Why we should be wary of React’s R-number estimate

It seems that Boris Johnson will not begin to think about lifting lockdown restrictions until we have clear evidence that the latest wave of the virus has almost been defeated.

So it was not exactly good news yesterday from Imperial College’s React Covid survey, which suggested that even though we are in lockdown, the R number is still almost at 1 in Britain – meaning the epidemic is barely shrinking.

As part of React’s ‘viral opinion poll’ swabs were taken from over 160,000 people in England between 6 and 22 January. And while the researchers rowed back on a claim in their previous report that active infections could be rising in England, the programme director, Paul Elliott, still painted a worrying picture:

“‘We’re not seeing the sharp drop in infections that happened under the first lockdown and if infections aren’t brought down significantly, hospitals won’t be able to cope’.

But is Imperial right to be so concerned?

We believe not. Based on our own research, we think it is clear that the third lockdown has been extremely successful in containing the disease, and has actually brought the R-rate down to about 0.6 – lower than at any time since June last year. If the R-rate is this low, that means infections will be dropping rapidly.

There are good reasons to think that the React survey is overly pessimistic about the current situation.

Two periodic infections surveys are carried out in England, both massive in scope. The first is the monthly React survey, and the second is run by the Office for National Statistics on a weekly basis. Both scale up their results to estimate the number of active infections in the country as a whole. But the React study tries to go further and will identify a trend within its sample as well. This trend led to the R-rate estimate of around 1 this time. The problem is that there are too many fluctuations in the daily data to make these kinds of estimates reliable.

To give an example, if you look at the last day of data collected by the React survey on 22 January, you can only confidently say there were between 340,000 and 1.4 million active cases in England. There is too much uncertainty with the data to narrow that number down. But these wide confidence intervals apply to all the other daily datapoints in the survey too, meaning it is very difficult to pick out reliable trends on a day-to-day basis. This is why the ONS takes the average number of cases of its whole sample, to cut through the noise.

When looking at their latest data, the React researchers thought their numbers pointed to an upward trend in infections in the first half of their survey and a downward trend in the second. They then applied clever mathematics to find an R-rate of 0.98, which suggests that infections are falling, but very slowly.

You can get a good idea of the thrust of React’s argument simply by looking at their interim and final estimates of the number of active cases in England in the first half of January, spaced four days apart. You can see these on the below chart (in black), which also displays the ONS readings and our prediction, based on a model we have developed at the University of Bristol, called the PCCF.

You can see that the two latest React points are showing a small downward trend in active infections. The eagle-eyed reader may discern, too, that the general direction of travel can be identified correctly from each of React’s previous three pairs of data points. But React is poor at capturing exactly how quickly infections are growing or decreasing at these times; indeed it seems to have an inbuilt tendency to understate growth and decline.

While both the ONS and React survey give us valuable information on the prevalence of the coronavirus in the country at specified points in time, their information is only available intermittently and it is 10 to 14 days out of date when it arrives. So it cannot be relied upon for taking decisions on a short timescale, as the government needs to with a fast-evolving epidemic.

The continuous trace provided by the PCCF offers a viable alternative. This measurement software uses the daily official coronavirus data to measure the key parameters of the Covid-19 epidemic in England, applying fairly simple mathematical models to reconcile the daily figures with the ONS and React studies.

The next chart shows the behaviour of the R-rate as measured by the PCCF, with figures deduced from the ONS weekly survey superimposed.

It is clear that the PCCF trace and the ONS infection survey are telling the same story, and that this lockdown is working to dramatically reduce the R-rate, to a level even lower than in November.

So instead of the gloomy reports from Imperial, it is clear that with vaccinations being rolled out and the latest lockdown having a significant impact, not only are active infections falling rapidly in England, but they should continue to do so.

The careful relaxation of restrictions requires precise control of the R-rate. This can only be done if the government has access to a measurement of the R-rate that is rapid, continuous and available every day. It is about time the government, nearly a year into this crisis, finally got a handle on the data.