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What are the risks of false negatives in pooled tests?

Text updated on 2020-10-15

Mixed with other samples, a sample containing little virus may not be detected as positive and this can pose a problem for individual diagnosis. Despite this risk (known as false negative), pooled testing is currently being used on many university campuses in the United States, the United Kingdom, and Belgium to contain the spread of the epidemic.

When a test is negative if you have the virus, it is called a false negative. The principle of group testing is as follows: instead of testing 100 samples, you can group them into 10 groups ("pools") of 10 and test each group with a single test. See the question Grouping tests ("pooling", "pools"): why and for what purpose?

Ideally, if a group is negative, then each sample in that group should be negative as well. However, pooling causes a dilution of the virus-containing sample(s) in the virus-free sample(s). This dilution is then likely to create false negatives: the viral concentration in the pool may become below the detection limit of the diagnostic machine. In this case, the result of the pooled test is negative (no infection) when there is actually an infected person in the pool.

The concentration of SARS-CoV-2 virus in a nasopharyngeal or salivary swab may vary by a factor of more than 10,000,000 times between two infected individuals. This is because the result of an RT-qPCR test is often expressed as a number of doubling cycles (called Ct, for Cycle threshold): 25 doubling cycles can separate samples with the highest virus concentration from those with a concentration close to the detection limit of the RT-qPCR test (2e^25~10e^7).

To fully understand the effect of this very large dispersion, imagine a society with the following distribution of wealth. The so-called "negative" population with 0 or less than $1 in its pocket. In the "positive" population, we imagine that the 5% of the population with the least wealth have, in their pocket, a fortune estimated between 1$ and 2$; the next richest 5%, a fortune between 2$ and 4$; the next richest 5%, between 4$ and 8$, and so on. 50% of the positive population has $1000; and for the richest 5%, it is a real annuity: between $500,000 and $1,000,000. 80% of the positive individuals in this society will then have a fortune of more than $16. Even diluted in a pool of 15 individuals, the wealth per individual will remain above 1.

The concentration of virus in different samples (from different individuals at different stages of infection) is distributed in the same way: 1$ then corresponds to the virus richness required for detection in the RT-qPCR device. A non-negligible fraction of the infected population (of the order of 5 to 15% of the total positive population) provides samples with virus concentrations close to the detection limits of RT-qPCRs in medical laboratories. These low positive individuals are therefore likely to be undetectable in a pooled test larger than 5. However, pooled tests are still effective in detecting a very large portion of the infected population (typically greater than 80% for a group of 16) whose specimens will carry a viral concentration well above the detection limit of a conventional RT-qPCR machine.

There areessentially two times when a sample from a positive individual may have a low concentration of virus: at the beginning and end of the infectious period. After infection, the virus concentration remains undetectable for a few days, then increases rapidly until it peaks about a day before the potential onset of symptoms, and then decreases to below detection limits a few days to weeks after infection. See the question How long is a person contagious?

Individually or in a group, a test can pose an epidemic risk management problem when it does not detect an individual during the incubation period: the person may believe that he or she is healthy but will be contagious in the following days. A less sensitive group test is therefore more likely to fail to detect an individual in the early infectious phase.

On the other hand, less detection of individuals at the end of infection is potentially less problematic for epidemic control because individuals at the end of infection are likely to have low levels of contamination. See the question What are the tests to find out if I've ever had COVID-19 ?

Modelling studies indicate that false negatives linked to pooling mainly concern individuals at the end of their infection. Indeed, the period of increase in viral concentration is very short compared to the period at the end of infection.

Two strategies can be implemented to compensate for the loss of sensitivity induced by dilution:

Antigenic tests to detect the presence of the virus represent a complementary solution to the pooled tests. These antigenic tests are particularly suitable for detecting individuals with high viral concentrations. However, their sensitivity is variable and lower than that of the RT-qPCR assays, with a detection limit 100 to 1,000 times higher than the detection limit of the individual RT-qPCR assay. According to this estimate, the risk of false negative in an individual antigen test would then be comparable to that of a pooled test with 100-1,000 individuals.

In conclusion, pooling makes it possible to test a large population more often. Despite the existence of some risks of false negatives, pooling is already used on many university campuses in the United States, Belgium, and the United Kingdom, and to screen health workers in Singapore, Germany, Uruguay, Israel, and Portugal.

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Historical article with the optimal size in the case of a perfect test (without increasing the risk of false negatives with the size of the group in the pool).

Dorfman, R. (1943). The detection of defective members of large populations. The Annals of Mathematical Statistics, 14(4), 436-440.

