Baking Even Better With ARIMA (part 3)
Assessing the influence of mass viral testing programmes on case positivity: are we experiencing a testdemic? (rev 1.1)
In part 1 of this series I conjured an ARIMA model for the prediction of new first episodes by specimen date and out popped unique people tested and LFD tests as highly statistically significant predictors of new first episodes (p<0.001 in each case). Whilst statistical significance gets the ball rolling it doesn’t tell us much about effect size; that is to say, the strength of the relationship between test activity and new first episodes. Subsequently, the coefficient of determination (a.k.a. R-square) was derived yielding R-square = 0.521, which means that variation in unique people tested and LFD test activity accounts for 52.1% of the variation we see in new first episodes for the study period of 30 Aug 2020 - 7 Jun 2022. This was taken as strong evidence of a ‘testdemic’ where around half of new first episodes being detected are being generated by the test regime itself.
A subscriber wished to know if vaccination rollout was also generating the testdemic (though we’d need to call it a vaxdemic!). This is not an easy analysis to make given the complexity of the situation, nevertheless, I decided to take a peak using a very simple four stage modelling procedure:
The study period was reduced to 29 Nov 2020 - 7 Jun 2022 to ensure I was looking at the very beginning of vaccination.
The dependent variable was set to daily new first episodes for which a null (baseline) ARIMA (2,1,2)(1,1,1) model was derived.
The independent variables of counts of LFD tests and unique people tested were added to the model to establish the basic ‘testdemic’ model (see part 1).
Daily time series for dose 1, dose 2 and third injection/booster were evaluated as potential additional predictor variables.
Hot From The Oven!
The time series for dose 2, the third injection/booster and total doses1 delivered daily were all found to be statistically significant predictors for new first episodes, with the time series for third injection/booster producing the best overall model fit. Herewith the ARIMA model parameters for dose 3 for all those feeling their inner geek this misty morning: