Feasibility of COVID-19 Screening for the U.S. Population with Group Testing [Abbreviated Version]

Feasibility of COVID-19 Screening for the U.S. Population with Group Testing

Prof. Peter Frazier, Massey Cashore, and Yujia Zhang, Cornell University, 24 April 2020

Based on a longer whitepaper with the same title

Population-level screening for COVID-19 is a critical tool for returning much of the population to their daily lives while preventing a second wave of the disease. At the same time, limited testing capacity prevents testing everyone in the U.S. We show that group testing, first proposed in 1943, can overcome this challenge. We propose a testing method that, under an assumption of 1% prevalence, would use at most 6M PCR laboratory tests per week while returning over 90% of the population to work by the end of a 4 week period, reducing the prevalence to 0.3%. Testing could be continued after to keep prevalence low while allowing a near-full return to normal daily life while awaiting a vaccine.

Group Testing: The key idea in group testing is to save test capacity by testing groups of samples from multiple people simultaneously. For COVID-19, this is done by pooling saliva or nasopharyngeal swabs from multiple people together into one RT-PCR laboratory test. This test then reveals whether or not there was at least one positive sample in the pool.

While several group testing methods exist, we focus on the square array protocol. In this protocol, samples (material we wish to test for virus particles) are placed into tubes in a square array (see the figure) and assigned to groups by rows and columns respectively. Each row and column is tested as a group. A sample is deemed positive if both its row and column groups test positive.

This protocol is extraordinarily efficient. For example, if our array is 70x70, then we can test 4,900 samples with only 2x70=140 PCR tests. While we would not save on swabs, PCR testing capacity is the limiting factor over the long term in scaling up testing.

In the typical use of a square array protocol, each sample comes from one individual. In our approach, each sample combines swabs or saliva samples from all members of a household, reducing the amount of viral transport media needed and reducing false negatives as explained below.

False Negatives and False Positives: Although its efficiency makes group testing an appealing countermeasure to limited PCR capacity, false negatives are a challenge: a test can say that an individual is not infectious (a negative) even when this is not true. This is dangerous because this individual can infect others. We show that two strategies can effectively combat false negatives when used together: repeated testing; and testing households together. False positives also occur: these cause individuals who are not infectious to be quarantined.

Household Testing: An infectious member of a household tends to infect the rest of the household. We can use this insight to combat false negatives and reduce testing resources. Our protocol calls for combining the swabs from all members of a household into a single tube for transportation to the lab. There, they would appear as a single sample in the above square matrix protocol. If a household is identified positive, all members would be quarantined.

This addresses false negatives: while it is possible that a swab or saliva sample would miss viral material in one infectious individual, it is less likely for this to be missed in all members of a household with multiple infected individuals. Testing households together also reduces the amount of viral transport media needed and eases the logistics of collection.

Repeated Testing: Despite household testing, false negatives will cause some infectious individuals to test negative. These infectious individuals will then enter the population at large and infect others. To mitigate this effect, we use repeated testing. As long as testing is frequent enough to remove infections from the broader population faster than they are created by not quarantining false negatives, overall prevalence can be reduced.

Proposed Design and Analysis: We combine these insights to propose a design that allows a significant fraction of the U.S. population to return to work in a short period of time while consuming a PCR testing capacity that we believe to be feasible. Specifically, this testing protocol adheres to a PCR testing capacity of 6 million PCR tests each week across the entire United States. Here are the details:

Testing happens once per week over the first 4 weeks, using square array protocols of sizes 62x62, 62x62, 29x29, and 41x41 households respectively. (62x62 means that we have 62 row groups and 62 column groups of 62 households each.)
Households testing positive are quarantined for 14 days. After this period, if they were infectious, our analysis assumes they are no longer infectious.

Assuming 1% prevalence in the initial population, our analysis (see our publicly available codebase) shows:

End of week 1: 69.7% of the population is out of quarantine. Overall prevalence (among quarantined and non-quarantined) is 1.3%; prevalence in the non-quarantined population is 0.4%.
End of week 2: 58.8% of the population is out of quarantine. This number drops because the positive cases from the first tests are still under quarantine, and the second test quarantines some more. Overall prevalence is 1.5%; prevalence in the non-quarantined population is 0.2%.
End of week 3: 86.5% of the population is out of quarantine. Overall prevalence is 0.6%; prevalence in the non-quarantined population is 0.1%.
End of week 4: 95.7% of the population is out of quarantine. Overall prevalence is 0.3%; prevalence in the non-quarantined population is 0.1%.

Afterward, prevalence can be kept low while a large fraction of the population continues to be out of quarantine by using a similar group-testing protocol to reduce prevalence even further. We may then reach a point where we can stop group-testing altogether and instead use contact tracing to identify and quarantine infectious cases, or we may continue group testing as a precaution until a vaccine is available.

Antibody Testing and Risk Groups: While our protocol does not make use of antibody testing or prioritization based on risk, these two tools can bring even more people out of quarantine safely while reducing the amount of testing required.

First, if reliable antibody testing for immunity can be done at scale, then those that are found to be antibody positive and not infectious (after at least two rounds of PCR testing) can be exempted from testing for a substantial period of time, reducing quarantines and testing resources required.

Second, testing can be prioritized to non-quarantined households that are most likely to be positive based where those individuals live and potentially an estimate of their frequency of interaction with others. Fine-tuning the proposed baseline protocol above based on local estimates of prevalence offers the opportunity to bring more people out of quarantine and reduce the resources devoted to testing resources while controlling prevalence.

Assumptions: In addition to the assumption of 1% prevalence and a limit of 6M PCR tests / week, this analysis uses several other parameter estimates, listed here:

We use a Monte Carlo simulation with a population of 22,500 individuals.
The simulation uses a 30% false negative rate arising from improper swabbing.

Erroneous swabs occur independently for each individual within a household, i.e. we assume there is no within-household correlation for erroneous swabs.
The PCR test always detects the presence of the disease whenever the group contains at least one infected individual with an accurate swab.

The PCR test has a 10% chance of returning positive for a group with zero infected swabs.
There is zero latency between time of swabbing, time of running the PCR tests, and the time at which resulting quarantine decisions are made. In the simulations, all of these events occur immediately at the beginning of each week.
The population has full compliance with testing.
Household sizes follow the US household size distribution in 2019 (assuming a maximum household size of 7 individuals). We do not account for any geographic variation in household size distribution.
When we form groups, if the number of remaining households in our population is lower than the group size in the protocol, we form a square array with a smaller group size.
Among the unquarantined population, the prevalence of the virus doubles every 3 days.
The probability that a positive individual infects another household member is 37.4%.
Perfect randomization is used to assign households into row and column groups.
Our simulation models correlated infection status within households at a detailed level to estimate the properties of a group test (fraction of infectious, susceptible, and recovered individuals classified as positive and negative), but does not model the dynamics of this correlated within-household infection status week-over-week. Instead, week-by-week infection and quarantine status are modeled at the level of fraction of the total population.
Quarantine lasts 14 days. After 14 days have passed all previously infected individuals exiting quarantine are assumed to either be dead or recovered from the disease and no longer susceptible.