Baking Better With Cochrane-Orcutt (part 5)

Assessing the influence of mass viral testing programmes on case positivity: are we experiencing a testdemic? (rev 1.1)

I am hoping that subscribers have picked up on the key take home message in these last few newsletters, this being that the time series for daily counts of new COVID cases by specimen date across England possesses strong serial correlation (autocorrelation) with a periodicity of 7 days that can only arise if we are living through a testdemic. Ergo we should be able to successfully predict case counts from test activity using Cochrane-Orcutt Estimation, and this shall be the subject of this newsletter.

Keeping It Simple

To keep things totally and utterly simple I am going to use just one dependent variable (newCasesBySpecimenDate) and just one independent variable (newVirusTestsBySpecimenDate), and I’ll select the time period of w/b 14 Mar 2020 – 7 Jun 2022 to ensure full coverage from the week when daily cases first exceeded the 1,000 mark.

The Reckoning

It took the Cochrane-Orcutt Estimation procedure three iterations to settle on a serial correlation coefficient of ρ = 0.971 (S.E. = 0.008). This reveals what we already know and that is there is a tremendous amount of serial correlation within the series for new cases by specimen date. The good news is that when this correlation is accounted for the Durbin-Watson statistic rises to 1.646, which places it within the 1.5 - 2.5 range that is considered acceptable for a decent model.

So what of the model itself? Well, new virus tests by specimen date figured as a highly statistically significant predictor of new cases by specimen date (p<0.001) and turned out a remarkable series for prediction of daily new cases. Take a look for yourself: