Cambridge Covid-19 test results don’t imply PCR tests are inaccurate

In the past few days, claims about Covid-19 testing at the University of Cambridge have been spreading on Twitter and Facebook, specifically relating to the number of “false positive” results. 

These claims need some context. It is not unexpected for the ratio of false positives (tests that incorrectly return a positive result) to true positives (tests that correctly return a positive result) to increase as the number of infections in the community decreases. The fact this may be happening does not show that the tests are especially inaccurate.

Cambridge’s data testing

Since the beginning of the academic year, Cambridge University has been offering all its students in university accommodation weekly tests for Covid-19, regardless of if they have any symptoms of the disease. 

The type of testing offered is called sample pooling and happens in two stages.

Firstly, different people’s samples (usually those in the same house) are collected and tested together.

Then, if the group tests positive, all the individuals are tested again separately to determine which people have the virus. 

But, if the group as a whole tests negative, there is no need to test each group member individually. 

All tests in this case are PCR tests which have been the main type of test used by the UK authorities, as opposed to rapid lateral flow tests, which have been introduced over the past few months. 

Sample pooling is efficient when viral prevalence in the community is low because, while some people do need to be tested twice, the total number of tests run is far lower than if everyone was tested individually in the first place. It is not currently used for standard testing of symptomatic people.

The University says that typically, if an individual test is needed following a positive result on the group test, it will happen the day after the group test. 

What the results show

In the latest week, around 9,400 students were successfully tested in 1,937 testing pools. 

Ten of those pools tested positive, but when the individuals in those pools were re-tested, none tested positive. (One post misinterprets the results suggesting all 9,400 students received false positives, which is wrong). 

This is quite a departure from the norm. Over the course of the nine week programme so far, out of almost 17,000 pools tested, 252 pools have tested positive. Of those 204 were confirmed positive with subsequent individual testing, while 44 subsequently tested negative (these were apparent “false positives” being referred to) and four were still awaiting individual results. 

In total, across the nine weeks, 0.3% of pool tests conducted have produced a positive result that was then followed by negative results in individual follow-up tests. 1.2% produced positive results that were confirmed in follow-up tests. 

It’s worth noting that we can’t say for sure that all the individuals in that 0.3% received a “false positive” result (at least, in the term’s common usage). It’s possible that some may genuinely have had detectable levels of virus when doing the group test, but then had lower, non-detectable levels when retested individually, which happened at least a day later.

However, it isn’t particularly surprising that the ratio of true positives to false positives has increased, as the virus’s prevalence in the community has decreased. 

As Professor of Respiratory Science at the University of Cambridge Stefan Marciniak puts it: “If you stamp out all true positives, it’s blindingly obvious that only false positives remain.”

Are tests accurate?

The fact that in one week 100% of group positive tests were actually found to be negative does not mean that tests are especially inaccurate. As we’ve written before, no test is 100% accurate. 

And as Professor Marciniak says, when there aren’t many infections in the population you’re testing, you would expect more of the positive results to be false. 

Perhaps an analogy helps explain the situation. Imagine a speed camera which fines a driver if they are caught going over 30 miles per hour and has a 99% accuracy rate. 

In the first month after installation 1,000 people drive past the camera while going above 30 miles per hour, and 1,000 drive past going under 30. 

The 99% accurate camera fines 99% (990) of the speeders, incorrectly letting 1% (10) off, and it correctly lets 99% (990) of the law-abiding drivers go, but incorrectly fines 1% (10).

In total, 1,980 people get the right decision, and 20 get the wrong decision. The camera is 99% accurate. 

The next month, after word has spread about the new camera installation, only 100 people drive past the camera going above 30 and 1,900 drive past going under 30. 

The camera fines 99% of the speeders (99 people), incorrectly letting 1% (1 person) off, and it correctly lets 99% (1,881) law-abiding drivers go but incorrectly fines 1% of them (19 people).

In total, 1,980 people get the right decision (the 1,881 careful drivers who aren’t fined and the 99 speeders who are) and 20 get the wrong decision (19 careful drivers who were fined and one speeder who was let off).

The camera is still 99% accurate, as it was in the first month of use, but the ratio of people who were fined correctly to those who were fined incorrectly has changed from 99:1 to almost 10:1.

It’s the same principle with PCR tests.You would expect the ratio of false positives to true positives to increase as the level of viral transmission in the community decreases, but this doesn’t undermine the overall accuracy of the tests.

That’s not to say that false positives are not an issue at all, and it is important to note that some people may have suffered detriment (by the requirement to self-isolate following a positive test) after having received a false positive.   

It is also important to note that while PCR tests indicate presence of the virus in someone’s body, they are not a medical diagnosis for the Covid-19 illness.

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