Do COVID Vaccines Work? (part 11)

I utilise data from an unknown NHS Trust in the further development of a staged multivariate logistic regression model in the assessment of vaccine efficacy

In part 10 of this lengthy series I revealed my daring next move:

My next move is to throw away the rather ambiguous meringue of dependent variable (COVID Dx) and replace it with Symptomatic COVID, then revise the model structure accordingly. To pull in the largest sample possible my definition of symptomatic COVID will simply be any in-patient who received both a positive test result and any respiratory diagnosis prior to death.

Get something under the grill and get something boiling on the stove ‘coz we’re about to launch Stingray…

Holed Below The Waterline

Well that was a semi-damp squib! The sample simply wasn’t big enough to cope with all of my desired filters so I had to abandon notions of dosing models and stick with any last dose for those aged 18 years and over for the period 2021 w10 – w37 who had received a final jab of some sort at least 14 days before death.

Symptomatic COVID

The classification table tells a sorry story of only 224 symptomatic COVID deaths in the sample of 5,366 in-hospital deaths (4.2%). Perhaps this is a lesson in its own right – despite what the talking heads were telling us, genuinely severe COVID cases were few and far between over the period 2021 w10 – w36.

The table of model coefficients should thus be taken with two pinches of salt but the model did yield a bizarre interaction that indicates age-related vaccine benefit: Age by Vaccinated (OR = 0.99, p<0.001). This result is probably best depicted graphically so what I’ve done is take the mean value for total diagnoses (3.26) and the mean value for case detection rate (1.46%) and bung them into a spreadsheet that turns the model into a pair of easy to understand lines. Here is the result:

I find this totally and utterly wacky baccy. Forget vaccine status for the moment - how is it possible that risk of symptomatic death decreases with age? The word is wergh - time for some cogitation!

When cogitating on complex logistic regression output I always find it best to go right back to the raw data and do something utterly simple like crosstabulating the basic data. Here’s such a crosstabulation of binned age group by symptomatic COVID. If the bin values look a little odd that’s because these cutpoints arise from an automated procedure that provides four equal-sized groups or as near dammit:

A Pearson Chi-squared test of association is telling me something is deffo going on here (p<0.001) and we can clearly see the percentage of symptomatic COVID drop from 6.5% for the under 72y group down to 3.3% for the 89+y group. The model didn’t lie to us and has unearthed a rather strange fact that symptomatic COVID (i.e. a positive test result with an accompanying respiratory diagnosis) is more likely in younger folk in this sample of 5,366 in-hospital deaths. This is a peculiar turnaround for a disease that notoriously attacked the elderly so are we looking at evidence of vaccine harm? And just exactly what was it that attacked the elderly – a diabolical virus or diabolical management protocols?

Something isn’t adding up in a most basic way here and because it’s not adding up we can’t really go pointing at the blue line and claiming the vaccine benefit we see is real. My guess is that the apparent benefit is a function of whatever it is that is reversing the age profile of the disease. Are we looking at survivorship bias? If so, are we looking at natural immunity from earlier infections and calling it vaccine-induced benefit?

Now that is a can of worms and a half! Not only have we no idea how healthcare professionals went about testing inpatients (I’m pretty sure this wouldn’t be random nor equal across patient sub-groups) but we also have no idea of levels of natural immunity. Ouch. On the other hand if that blue line does indeed represent a genuine benefit then vaccination, at best, appears to shave 2% - 3% off the risk of symptomatic COVID, but this claim ignores the rather awkward finding that the risk is higher for younger people.

Asymptomatic COVID

I’ve included the results for asymptomatic COVID even though the sample size is far too small for this sort of statistical work (82 cases) and the model utterly inadequate in doing anything but assuming nobody suffered from this condition (whatever asymptomatic COVID means in the real world apart from indicating a likely false positive test result). Given the nonsensical position we might just note two odds ratios slightly above unity for Age by Vaccinated (OR = 1.05, p=0.003) and Age by Diagnoses by Vaccinated (OR = 1.00, p=0.042), with the latter being a subgroup of the former. These indicate increasing risk of asymptomatic COVID with age and vaccination and although this result makes more sense (and points to potential vaccine harm) we can’t read too much into it.

A disappointing brace of results, methinks, but then again the sample size is lacking. I shall wrap things up for today and have a think how best to proceed given the ambiguity inherent in COVID designation prior to death.

Kettle On!