Estimating Daily People Tested (part 7)

Estimation of the number of people undergoing virus tests in England prior to de-duplication of data records (rev 1.1)

Belt & Braces

If you are going to accuse Her Majesty’s Government of not being able to count it’s always best to confirm that your own counting is on the mark. I shall thus pull down the pillar 1 and pillar counts of unique people tested each week from the England Test & Trace crew, add them together and stick the total on a plot along with values of uniquePeopleTestedBySpecimenDateRollingSum corresponding to the test and trace week ending date and values of the variable I have concocted through modelling. Herewith the results of getting my crayons out:

We observe a pleasing correspondence right up to the moment when testing hell broke out (self-inflicted nose poking at home, work, rest and play) with the introduction of lateral flow devices and home kits. After this point the UK GOV coronavirus dashboard team reckon on less unique people being tested on a rolling weekly basis compared to the weekly counts arising from the Test & Trace crew. Obviously the numbers are not going to precisely match owing to the different counting systems but we’d expect much better agreement than this! My own concoction (green line) is tracking the test & trace weekly totals for pillar 1 and 2 quite nicely given that this count was estimated from the number of tests and positive cases detected. I shall thus break into the Bourbons and cogitate on where we go from here.

Bourbon Thoughts

It is quite clear that HMG are underestimating the number of people tested across pillar 1 and 2 schemes and so they’ll be overestimating case positivity rate. Somehow they’ve got rid of a large number of people and even larger number of negative test results. However the thorn remains in our side in that no matter how well I can model people tested it still is only unique people tested and not total people tested i.e. repeat test results across England have been ignored in case positivity calculations thus making the pandemic look worse than it really is. How can we circumvent this dastardly sleight of hand?

The Answer Is Not To Try

After sufficient Bourbons we come to a place of enlightenment whereby we realise that the answer is not to try and estimate all the missing negative test results. We have data for the total number of viral tests across pillars 1 and 2 in our left hand and we have less nefarious counts of unique people tested in our right hand. If we clap we will not hear the sound of one hand clapping but we will derive a time series for the number of tests per person. BONG!

And there it is! At only one dodgy point does the series dip below the value of 1.00 (by definition a tested person must have had at least one test) but I shall put this down to admin issues and data processing lags. We can see that the Test & Trace crew got off to a flying start before things settled down to a smidgen of just over one test per person every 7 days until Mar 2021 when they went nose-poking crazy. The average turns out to be 1.3 pokes per person every 7-days for those persons registered in the Test & Trace system. Please bear this definition in mind because that isn’t 1.3 pokes per person on a nationwide basis!

Why Am I Excited About A Boring Graph?

Because that graph turns out to be a golden key that opens the door on the problem we thought was intractable. Virus tests per person can be used as a proxy that accounts for all those eradicated negative test results!

We can use the reciprocal of virus tests per person as a factor to adjust estimates of case positivity (a.k.a. detection rate, a.k.a. disease prevalence) that have otherwise have been inflated. I shall call this a Bourbon moment and I shall use the term ‘bias’ to mean inflated (a.k.a. fudged).

Biased and Unbiased Detection Rate

So here it is. Here is the reason why I’ve been spending all this time fiddling with estimation of people tested. In these two graphs I’ve plotted out the detection rate (positive test results per 100 people tested) for that is what it really is, though officials like to pretend this is a plot of case rate (a.k.a. positivity). The first graph reveals the pandemic in full glory and the second graph picks up from Jun 2020, thus avoiding the initial spike that was based on a handful of pre-hospitalised cases.

Back in the good old days of 2020 we observe excellent correspondence between the red and blue curves though we can see that the 2020/21 winter peak was over-egged as a result of an increase in repeat testing. Things really went astray from Jun 2021 onward as a result of the LFD nose poking frenzy that went unaccounted for in official statistics, and the thin red line is my best estimate of what was really happening on the ground as opposed to what the authorities were claiming (thick blue line). It is a sobering thought that capable crunchers working for HMG must realise the situation full well.