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A guide to R — the pandemic's misunderstood metric - Nature.com
Jul 03, 2020 4 mins, 21 secs
The nation, said Johnson, would set a COVID-19 alert level, to be "primarily determined" by the number of coronavirus cases, and by R, the reproduction number.

To infectious-disease experts, Johnson’s focus on the reproduction number as a guiding light for policy was worryingly myopic.

They worry about placing too much weight on R, the average number of people each person with a disease goes on to infect.

Too much attention to it could obscure the importance of other measures, such as trends in numbers of new infections, deaths and hospital admissions, and cohort surveys to see how many people in a population currently have the disease, or have already had it.

“Epidemiologists are quite keen on downplaying R, but the politicians seem to have embraced it with enthusiasm,” says Mark Woolhouse, an infectious-diseases expert at the University of Edinburgh in the United Kingdom, who is a member of a modelling group that advises the British government on the pandemic.

First used almost a century ago in demography, R originally measured the reproduction of people — whether a population was growing or not.

In epidemiology, the same principle applies, but it measures the spread of infection in a population.

So it is usually estimated retrospectively: disease modellers look at current and previous numbers of cases and deaths, make some assumptions to find infection numbers that could have explained the trend and then derive R from these.

One variant of R, R0, assumes that everybody in a population is susceptible to infection.

But when politicians and scientists talk about R, they usually mean another variant called Rt (sometimes called Re, or ‘effective R’), which is calculated over time as an outbreak progresses and considers how some people might have gained immunity, perhaps because they have survived infection or been vaccinated.

Confirmed cases and mortality figures can be used to infer the total number of infections, but both come with a significant lag — which scientists estimate could be anything from a week to three weeks or more.

With a mathematical trick called nowcasting, researchers can use the observed statistical distribution of reporting delays to predict how much higher the number of fresh infections will be in, for example, two weeks.

Some estimates of Rt already rely on nowcasting infection data in this way: it is "the method with the least guesses", says Lars Schaade, vice-president of the Robert Koch Institute in Berlin, Germany’s main public-health agency, which reports a daily and seven-day Rt value based on infections reported by state health authorities.

An issue with nowcasting is that it swaps one problem for another, says Sebastian Funk, a disease modeller at the London School of Hygiene and Tropical Medicine, who is also advising the British government on this pandemic.

There’s no way that you can know how many cases would still be observed that have already been infected,” he says.

Another is results from random testing of a population to see how many people currently have COVID-19, or have had it.

“There’s a bit of a trade-off here,” says Funk.

Groups of epidemiologists, Funk says, each have their own approach to combining and using these disparate sources of data to work out Rt, relying on their own statistical models to look at trends in presumed infections.

Conversely, high incidences of infection among a spatially distinct smaller subsection of a population can sway a larger region’s Rt value.

And most experts say that the Rt for the United Kingdom is kept artificially high by the very large numbers of infections and deaths in care homes for older people, and does not reliably represent the risk to the general population.

But regional Rt numbers become less accurate as they are applied to smaller populations, especially when absolute infections are low.

The Harvard site produces numbers for US counties — which can range from thousands to millions of inhabitants — but one of its creators, Xihong Lin, says that hyperlocal data come with big uncertainties.

Used properly, the data could help public-health officials to identify hot spots of infection to prioritize resources such as testing, she says.

As few as 10–20% of infected people seem to cause 80% of new COVID-19 cases, Leung says.

When countries consider when to reopen schools and offices, a key question is not only Rt, but what the actual number of infected people walking around is.

Denmark and the United Kingdom have similar Rt values for instance, but because the number of infected people walking around Denmark is ten times lower, it’s safer for their schools to be reopened.

“When infection numbers are low, maybe you don’t care so much about what the reproduction number is, or at least don’t care if there’s some uncertainty in it,” says Funk.

A test for the United Kingdom, says Woolhouse, will be whether the country overreacts if case numbers are low but modellers estimate that R is above oneJ

For countries recovering from the first wave of the pandemic — such as the United Kingdom — researchers say it’s far more important to watch for clusters of cases and to set up comprehensive systems to test people, trace their contacts and isolate those infected, than to watch the needle swinging on a colourful dial.

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