoV-2. We used limited data from Bateman et al who estimated that pools of 5, 10, and 50 specimens led to false-negative rates of 7%, 9%, and 19%, respectively. 16 Based on the shape of these data, we hypothesized that the model would follow a decaying nonlinear trend as a function of pool size.

We then tested several models: linear, logarithmic, exponential, and polynomial models. The log transformation model performed the best in terms of the following metrics: R-squared, root-mean-squared error (RMSE), Akaike information criterion (AIC), and Bayesian Information Criterion (BIC) (Appendix Table 1 and Appendix Figure 1 

Where se d is the diluted sensitivity due to pooling.

We used this prediction model to estimate the decreased sensitivity as a result of pool size. For instance, when the pool size = 1 (i.e., reverts to individual testing), E(se d | se, S=1) = se, that is, the sensitivity is unchanged. 

We first applied these formulas and algorithms to a hypothetical scenario and then to Los Angeles County SNFs.

For illustration, generalizability, and for quick decision-making, we provided a chart of test volume and cost-saving according to varying degrees of sensitivity, specificity, prevalence, and pool sizes (Table 1) .

This chart was built using 100 specimens.

The data for this application came from the CDC's National Healthcare The prevalence of COVID-19 in the SNF was calculated as the number of currently isolated residents with suspected or confirmed COVID-19 plus divided by the number of residents in the SNF for that week. The total number of specimens collected included specimens from residents and staff for response or surveillance testing in one week for that specific facility ( Figure 1 ).

All the analyses were conducted in R and the calculator built in R Shinyapp version 3.6.3 and can be found at: https://nianogo.

shinyapps.io/pooled_testing.

From Table 1 and Figure 2 , we can infer the following: for a given test performance, as prevalence increases, the optimal pool size NIANOGO ET AL. there is a least one case in the batch of specimens (i.e., prevalence >0). When the prevalence is 0 and test specificity =1, the optimal pool size for a population of 100 specimens would be as expected, 100. Lower prevalence predicted a lower number of tests needed. In this hypothetical scenario, the number of cases missed due solely to dilution appears to be low (less than 1) for a batch of 100 specimens. Uniform pool sizes of 4 tended to yield better return in the number of tests needed as well as cost savings compared to uniform pool sizes of 10. (Appendix Table 3 and Table 4 ). using an optimal pool size ( Table 3) .

This study evaluated the relative utility in terms of the number of tests saved and the cost (savings) of pooled testing accounting for imperfect test performance and the potential dilution effect due to pooling. In our hypothetical scenarios with varying degrees of prevalence, test performance, and pool size, the optimal pool sizes ranged from 1 to 12 in instances where there was a least one case in the batch of specimens to be tested. In addition, as expected, a lower prevalence of COVID-19 predicted a lower number of tests needed.

Conversely, for given test performance, as prevalence increases, the optimal pool size decreases, and the number of tests needed would increase.

Furthermore, the number of cases missed due solely to dilution appears to be low (less than 1) for a batch of 100 specimens. When sensitivity is high (close to 100%), the number of specimens in a batch is small (<100), and when optimal pool sizes are less than 10, there are virtually no cases missed as a result of the dilution effect due to pooling. Uniform pool sizes of 4 tended to yield a better return in the number of tests needed as well as cost savings when compared to uniform pool sizes of 10. In Los Angeles SNFs, using an optimal pool size strategy would require fewer tests needed and therefore lower cost. For these facilities as a group, a uniform pool size of 4 (following the FDA recommendation) 7 yielded an approximately similar number of tests needed and corresponding costs to those when using an optimal pool size strategy, regardless of test performance and prevalence. This is potentially due to the relatively low prevalence of COVID-19 in most Los Angeles SNFs during the study period. Furthermore, if SNFs used a pooled testing strategy during response-testing, the expected total number of cases missed due solely to dilution was lowest when the SNF used an optimal pool size.

Our findings add to those of Cherif et al. 15 These data were retrieved for July 7th, 2020 (Data accessed on July 7, 2020) and exclude SNFs with missing data on required elements ("Current Isolated COVID+" or "Suspected Residents in Facility") or who did not report any staff members at the SNF in the last 24 h. 

The authors declare that there are no conflict of interests.

The peer review history for this article is available at https://publons. com/publon/10.1002/jmv.27054

All data generated or analyzed during this study are publicly available at https://data.cms.gov/. An online calculator with graphing capabilities which gives immediate information for pooled testing can be found at: https://simrock.shinyapps.io/pool_testing/. Total number of false-negative tests expected using pooled testing (4 specimen/pool) c 23 0

Total number of false-negative tests expected using pooled testing (10 specimen/pool) c 34 0

Total number of false-negative tests expected using pooled testing (optimal pool size) c 17 0

Number of false-negative tests expected per facility using individual testing d 0 (0, 0) 0 (0, 0)

Number of false-negative tests expected per facility using pooled testing (4 specimen/ pool) d 0 (0, 2) 0 (0, 0)

Number of false-negative tests expected per facility using pooled testing (10 specimen/ pool) d 0 (0, 2) 0 (0, 0)

Number of false-negative tests expected per facility using pooled testing (optimal pool size) d 0 (0, 1) 0 (0, 0) a These data were retrieved for July 7th, 2020 and exclude SNFs with missing data on required elements ("Current Isolated COVID+" or "Suspected

Residents in Facility") or who did not report any staff members at the SNF in the last 24 h. 15 

Moira Inkelas

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