What are the risks of false negatives in pooled tests?

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:

• further reduce the threshold concentration above which a sample is considered positive. This strategy has the disadvantage of increasing the risk of false positives (the risk that the test is positive when the virus is not present).
• use machines with higher sensitivity. Using another PCR technique, called "droplet digitial PCR", a team from Bichat Hospital (France) claims to detect a positive individual in a pool of 15 negative samples with a higher sensitivity than a standard individual RT-qPCR test.

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.