Chicken Or Egg?

Assessing the influence of mass viral testing programmes on case positivity: are we experiencing a testdemic? (rev 1.0)

This morning my first thoughts upon waking were, “shall I try vector autoregression (VAR) or vector error correction modelling (VECM)?” Yes, really.

Whenever I start to tread down the path of ever more sophisticated statistical techniques like this I stop and go back to the beginning. We have positive test results we inappropriately call ‘cases’ and we have viral tests (PCR/LFD) that are chest-deep in controversy.

The Game

We all know the game. Asymptomatic folk will stick a swab up their nose repeatedly until they get a positive result; somehow this makes them feel better. This sounds acceptable until you realise the jargon is disguising some seriously disturbing behaviour; that is, somebody who is completely and utterly healthy is checking to see whether they are carrying a virus that isn’t making them ill, and they won’t rest until a test that can churn out false positive results (and uses primers that are not novel or unique to SARS-COV-2) tells them they they just might be carrying some form of virus (assumed from a match in a modest base sequence) that may or may not be active and may or may not be capable of infecting anybody else. In the old days we’d call this psychotic, today it’s been re-branded as ‘saving’ granny and granddad, who were shipped out to care homes to inexplicably die of non-COVID causes in their thousand.

Looping The Friggin’ Loop

Any analyst tugging on their beard will realise all this can lead to a volatile situation in which positive feedback becomes a driver: more tests means more cases which means more nose poking. The only way out of this loop is if the test was incapable of generating false positive results. It ain’t, so there’s no escape until we realise we’ve gone crackers. In effect we’re trying to eradicate nature (and not doing terribly well). It was this loop idea that got me racing to my workstation at 6am because I realised I hadn’t done something very obvious: I hadn’t checked to see how testing and test result played against each other over time. This called for that most fabulous of fabulous signal processing tools known as cross-correlation.

Which Came First, The Chicken Or The Egg?

You can’t beat a good Koan to get the blood flowing, so let us re-phrase this chestnut and ask whether the PCR test or the PCR test result (a.k.a. ‘case’) came first. In the beginning in the UK a few very sick people in hospital showed symptoms commensurate with the WHO’s notion of COVID-19 (a notion which changed over time) and PCR tests confirmed that certain primers were triggered by sequences also found within these patients. In the beginning we at least had a notion of causality even though this was effectively based on circumstantial evidence¹. Once mass testing of anybody and everybody was wheeled out and folk started talking about asymptomatic cases (an oxymoron if ever I heard one) then we moved deep into chicken and egg territory.

Using Cross Correlation To Solve Koans

When it comes to detecting and reporting ‘confirmed cases’ the PCR test is where it’s at, so I’ve taken the rolling 7-day count of PCR tests by specimen date for England over the period 16 Sep 2020 - 7 Jun 2022 and run this through a cross correlation procedure along with the rolling 7-day count of new cases detected/confirmed using PCR (i.e. the sum of this series and this series). Here’s what we get:

Before we get stuck in there are a couple of points to note. Firstly, the small print mumbles on about first order differential which is a fancy way of saying I’ve analysed the day-on-day variations in rolling case counts and tests. This is important because it removes artefactual correlation introduced by things changing slowly over time - an analytical trap that I may well cover in a future newsletter. Secondly, if the situation we face was a pure testdemic we’d see a narrow block of positive correlations hanging around the zero lag and nothing much else; that is to say a test instantaneously becomes a ‘case’.

So what do we see?

Well, we observe a sizeable hump of positive correlations centred on a lag of -4 days and an island of positive correlations clustered around a lag of +14 days. This is most curious. In plain English this first result means a change in PCR-detected case numbers will appear just a few days before a change in PCR test activity, thus if cases go up tests will go up 1 - 10 days later, and if cases go down then tests will go down 1 - 10 days later. This could be explained by a national test programme that is responding to the situation on the ground, though I’m finding it hard to imagine the response could be this rapid! Then we’d need to explain why the programme would entertain such a decline. My money is on oscillation of an unstable system prone to positive feedback, which is a long-winded way of declaring a testdemic.

The second result means a change in PCR-detected case numbers will appear a few days after a change in PCR test activity, thus if tests go up cases will go up 11 - 18 days later, and if tests go down then cases will go down 11 - 18 days later. Although this is indicative of a testdemic the situation may also arise if the national testing programme is accurately anticipating a rise in cases. Is this possible or are we looking at yet more oscillation in an unstable system? Besides which that lag figure of +14 bothers me because it smells of administrative delays.

Flapjack Brings Clarity

Whilst munching on flapjack I decided that the best evidence against a testdemic would be a cross correlation plot full of insignificant coefficients; that is to say variations within the differential time series for rolling 7-day PCR tests and variations within the differential time series for rolling 7-day cases detected through PCR would be randomly placed in time in relation to each other (i.e. stochastic). It is clear that this is far from the case and the two series are intimately tied to each other in a manner we would not expect. Something very deterministic is going on whatever that something is.

Going For A Deterministic Walk

We can see this structure in the following scatterplot of rolling 7-day cases against rolling 7-day PCR tests that I’ve colour coded according to pandemic phase (see the Bakewell tart method in this newsletter to get a grip on how I’ve sliced the time series):

This colourful chart reveals the excursions both data series make as they skip along hand-in-hand, it being blindingly obvious that there is a great deal of hugging. Much of this structure comes from using rolling 7-day sums which smooth the noise of daily counts, but this smoothing permits us to see a dynamic that would otherwise be hidden within scatter.

Testdemic Duality

As your eye traces these loops it is tracing the passage of time. If tests are rising in number but cases are not then this may be taken as evidence against the testdemic hypothesis, this being indicative of a situation when infection is minimal and the tests are picking up nothing. If cases are rising rapidly but tests are not then this may also be taken as evidence against the hypothesis, this being indicative of a situation where infection is genuinely spreading throughout the population. In between these two extremes - characterised by horizontal and vertical patterns respectively - we find the angular evidence favouring a testdemic. There’s quite a lot of this. In fact I would go as far as to say the general situation favours a testdemic punctuated by periods of what appear to be genuine situations.

Where next?

This analysis has caused me to wind the window down and hang a right. It’s obvious that we can’t treat the data as homogeneous over time, and we have to face a situation where a testdemic - or at least the potential for a testdemic - is flipping in and out of play. I’ll be running a similar analysis to see how lateral flow devices fare in comparison and thinking of ways in which we may characterise the response of the test regime to the situation. A squizz at scatterplots of daily and weekly counts might also be handy, and then there’s deriving rates such as cases per 1,000 tests for PCR and LFD separately. After this I might unleash some of those fancy techniques I mentioned at the outset, but for now it’s…

Kettle On!

1. Fire fighters are always to be found at the scene of a fire.