Do COVID Vaccines Work? (part 8)

I utilise data from an unknown NHS Trust to forge multivariate logistic regression models in the development of a more reliable indicator for COVID status

In part 7 of this series we came to a rather frustrating conclusion that the COVID status flag in the EPR of deceased inpatients (COVID Dx) wasn’t as reliable as it should be. We can see this clearly in the simple crosstabulation below of incidence of respiratory conditions (both acute and chronic) against mention of COVID in the EPR of deceased inpatients aged 18 years and older for the period 2021/w1 – 2021/w37:

Out of a total of 1,437 ‘COVID deaths’ we find 524 (36.5%) without mention of any form of respiratory diagnosis, which puts us on rather shaky ground if we are using COVID Dx to mean genuine respiratory COVID-19 and not some false positive result or, perhaps, a true positive result of a previous infection from which the deceased had recovered prior to death. Historic infection is not what we want when assessing outcomes in relation to vaccination.

We have been sold the idea of COVID-19 as a respiratory disease arising from not just a coronavirus but a coronavirus capable of inducing SARS (Severe Acute Respiratory Syndrome), and a novel coronavirus at that (SARS-COV-2), which then goes on to mutate into several acknowledged variants. It should be respiratory symptoms all the way down, but not only is this not the case (hence the rise of the rather dubious term ‘asymptomatic’), but other features have come to the fore. I’ve lost count of symptoms allegedly associated with COVID-19 and stopped counting at hair loss. A GP I know is cheekily blaming his haemorrhoids on COVID (see what I did there?).

So what should we consider as indicative of a genuine, non-historic SARS-COV-2 infection that impacted on the health of those 1,437 deceased? A darn good question, but the answer requires a painstaking amount of work since several thousand medical diagnoses need to be boiled down into relatively few major headings. The ICD-10 disease classification system has helped greatly in this but I went a step further and used factor analysis to boil diagnoses down into the following headings of interest:

Hopefully these are self-explanatory otherwise I’ll need to roll out several comprehensive lists of ICD-10 codes so you can see what was precisely included in each category. The column headed ‘Mean’ is rather useful in that it provides the incidence of each category within the sample of 8,714 in-hospital deaths. Thus, for instance, 30.6% of deaths carried at least one cancer diagnosis, with 25.8% of deaths carrying at least one chronic respiratory diagnosis. Please note that these are not necessarily the cause of death and are merely mentions within the diagnostic field array of the EPR. I am sure there will be a few readers surprised at how low COVID appears in the fateful scheme of things given the unprecedented attention it was given.

Down ‘n’ Dirty

I am going to be a lazy so-and-so and use logistic regression to tell me which of these categories are linked to COVID-19 by setting COVID Dx as the dependent variable and submitting everything else in a conditional (forward) selection procedure. Here’s what transpired when I did this:

Isn’t that utterly fascinating? Every darn category apart from blood/clotting disorders (p=0.615) and inflammatory conditions (p=0.063) appears to be linked to the incidence of a positive test result in some way. There are three categories with odds ratios greater than unity, being Acute Respiratory (OR=9.33, p<0.001), Immunocompromised / diabetic (OR=1.22, p=0.012) and hypertension (OR=1.26, p=0.006). We can safely assume acute respiratory is the real severe deal and both the immunocompromised and diabetic are widely acknowledged to be at risk from severe infection, so it is comforting to see this story drop out of the model. Hypertension (essential primary hypertension) is the slippery customer I’ve been recently chasing, and this appears to arise only in conjunction with vaccination.

Crazy Cancer

Now that’s the good news, since all is sensible. What is not so sensible, and deserving of a WTAF (what the actual flapjack) moment, are the remaining eight categories with statistically significant odds ratios less than unity. If we suppose, for example, that incidence of cancer has absolutely nothing to do with incidence of a positive test result then the term Cancer Dx(1) would be sitting in the bottom table of variables not in the equation with a p-value of p>0.05. But it isn’t; it is sitting fair and square in the top table as a significant negative predictor of a COVID diagnosis. WTAF? Quite!

Not only that but an odds ratio of OR=0.27 also means inpatients with a cancer diagnosis were 3.7x less likely to receive a positive test result prior to death. How is that possible? Does it mean they were 3.7x less likely to be given a PCR test given their condition? Did cancer inpatients tend to refuse testing? Were nursing staff reluctant to undertake a test? Many questions arise but this issue it isn’t limited to just cancer - how come the likelihood of a positive test result is mysteriously lowered for eight broad diagnostic categories?

