How should we allocate limited capacity for coronavirus testing?

Re-opening the economy while minimising infections requires testing – but capacity is limited. To target testing well, policy-makers must consider the types, quality and timing of tests, the costs of errors and the risks of infection across different social groups.

Governments around the world are having to make difficult choices about the allocation of limited testing capacity. Some are testing mainly symptomatic individuals and, if it is possible, giving priority to tests for staff working in hospitals and care homes. Others are also testing non-symptomatic individuals to trace key spreaders of the virus. Figure 1 illustrates different testing strategies adopted across countries.

Figure 1: Testing policies around the world

Map showing Covid-19 testing policies around the world

When one person is tested, this means that someone else cannot be tested. This is what economists call an 'opportunity cost'. These opportunity costs arise not only when we need to decide who should be tested, but also how and when. The testing policy that saves the most lives takes account of all of these opportunity costs.

What are the costs and benefits of testing?

A test allows policy-makers to become better informed about the health status of an individual. The benefit of a test is that it provides information that allows more appropriate actions to be taken. For example, if the test is accurate and the policy-maker observes that an asymptomatic individual is currently ill, then the individual could be quarantined with the benefit of avoiding further contagion.

We can think about the cost of a test in different ways. One way is to think about the cost of buying and administering an additional test. Another way is in terms of the opportunity cost of the test: this is the benefit of allocating the test to another individual (today or in the future), who would not be tested otherwise.

Understanding all the relevant costs and benefits is important for the government to understand the groups of people for whom testing should be a priority. The criteria for making testing a priority for a particular group should be based on the benefits and the costs of testing an additional individual in that group. We briefly explain what determines those costs and benefits.

Who should be tested? Why group prevalence matters

Prevalence in a group is the chance that an individual from that group is infected. Prevalence is determined by the demographics of the individual (such as their age, sex and ethnicity), their symptoms, their medical records or information from track-and-tracing technologies.

Prevalence is the key input to determine the benefit of testing an individual. Suppose Alice has all the symptoms of Covid-19: she is coughing, has a high temperature and blurred vision. The prevalence in Alice’s group of people with similar symptoms and demographics is very high. By testing Alice, the policy-maker is likely to learn very little information because the test will, most likely, confirm the initial information.

Since the policy-maker learns very little from the test, their action towards Alice (that is, quarantine) would be the same with or without the test. In other words, the test is wasted. The same logic applies if Alice is very likely to not be infected with Covid-19 (for example, because she has been isolating for several weeks).

Finally, suppose that the policy-maker estimates that Alice has a 50% chance of having Covid-19. Then, testing her is very valuable: the policy-maker will learn a lot by finding out whether she is ill or not, and this information will guide the choice of the policy-maker (see Figure 2).

Figure 2: Benefits of testing are highest for moderate prevalence levels

Simplified graph showing how benefits of testing change according to prevalence

Lesson: Testing should be targeted at groups with a moderate level of Covid-19 prevalence.

Who should be tested? Costs of errors

The allocation of tests depends on the objectives of the policy-maker. A government might care about social costs of the disease: that is, the total health cost, the cost of lost economic output, the cost of children being out of school and so on. A business, on the other hand, might care about its profitability, its employees and its customers. The objectives of governments and individual businesses may diverge in test allocation.

To stop a new wave of Covid-19, governments need to find and isolate infected people. To re-open the economy and society, governments need to relax social distancing measures with the risk that infected people (maybe asymptomatic) restart the contagion.

In other words, governments need to balance quarantining an individual and releasing an individual. If the policy-maker does not test an individual (or if the test is imperfect), they can incur two types of costs. One cost is the cost of false quarantine, that is the cost of isolating individuals who are not, in fact, infected. The other cost is the cost of false release of individuals who are, in fact, infected.

The costs of false quarantine and false release differ a lot in the population. For example, they depend on the economic sector in which the individual is employed. For some sectors, social distancing is not feasible, so false release is very costly: infected people in those industries can contribute disproportionately to the likelihood of spread, for example, the entertainment and sports industries. Testing is valuable in such sectors unless the prevalence is already very high.

On the other hand, in industries where working from home is a good substitute for traditional office-working, the cost of false quarantine is not particularly high. Testing these workers is less valuable. Of course, for some workers, such as those on the NHS frontline, the costs of both false quarantine and false release are very high, and testing is very valuable indeed (see Figure 3).

Lesson: Tests should be targeted at individuals for whom a false quarantine or a false release is costly. If false release costs are low, do not test the individual if the prevalence is low (release them instead). If false quarantine costs are low, do not test the individual if the prevalence is high (quarantine them instead).

Figure 3: Costs and benefits of testing

Simplified graph showing the costs and benefits of testing as prevalence changes

What tests are available?

There are two main types of Covid-19 tests: serological; and polymerase chain reaction (PCR). Serological tests detect antibodies and therefore they are useful to determine how many people have already had Covid-19. PCR tests (swabs) detect the presence of Covid-19, and therefore they are useful in estimating the current infection rate in the population.

Serological tests help to estimate the prevalence in a group. Many governments, including in the UK, are now running serological testing programmes for representative samples of the population. The outcome of those programmes allows policy-makers to estimate the prevalence across different groups.

