Frightening graphs of the exponential growth in the number of people testing positive for the coronavirus are not the full picture.
Jill Margo
Mar 20, 2020
AFR
As the coronavirus pandemic moves towards its peak in Australia, clearing up some of the statistical confusion about it may help to calm the panic. Just as a picture is worth a thousand words, so is a statistical graphic.
Every day now, we peer at frightening graphs showing the exponential growth in the number of people around the world who have tested positive for the virus.
There is no doubt the virus is spreading but these graphs only show part of the story – the scary part.
They do not show how many people were tested to get that result or how many of the people with a positive result are actually feeling fine. All we see are raw, rising numbers.
“To get a sense of what proportion of the community is getting this infection, we need to know how many were tested, not just how many tested positive,” says ANU Medical School’s Professor Peter Collignon, who is an expert on infectious disease.
Communicating proportionality may dampen alarm.
Australia’s current graph of positive cases begins around the middle of January and stays flattish until March, when it starts to climb dramatically.
Looking at it, a citizen might think we were doing fine initially but then suddenly, things got worse with a rush.
But what the graph reflects is that we did no testing initially. Once we started, the more people we tested, the more cases we found.
As of Friday morning, over 104,000 tests had been performed in Australia and 708 cases had been confirmed.
Theoretically, even if the number of infected people had been stable, the number of positive cases would have increased because testing increased and more cases were found.
One day this week, when the numbers of new cases dropped a little, some people may have thought this was cause for optimism. What it reflected, however, was that we are running low on test kits while we wait for new stocks to be distributed next week.
Australia’s scary graph, however, does serve a purpose. It raises panic but it also helps people to understand why radical action is necessary.
The balance is delicate and while this graph is an important part of the package presented to the public, a companion graphic showing the percentage of people testing positive could mitigate the panic.
The power of ‘percentage positivity’
Here’s the difference. If one day we test 100 people and we find one case, that equals a 1 per cent positivity rate. If the next day we test 1000 people and we find 10 cases, that still equals a 1 per cent positivity rate.
So, while the raw numbers of confirmed cases on the second day is bigger and potentially alarming, the percentage positivity hasn’t increased.
Deriving positive percentage is simple. It just means dividing the number of positive cases by the number of tests performed and multiplying the result by 100.
There are various ways to depict this. A bar chart could be used. So could a pie chart with the whole pie being the total number of tests performed, and a slice being the number of positive tests.
A series of pies could enlarge as testing increases. Watching the pies could put the issue in perspective and be less terrifying than watching the raw numbers rocket.
And here’s why. As of Friday morning over 104,000 tests had been performed in Australia and about 708 people had tested positive. If we assume each person had a single test, the percentage of positivity overall would be about 0.7 percent.
But the number of tests does not necessarily reflect the number of people tested, because some have additional tests to confirm a positive result or to clear them of infection.
Even if 30,000 of these tests were repeats, the overall percentage of positivity would be under 1 percent.
While pie charts are generally not well liked by statisticians because they can oversimplify percentages, they do allow the public to make an instant appraisal.
Providing percentage positivity would be useful, but it is logistically more complex to do on a daily basis, says Dr Meru Sheel, an infectious diseases epidemiologist at the National Centre for Epidemiology and Population Health at ANU.
The 100,000 testing kits about to hit the ground will be heavily rationed, meaning many infected, asymptomatic people will not qualify.
New cases are readily reported the same day but there can be a lag reporting the number of tests performed. While testing widely is important, she says it needs to be systematic, comprehensive and consistent, so we know who was tested.
At the moment, the shortage of tests means strict we need to have criteria for testing. This gives us an idea of who is being tested, although the guidelines do allow a margin for clinical judgement.
Testing criteria skews numbers
As can be seen in the bar graph above, South Korea shows the number of people tested and the number confirmed positive.
It has now tested almost 300,000 people and amassed the most comprehensive data in the world.
It has also become the most credible source of data on this virus and has shown the world that diagnostic capacity, which allows for wide testing at scale, is key to epidemic control.
South Korea rolled out testing everywhere, with drive-through clinics where healthy people could show up and get tested.
Our criteria, which include having a fever, having returned from abroad or having been in close proximity to someone who is infected, produces a biased sample of the population.
It is also the sample from which conclusions are being drawn to justify shutting down society. While progressive shutting down is the right thing to do, the decisions are not being made on much hard evidence.
And the 100,000 testing kits about to hit the ground will be heavily rationed, meaning many infected, asymptomatic people will not qualify.
“That may well mean we won’t see the bulk of the iceberg that lies below but I do think that proportionately, compared to most countries, we have done well with testing,” says Professor Collignon.
He says there is guidance in the Korean data, which clearly shows the relationship between age and risk of dying from this virus.
If things got really bad in Australia, he says a staged age-related closedown would be appropriate. “I think we should protect people over 70. When there is more spread, we might advise people over 60 to self-isolate and if it becomes widespread, revise this to people over 50.”
Another way of calming panic may be to contextualise death. Every death is a tragic loss and in the past month, seven Australians have died from this virus.
This figure might cause less anxiety if people knew that in the same time period, more than 13,000 Australians died from other causes.
There may be some comfort in the relativities – not for those who are bereaved, but for those feeling overwhelmed by the threat of the virus.
And there is more from comfort from Korea, where no citizen under the age of 29 has been lost to the virus so far, and only two under 50 have died.
COVID-19 could vaporise post-Millennial narcissism epitomised by the Kardashians, Paris Hilton and other Instagram influencers.
On the other hand, The New York Times suggested this week that the new virus would gain a place among the top causes of death in the US.
It suggested that after heart disease and cancer, it would come in third, pushing Alzheimer’s and other brain degeneration to fourth position.
Around the world there is statistical confusion about the death rate. The simple fact is that until the outbreak is over, no one will really know.
Until then, all Australians have is a ratio based on the number of people who died among those who tested positive for the virus – a figure that will be delayed because it takes time for infected people to recover.
On Friday, a spokesman for the Health Department said it was planning to add more graphs to its website.
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