This smacks of systematic bias in the selection of cases for testing. Either that or something wacko is going on with suppression of positive test results for certain conditions and their treatment – I shall need to do some more digging! Just to check I wasn’t hallucinating following a tray of under-cooked sausage rolls I decided to thrash out a simple crosstabulation of cancer diagnosis against positive test result. Try this for size:

We now see that 169/2,669 (6.3%) of cancer inpatients received positive test results compared to 1,268/6,045 (21.0%) of non-cancerous inpatients, with the crude odds ratio fetching-up at 0.30. If you didn’t follow my earlier rambling I am hoping this little table has done the trick in alerting our brains to some wacko results.

This ain’t right folks, but I am hoping there is a simple explanation that I have overlooked. Right now my money is (tentatively) on nursing staff not wishing to stress cancer cases prior to death. This is as it should be, but it means that any analysis will be loaded to the gills with bias.

The Devils’ Avocado

At this point it is worth playing the Devil’s avocado and asking why we see an odds ratio greater than unity for acute respiratory cases but an odds ratio less than unity for chronic respiratory cases prior to death. If nurses were reluctant to administer tests to those dying with chronic respiratory disease surely they’d be equally reluctant to administer tests to those dying with acute respiratory disease, if not more so! And why bother to test diabetics near death but not those with major CNS morbidity?

Very little is making sense here other than acute respiratory, immunocompromised, diabetic and hypertensive conditions being positively linked to positive test results and indicative of a current infection. Why would anything else be negatively linked? Are we looking at a barrage of false negative test results? If so then why for certain conditions and not all?

To try and get a handle on this for cancer I ran one of those kitchen sink 3-way factorial models for the prediction of COVID diagnoses. Here’s the nitty-gritty:

Ignore everything and just look at the three terms that involve Cancer Dx(1). Right at the top you’ll see an odds ratio of OR=0.10, p<0.001 for the main effect. This is telling us that cancer cases, overall, are 10x less likely to receive a positive test result compared to non-cancerous cases. This basic result is modified by the interactive term Cancer Dx(1)*Diagnoses (OR=1.01, p<0.001). Given that Diagnoses can take on a value between 2 and 10 then the odds ratio for somebody with a single cancer diagnosis and single COVID diagnosis comes out at 2.05¹. The odds ratio for somebody with a full diagnostic record comes out at 35.9². Multiply these by 0.10 to take account of the overall odds ratio for Cancer Dx(1) and we arrive at combined odds ratios ranging from 0.21 to 3.59.

I appreciate this will bend brains but all it is saying is that the likelihood of a positive test result depends on the complexity of the cancer case. Simple cases are less likely to return a positive test result and complex cases are more likely to return a positive test result. What is baffling is why there should be this distinction: why should presence or absence of cancer be mixed up with presence or absence of a COVID diagnosis? I can understand a linkage through cancer cases tending to be immuncompromised and thus prone to infection but this would serve to increase the likelihood of positive test results not reduce it!

One perverse possibility lurking at the back of my mind is that immuncompromised cancer patients were infected with COVID back in 2020, thus building natural immunity sufficient to reduce likelihood of further infection in 2021. This argument appeals for it is less conspiratorial, but the bother here is that I can’t see how this would wash with the 7 remaining categories: how would this work for Acute Myocardial Infarction (OR=0.73,p<0.001), for instance?

The final term of Cancer Dx(1)*Period(1)*Sex(1) is rather unsettling. With an odds ratio of OR=0.21 (p=0.008) what this interactive term is telling us is that women suffering from cancer in the later period (2021 week 19 -27) were 4.8x less likely to receive a positive test result. We might blame this on varying levels of disease prevalence were it not for the fact that Case Detection Rate and Period are present in the model and soaking up this variance across five terms. We might also note that Cancer Dx(1)*Period(1) fails to reach statistical significance (p=0.953), so we really can’t go blaming things changing over time. What this boils down to is a genuine sex effect. Either cancerous women in the later weeks of 2021 were less likely to return a positive test result for some mysterious reason or they were precluded from the testing regime.

Right now my brain is flagging, and I shall assume yours is also. If I were to try and put this all in one sentence it would be to say that the COVID test results are not making as much sense as they should in relation to various medical diagnoses. Something wacko is going on for certain! Positive relationships with certain diagnoses are one thing but statistically significant negative relationships are something else and somewhat baffling. I may have missed something obvious so I’ll put the lid on the biscuit tin and go cogitate for a while.

Kettle On!

1. EXP(0.358 x 2)

2. EXP(0.358 x 10)