# Testing, testing, 1 2....What do Lateral Flow Tests Really Tell us?

Here in England, everyone can now be given two lateral flow tests a week to test if they have COVID-19, in an extension of the government’s testing programme. Lateral flow tests (LFTs) are rapid tests and are convenient as they can give a result in around 30 minutes and don’t require a laboratory. They use a swab of the nose and/ or throat and the testing kit itself is a small plastic device, similar to a pregnancy test. They are intended for picking up additional infected individuals who may otherwise have been missed because they don’t have any symptoms. LFTs have been used in schools since they reopened and have caused quite a bit of controversy as it is known that LFTs are not as accurate as polymerase chain rection (PCR) tests. PCR is the most accurate test for COVID-19 infection and if a symptomatic person has a positive PCR test, this is likely to accurately indicate infection. For the purposes of the remainder of this article we shall assume that a positive PCR test corresponds to a true positive and a negative PCR corresponds to a true negative.

On 15^{th} April, this BBC report stated that 82% of positive rapid tests ‘were correct’. So, is this suspicion surrounding LFTs founded? Some of the terminology surrounding testing can be a bit tricky to understand, so let’s look at it in more detail. Let’s consider a 2x2 contingency table which looks at positive and negative LFTs and PCR tests for a given sample and determines the status of the outcome of the LFTs:

You may have heard the terms sensitivity and specificity; but what do they mean? Sensitivity is the probability that someone who has COVID-19 gets a positive LFT result, which would be the number of true LFT positives divided by the total in the positive PCR column. Specificity is the probability that someone who is not infected with COVID-19 gets a negative LFT result, so the number of true LFT negatives divided by the total in the negative PCR column.

Neither sensitivity nor specificity, however, answer the two main questions that we may ask of LFTs:

- If my LFT is positive, what’s the chance that I actually do have COVID-19?
- If my LFT is negative, what’s the chance that I really don’t have COVID-19?

The BBC article tells us that from 8^{th} March to 4^{th} April, 26,144,449 LFT results were recorded by Public Health England and 30,904 of these recorded a positive test result. Just over half of these positive LFTs were sent off to the laboratory for a follow-up PCR test and of these, 18% came back negative with the other 82% coming back positive. This means that 82% of the tested positive LFTs were true positives and 18% were false positives resulting in needless self-isolation.

Positive predictive value (PPV) and negative predictive value (NPV) are the two quantities that answer our two questions above. PPV is the probability that a positive LFT is a true positive and is calculated by dividing the number of true LFT positives by the total in the positive LFT row. NPV tells us the probability of a negative test being a true negative and is the number of true LFT negatives divided by the total in the negative LFT row.

PPV and NPV are important in determining the performance of LFTs, but a complication of these is that they are affected by the underlying virus prevalence in the population. Let’s assume that we have a test that has 90% sensitivity and 80% specificity, and we decide to test 1,000 people.

If the underlying prevalence is 70%, we would get the following continency table:

This gives a PPV of 630/690 = 91.30% and NPV of 240/310 = 77.42%. But if the underlying prevalence is just 10%, we would get the following continency table:

This gives a PPV of 90/270 = 33.33% and NPV of 720/730 = 98.63%. So, we can see that when the prevalence is higher, we get better PPVs, but lower NPVs and when we have a lower prevalence, the PPV reduces, but the NPV increases. What this means is that when prevalence is high, if you receive a positive test result, the chances are that you truly are positive, but if you receive a negative test result, then there’s a pretty good chance that it could be a false negative. If prevalence is low, a positive test result is quite likely to be a false positive, but a negative test result is likely to mean that you truly are negative.

What does all this mean for the data presented in the BBC article? Well, the main take home point is that the 82% figure presented is based on the COVID-19 prevalence observed in March. If there is one thing that we’ve learned about COVID-19 over the last year, it’s that the prevalence in the UK fluctuates widely with numerous waves and periods of lockdown, so that 82% figure is likely to already be out of date and the PPV of LFTs may now be smaller that 82% in line with a reduction of COVID-19 prevalence.

I‘m slightly confused as to why there is so much focus on the PPV of LFTs and no discussion of the NPV of the tests. I understand that if a person tests positive for COVID-19 when they don’t actually have the virus, this means they will have to needlessly self-isolate meaning disruption and possibly days missed at work and school. When the government first introduced mass testing in schools, they said that positive LFTs didn’t need confirmatory PCR and pupils needed to continue to self-isolate following a positive LFT even if a follow-up PCR test came back negative. But now, if an LFT comes back as positive, a PCR test is carried out to confirm the diagnosis. So, whilst a false positive LFT would result in needless self-isolation, this should only be for a couple of days whilst the results of the PCR test are confirmed. Annoying? Yes. But, hugely damaging? I’m not so sure.

But why is nobody asking what the implications are of a negative LFT? If the intended use of LFTs is to control the spread of COVID-19, it is surely imperative to know what is the probability that a person is truly negative if they receive a negative LFT result. This data could have easily been collected using the LFTs carried out in schools. A random sample of the negative test results could have been tested using PCR to estimate the NPV of the tests. With mass testing now expanded to the entire population I know that if I get a positive test result, I will need to self-isolate until I receive the results of a confirmatory PCR test. But if I get a negative test result, I have no idea what this means in terms of my true COVID-19 negative status. Not exactly what I would call useful!