Do COVID Vaccines Work? (part 4)

In this article I utilise data from an unknown NHS Trust and use split-file staged multivariate logistic regression in the prediction of vaccination status prior to death

In part 3 of this series we ended up considering split-file logistic regression models for the prediction of vaccination status prior to death using a fairly simple list of ingredients pulled from my pantry. The vaccines didn’t exactly come up smelling of roses and, in fact, came up smelling of something else.

That being said we saw a weeny drop of evidence that tentatively suggested benefit in terms of reduced incidence of COVID-19, with the odds ratio for a COVID diagnosis dropping from OR=0.428 (p<0.001) for the period 2021/w1 – 2021/w18 to OR=0.368 (p<0.001) for the period 2021/w19 – 2021/w37 in the prediction of folk who were vaccinated prior to death. The question here is whether this is indicating a genuine benefit arising from the boosters or whether those who were seriously sick with heart trouble, cancer etc but were testing positive for COVID (whether false positive or true positive) were refusing the jab or simply too sick to be vaccinated.

This is an important issue and I am going to suggest we can solve the problem by considering incidence of COVID in relation to respiratory illness. The logic is straightforward: COVID is held to be a respiratory illness first and foremost, so if the vaccines are working as claimed then we should see not just a reduction in incidence of COVID but a reduction in incidence of concomitant respiratory diagnoses whether acute or not, but especially if acute.

In short we can run the model of part 3 again but with a few tweaks. My raw ingredients now look nice and compact like this…

Staged Logistic Regression

We covered the ‘split-file’ bit in part 3 but what does the ‘staged’ bit mean? Well, it means that I am going to fit the logistic model to the data in two stages. In the first stage I am going to consider basic demographics in more depth by submitting the following four independent variables (bold) and their possible interactions using a conditional (forward selection) model building strategy:

• Age

• Sex

• Total diagnoses

• Case detection rate

• Age * Sex

• Age * Total diagnoses

• Age * Case detection rate

• Sex * Total diagnoses

• Sex * Case detection rate

• Total diagnoses * Case detection rate

• Age * Sex * Total diagnoses

• Age * Sex * Case detection rate

• Age * Total diagnoses * Case detection rate

• Sex * Total diagnoses * Case detection rate

• Age * Sex * Total diagnoses * Case detection rate

In the second stage I’m going to enter (force) the following two independent variables and their interaction:

• COVID-19 diagnosis

• Any respiratory diagnosis

• COVID-19 diagnosis * Any respiratory diagnosis

To maximise statistical power and to give the vaccine the best chance of showing genuine benefit (by maximising bias) I shall start out by running the model on the entire data sample of 8,714 deaths for the period 2021/w1 – 2021/w37. Herewith the classification table that reveals a well-performing model exhibiting a true positive rate of 86.9% for vaccinated individuals and true negative rate of 55.5% for unvaccinated individuals:

This should give us confidence that the model is doing its thing reasonably well, with an overall classification performance of 73.7% of vaccination status at death correctly classified. There are those among us who like to consider ROC curves for classificatory performance  (Receiver Operating Characteristic), so the following is for them:

‘Normal’ people can decipher this by considering the green diagonal line - a classification result that hugs this is doing no better than tossing a coin. We can see the model results (red curve) bloom up and to the left like a big red banana. This tells us the predictive model is doing far better than tossing a coin, thank you very much, with an area measured at 0.771 (p<0.001); that is to say, the model gives us a 77.1% chance of correctly nailing vaccinating status at death. With that I guess we better look at the model to see what it says about COVID diagnosis and respiratory illness. Grab your tin hat, ‘coz you’re gonner need it!

BOOM!

I may well have just blown any notion of genuine vaccine benefit out of the water:

Here is a decent-fitting staged multivariate logistic model for a sample of 8,714 in-hospital deaths that identifies vaccination status with 77.1% correct classification that tells us something very important indeed. It tells us that the interactive term COVID-19 diagnosis by Any respiratory diagnosis is statistically insignificant by a long way (p=0.303). In plain English, the vaccines have not reduced incidence of COVID death associated with respiratory conditions. If they had done so then this interactive term would pop up as statistically significant.

All that has happened is that the likelihood of a positive test result is lowered for those who were jabbed prior to death. I suggest that this may arise through patient choice and/or because protocol dictates vaccinated in-patients are tested less aggressively and/or because protocol dictates that the sickest patients should not be exposed to the vaccine. There may be other reasons, but what is abundantly clear to me right now is that we’re looking at the biggest cover-up in the history of medicine.

You can see to the heart of the issue for yourself by considering the independent variable COVID-19 diagnosis (OR=0.284, p<0.001) together with the critical interactive term (OR=0.857, p=0.303). The former gives the impression that the vaccines have reduced incidence of a COVID diagnosis, but the latter reveals this has nothing to do with respiratory illness.

Belt And Braces

Now that a bomb has exploded I better detonate an unexploded bomb and run a split-file staged multivariate logistic regression to double check. If we’re on to the truth in a big way then the COVID-19 diagnosis by Any respiratory diagnosis interaction term should fetch up as statistically insignificant within each of the two study periods I’ve been playing with. This is exactly what we find:

Even in the heat of the third wave and truck loads of COVID death the key interactive term manages p=0.096 at best, this falling short of the ubiquitous 95% level of confidence. The interactive term seriously falls away in the period of secondary dosing and boosters, managing a rather grim p=0.791 at a time when you’d think vaccine benefit for COVID as a respiratory disease was at an all time high. Not so!

Onward And Upward

It will be interesting to see what happens if I develop the model further by adding more ingredients from the pantry like underlying cardiac and chronic respiratory conditions and frying up a time-dependent indicator to avoid all this split-file jiggery-pokery

Kettle On!