Estimation of the distribution of the SARS-CoV-2 virus concentration  in oral or nasopharyngeal samples for different age groups at La Charité Hospital in Berlin (Germany) before June 6, 2020.

Jones, T. C., Mühlemann, B., Veith, T., Biele, G., Zuchowski, M., Hoffmann, J., ... & Drosten, C. (2020). An analysis of SARS-CoV-2 viral load by patient age. medRxiv.

Distribution of viral loads observed in a large sample of nursing home populations in the United States. Viral loads measured in symptomatic and asymptomatic individuals are similar.

Lennon, N. J., Bhattacharyya, R. P., Mina, M. J., Rehm, H. L., Hung, D. T., Smole, S., ... & Gabriel, S. B. (2020). Comparison of viral levels in individuals with or without symptoms at time of COVID-19 testing among 32,480 residents and staff of nursing homes and assisted living facilities in Massachusetts. medRxiv.

Article on modeling the risk of false negatives in pool testing for SARS-Cov2 detection. Application to prevalence measurement (without identification of positive cases in pools) for epidemiological surveillance of a closed community, nursing home type. Prevalence, i.e., the proportion of positive individuals in a community can be estimated with high precision even without identification of positive cases in pools.

Brault, V., Mallein, B., & Rupprecht, J. F. (May 14th 2020). Group testing as a strategy for the epidemiologic monitoring of COVID-19. arXiv preprint arXiv:2005.06776 .

Article modelling the impact of changes in susceptibility of pooled tests during an SARS-Cov2 infection with application to epidemiological surveillance in a closed community. The loss of pool sensitivity is mainly attributed to individuals sampled at the end of infection. Prevalence, i.e., the proportion of positive individuals in a community can be estimated with high precision even without identification of positive cases in pools.

Cleary, B., Hay, J. A., Blumenstiel, B., Gabriel, S., Regev, A., & Mina, M. J. (October 6th 2020). Using viral load and epidemic dynamics to optimize pooled testing in resource constrained settings, medRxiv.

An evaluation of the ability to determine the presence of SARS-CoV-2 in very highly diluted samples. A sample with a fairly average virus concentration remains detectable in several pools of 49 negative samples (10 out of 10 tests) as well as in a pool of 499 negatives.

Gan, Y., Du, L., Damola, F. O., Huang, J., Xiao, G., & Lyu, X. (2020). Sample Pooling as a Strategy of SARS-COV-2 Nucleic Acid Screening Increases the False-negative Rate. medRxiv

Application of a digital droplet PCR (ddPCR) technique for viral detection of SARS-CoV-2 when a positive sample with a low concentration of virus is included in a group of 15 negative samples.

Martin, A., Storto, A., Andre, B., Mallory, A., Dangla, R., Visseaux, B., & Gossner, O. (2020). High-sensitivity COVID-19 group testing by digital PCR. arXiv preprint arXiv:2006.02908.

Pooled tests (size 5 to 20) in saliva samples by the Yale University team, who are behind the SalivaDirect test.

Watkins, A. E., Fenichel, E. P., Weinberger, D. M., Vogels, C. B., Brackney, D. E., Casanovas-Massana, A., ... & Cruz, C. S. D. (2020). Pooling saliva to increase SARS-CoV-2 testing capacity. medRxiv.

Discussion of the value of antigenic tests despite lower sensitivity, citing a viral detection limit 100 to 1000 times higher in antigenic tests than in the individual RT-qPCR test.

Mina, M. J., Parker, R., & Larremore, D. B. (30 September 2020). Rethinking COVID-19 test sensitivity-A strategy for containment. New England Journal of Medicine.

The potential for transmission, as estimated by the ability to infect cells in culture, appears to be limited to individuals whose samples have a high concentration of virus.

Rhee, C., Kanjilal, S., Baker, M., & Klompas, M. (2020). Duration of SARS-CoV-2 Infectivity: When is it Safe to Discontinue Isolation?. Clinical Infectious Diseases.

Discussion of the status of pool testing in universities in the UK. The SAGE Scientific Council recommends regular testing of students and university staff.

Mahase, E. (2020). Covid-19Universities roll out pooled testing of students in bid to keep campuses open.

Further reading

Grouping tests ("pooling", "pools"): why and for what purpose?

False positives, false negatives, sensitivity, specificity of COVID tests: what are we talking about?

What approaches could accelerate large-scale screening?

What is the baseline test to find out if I am infected with SARS-CoV-2?