Needle To Door Time (part 2)

In this miniseries I use survival analysis techniques to investigate delays between vaccination and death for 5,039 cases over the period 2020/w53 – 2021/w36 using data from an unknown NHS Trust

Today is the day for a spot of Cox Regression, being a method for deriving a proportional hazards model. Wiki summarises the technique rather nicely as follows:

Proportional hazards models are a class of survival models in statistics. Survival models relate the time that passes, before some event occurs, to one or more covariates that may be associated with that quantity of time. In a proportional hazards model, the unique effect of a unit increase in a covariate is multiplicative with respect to the hazard rate. For example, taking a drug may halve one's hazard rate for a stroke occurring, or, changing the material from which a manufactured component is constructed may double its hazard rate for failure.

I appreciate that this is tantamount to gibberish so I shall explain in the plainest English possible with reference to the NHS data dump I keep messing with…

There are 5,039 vaccinated adult in-hospital deaths in the data sample, each offering a date of vaccination and date of death. We may thus calculate the needle-to-death delay for each individual and thereby establish the commonly used clinical endpoint of 28-day survival. The progression of death over time may be analysed and we can establish which factors, if any, seem to have any impact. Thus, we might ask if age has any bearing on survival as well as sex.

In many ways the method is akin to bog-standard linear regression in that we’re trying to fit a statistical model that eats up the variance in the dependent variable (risk of event per unit time). Please do bear in mind that eating up the variance is an associative thing and not a causal thing – at no point can we jump up and down and declare causality (though we might infer such in accordance with our belief).

In part 1 of this miniseries we saw a statistically significant difference in 28-day survival between dose 1 and dose 2 and cogitated on why this should be so. Some may leap to the conclusion that the initial dose was extremely harmful and whilst this may indeed be so it is not necessarily the only explanation. My job, as a statistician, is to keep poking the data in the hope that other explanations are brought to light (assuming there are any) and, in this regard, I may be considered as a right pain in the Aga!

Let us then get our kettles on, grab some buttered toast, and start by looking at a simple example to get the ball rolling and pan sizzling. To do this I shall consider age and sex, along with their interaction; and the clinical endpoint shall be 28-day survival from whatever their last dose was.

Age & Sex hors d'oeuvre

It’s always a good idea to start with some basic summary statistics and here they are:

We observe a near identical split between males (n=2,521) and females (n=2,518), with females being slightly older as expected. There’s not much of a difference in terms of 28-day survival either, with 1,983/2,521 (78.7%) of males making it through compared to 2,021/2,518 (80.3%) for females. A Pearson Chi-square test of association yielded a p-value of p=0.163 so we must brace ourselves for nothing spectacular in the Cox Regression, and this is precisely what the model churns out:

Ignore the upper table and zoom right in to the lower table. Under the column headed ‘Sig.’ you’ll see values of p=0.865 for Age, p=0.465 for Sex and p=0.596 for the Age * Sex interaction term. This is what we have already inferred from the basic summary stats but it’s nice to see this nothingness confirmed with a fancy spanner!

This nothingness is not actually nothing for it means we can go ahead and pool the data by age and sex before we proceed, this being a mighty handy way of maximising statistical power. This nothingness also tells us something important; it tells us that males fare as well as females when it comes to 28-day survival. Strange as it may seem it also tells us that younger folk don’t fare any better than older folk!

This last point is worth decent cogitation for it rubs against pretty much anything medical. Older folk always come off worse pretty much no matter what aspect of medicine we are studying but here we have a situation where being young confers no biological advantage. Is that most odd or what?!

I am going to tentatively conclude that we’re likely not looking at the impact of disease (acute or chronic) as a driver for 28-day survival, which means the finger of blame must shift to vaccination. This is arguably the most significant nothingness I have baked to date!

Somethingness

So what sort of something might impact on 28-day survival? This is where Cox Regression comes into its own because we can line up a number of covariates and submit them to the modelling procedure in a (forward) conditional selection procedure. In plain English we get to see what is likely having a genuine impact on survival. Here’s my shopping list:

Below ‘Age’, ‘Total diagnoses’ and ‘Prior Risk Of Death¹’ we have a listing of 13 indicator variables whose mean value indicates the frequency within the sample of 5,039 adult in-hospital deaths. Thus we see 0.23 (23%) of cases exhibited a chronic respiratory disease, with cancer leading the way at 0.32 (32%). Let us now take a look at what Cox Regression threw out:

Now this is utterly butterly fascinating! The middle table is what we need to focus on for this is the final listing of all covariates that made the grade in predicting 28-day survival post-vaccination. Note that COVID now appears as a three-level factor (non-COVID; asymptomatic; symptomatic) with non-COVID as the reference category for risk estimation.

The column headed ‘Exp(B)’ gives us a measure of the relative impact. Thus, leading the way with a whopping great risk factor of 3.044 (p<0.001) is possession of an asymptomatic COVID diagnosis (folk with a positive test result but no respiratory indication). What on Earth was going on in this Trust such that symptom-less COVID ‘cases’ were less likely to survive the first 28 days post vaccination?  Is this a general pattern or just a local blip?

Symptomatic COVID cases make sense with a risk factor of 2.150 (p<0.001), but to be pipped into second place by symptom-less COVID is downright bizarre! Here’s the graphical output that expresses this weirdness visually:

It is interesting to see Acute Myocardial Infarction (heart attack) up there with a risk factor of 1.393 (p<0.001), which brings me full circle to my door-to-needle work in my old NHS Trust. I am sure some readers will ask if these include COVID cases and the answer is yes they do – if sample sizes permit I’ll break the data down into COVID and non-COVID cohorts and/or AMI and non-AMI cohorts and re-run this analysis.

Presence of a cancer diagnosis along with prior risk of death (PROD) are associated with reduced risk of a 28-day death since their odds ratios are less than unity. I would suggest that these paradoxical covariates are pointing to chronic cases with complex morbidity, as opposed to acute cases with a well-defined morbidity.

It is worth noting that acute (p=0.222) and chronic (p=0.650) respiratory conditions didn’t make the grade in the prediction of 28-day survival along with their combined impact (p=0.651), with all the going being made by anybody with a COVID tag. This worries me for why would rather serious acute respiratory conditions such as pneumonia only become a significant predictor of 28-day survival when given a COVID tag? Is there something about that tag that is influencing the clinical outcome? By that I do not mean COVID-19 symptoms causing trouble but the manner in which tagged COVID cases are handled or treated. Is this evidence of iatrogenic death?

I guess I better make a start on part 3!

Kettle On!

Summary

1. Cox Regression was used to investigate 28-day survival for 5,039 vaccinated adult in-hospital deaths in a single, anonymous NHS Trust for the period 2020/w53 – 2021/w36.

2. Age and sex were discovered not to be statistically significant predictors of 28-day survival. This most peculiar finding for age suggests that whatever is driving post-vaccine survival is not disease related, and this may be indicative of vaccine harm.

3. The greatest risk for early death was imposed by asymptomatic COVID (OR = 3.044, p<0.001), rather than symptomatic COVID (OR = 2.150, p<0.001). Paradoxically, acute respiratory (p=0.222), chronic respiratory (p=0.650), and combined chronic with acute respiratory conditions (p=0.651) failed to reach statistical significance as predictors of 28-day death post-vaccination. This is a rather strange result that is cause for concern: is the COVID ‘tag’ leading to inappropriate patient management and/or treatment, or is something else at play?

1. Please refer to my three part article series Prior Risk Of Death for an explanation.