PCR tests give the policy-maker actionable advice about whether they should quarantine or release an individual. Therefore, PCR testing should be based on the prevalence in a group. The policy-maker can estimate prevalence based on all the serological and PCR tests conducted in the group.

As a result, PCR tests and serological tests are substitutes for learning about Covid-19 prevalence. But if the policy-maker believes that PCR testing is likely to be necessary in a particular group (because it has high costs of false quarantine and false release), then serological testing and PCR testing can be complementary for that group.

Lesson: Serological tests should be used to learn the prevalence of different groups that the policy-maker wishes to monitor for the possibility of further Covid-19 outbreaks. The policy-maker can then use the more accurate prevalence information to target PCR tests to these groups more effectively.

How should people be tested when testing is imperfect?

Even if tests are often imprecise, they are still very useful. The specificity and sensitivity of a test summarise the precision of a given test (Ely et al, 2020):

Test sensitivity describes the probability that the test correctly detects infection.
Test specificity describes the probability that the test correctly detects lack of infection.

Governments and health authorities often have a portfolio of tests available to them, each with distinctive sensitivity and specificity parameters. The ideal is a test that is high in both dimensions. A test that is low in both dimensions should, all else being equal, not be used.

But what about tests that are high in one dimension and low in the other? The policy-maker can target the portfolio of tests to the individuals who are most likely to reduce social costs.

For example, tests that are highly specific (correctly identify if not infected) but are not very sensitive (poor at detecting if infected) are better targeted at individuals who are likely to be in contact with many others because, for those individuals, the government wants to avoid false release. Examples of individuals with above average contact rates are healthcare workers or workers in highly concentrated transport hubs.

In contrast, tests that are highly sensitive but not very specific are better targeted at individuals with high costs of false quarantine, for example, those who cannot work from home and where social distancing can be assured in the workplace.

Some Covid-19 tests are highly imperfect, but they are very cheap and quick to administer. In this case, it might be possible to test the same individuals repeatedly. If the imperfection of test results is random in the population, then repeated testing can potentially overcome test imperfection (Kamalini et al, 2020).

Lesson: Specificity and sensitivity need to be considered carefully when allocating tests.

Who should be tested when? Learning about prevalence

Testing someone does not just benefit society today. It also gives the policy-maker information about prevalence for different groups, which helps to inform better decisions about whom to test and whom to quarantine in the future.

The problem of deciding between testing someone today to make a better quarantining decision for this person versus testing someone else to make better testing and quarantining decisions in the future is a very difficult one.

Fortunately, there are 'adaptive algorithms' that provide guidance about the best allocation of tests when we have both objectives (Kasy and Teytelboym, 2020). These algorithms are similar to those used by internet giants like Netflix to learn about your movie preferences (that is, disease prevalence) and recommend the best movies to you (that is, take the best testing decision for the current individual).

These algorithms suggest that when the policy-makers are unsure about prevalence, they should test groups with low and high prevalence in order to estimate the prevalence.

For example, suppose that in the absence of dynamic considerations, the policy-maker would have tested Alice if the prevalence in her group is between 30% and 50%. Initially, an adaptive algorithm might recommend that the policy-maker should test Alice even if her group prevalence is between 10% and 90% Eventually, when prevalence is well estimated, policy-makers can make decisions based on the short-run value of information described above.

Lesson: If there is uncertainty about prevalence, policy-makers should consider testing groups with higher and lower prevalence in order to gain more information about prevalence in these groups.

Should the government provide incentives for private firms to carry out testing?

An effective testing strategy must take consideration of the incentives for individuals and firms to be tested.

Voluntary testing and track-and-tracing systems which prescribe that people who test positive or their contacts should quarantine are difficult to implement successfully without the government subsidising some of the costs that individuals have to incur during any subsequent quarantine.

Similarly, as governments start easing lockdowns and opening economic sectors, the workplace will become one of the most risky environments for contagion. To avoid new Covid-19 outbreaks and minimise economic disruption, it is important that testing programmes are implemented within companies. Governments will need to give organisations clear guidance, and ensure that they have incentives to test their members and employees.

Some organisations, such as the Premier League, may have sufficient private incentives to invest in testing programmes to restart their businesses. Indeed, the Premier League has invested £4 million in a testing programme that allows players and staff to be tested regularly twice a week.

But for smaller businesses, the costs of testing can be too high. In these cases, drastic quarantining decisions can discourage businesses from testing unless they are combined, for example, with targeted furlough schemes for those quarantined.

Lesson: Governments should ensure that subsidy and furlough schemes encourage testing and so support the effectiveness of testing systems.

Where can I find out more?

The value of testing: Andrea Galeotti, Paolo Surico and Jakub Steiner describe the social and individual value of testing at VoxEU.

How a Covid-19 testing model no one is talking about could save thousands of lives: Andrea Galeotti describes the usefulness of antibody tests in Time magazine.

A framework for testing: Andrea Galeotti discusses how to target tests.

Is there a better Covid-19 test method for the UK? Kamalini Ramdas explains how the repeated use of cheap and rapid tests could complement existing testing strategies.

Testing in a pandemic: Max Kasy explains how adaptive targeted testing works.

Coronavirus testing data on Our World in Data: Data on testing around the world.