## COVID 19: Day 264: Worrying about the effect of ‘false-positive’ tests

Click for a larger version. The upper graph shows the number of Pillar 1 (Hospital) and Pillar 2 (Community) tests per day versus the day of year. The middle graph shows the number of those tests yielding positive results for COVID-19. The lower graph shows the ratio of the upper two graphs to show the fraction of tests which are positive. The minimum value of that ratio is shown as a dotted line and represents a reasonable best guess at the MAXIMUM rate of ‘false positive’ tests. All data are 7-day retrospective averages.

I wrote yesterday about the difficulty of interpreting the recent rise in positive COVID-19 tests.

One point that I did not cover was the issue of false positive results.

Now that we are testing 200,000 people each day, even a small rate of false of positives (say 1%) would give rise to 2000 positive results each day. This can be compared with roughly 4000 positive tests per day at the moment.

Prof. Carl Heneghan argues that the tests may include many false positives caused by detection of ‘dead’ viral fragments.

But unfortunately nobody knows what the rate of false positive results actually is!

However we can estimate an upper limit.

Estimating the upper limit of false-positive tests#1

To estimate the upper limit of false positive tests we assume that

• The false positive rate has not changed significantly during the course of the crisis.

Then we look for the minimum registered fraction of positive results – and assume that they were all false positives. This is likely to be an overestimate of the false positive rate

I have downloaded data from the Governments Coronavirus ‘Dashboard’ to evaluate this. The data – all shown as retrospective 7-day averages – are shown in the figure at the start of the article and plotted versus the day of the year

• The upper graph shows the number of Pillar 1 (Hospital) and Pillar 2 (Community) tests per day.
• The middle graph shows the number of those tests yielding positive for COVID-19.
• The lower graph shows the ratio of the upper two graphs to show the fraction of test which are positive.

The minimum value of that ratio (0.0052 or 0.52%) is shown as a dotted line and represents a reasonable best guess at the MAXIMUM rate of ‘false positive’ tests. The true rate is probably lower than this.

Estimating the upper limit of false-positive tests#2

We can also perform a similar analysis for the Pillar 4 tests – those used for the ONS Survey – that I mentioned in a recent post.

Click for a larger image.

Looking at the data from July 3rd to 16th, the positivity rate was just 0.05% – 10 times lower than the maximum false positive rate from the Pillar 1 & 2 data. The maximum false positive rate cannot be higher than this.

Conclusion

There is no evidence that the false positive rate is materially distorting our view of corona virus spread.

Using either estimate does not materially change any of the conclusions I drew yesterday.

The demonstrably low rate of false-positives also speaks against the concerns of Professor Henegan that the government may be ‘chasing shadows’.

Living with the virus…

The BBC ask today Is it time we learned to live with the virus?

This article draws on the arguments of Prof. Heneghan who argues – reasonably – that we should focus on the harm caused by the virus (disease and death) rather than just the mere presence of the virus or of an infected person.

He and others argue that while COVID-19 may be worse than Flu, it is a disease in the same category of respiratory viruses.

And in the same way that we accept deaths from flu of between 20,000 and 50,000 per winter, and we should accept a similar rate of loss to COVID-19.

This is a good point. But the difficulty is that if the wrong choices are made, the death toll could be up to 10 times higher.

Edit at 16:30 on 21 September

Altered text to add a second way of estimating false positives.