Bed Loss & Bedlam (part 2)

A look at bed occupancy within NHS England over the last 13 years

In part 1 of this series I derived a variable I am calling Bed Loss Fraction (BLF), this being mean daily proportional bed occupancy across service providers within NHS England in comparison to the maximum mean daily beds occupied over the period 2020/w1 – 2022/w33 (128,079 beds).

We observed a worrisome BLF peak of 0.59 (59%) during 2020/w14 (w/e 3 April 2020) and noted the rapidity with which bed loss was achieved. Hailed as a necessary preparation for the computer-predicted incoming mega-wave of seriously sick folk, the irony is that the government took the decision to sacrifice hospitalised grannies whilst blaming folk for not wearing a mask (futile) or standing 2.0m from the next person in the queue (also futile). The mega-wave never came and bed occupancy crept back to ‘normal’ levels over a period of two years, with bed loss falling to its half-life value of 0.30 (30%) over a period of 8 - 9 weeks.

BLF & COVID

The relationship between BLF and COVID occupied beds is interesting, so I suggest we get the coffee on the stove, open something to nibble and have a squizz at this dual time series plot:

In the beginning we observe extreme bed loss and a modest wave of bed-ridden COVID cases. At this point I feel I ought to remind readers once again that a bed-ridden COVID case isn’t necessarily bed-ridden because of COVID. What we have here is a count of PTBs (positive test beds) whereby anybody in bed for any reason will count as a COVID ‘case’ if a single test result turns out to be positive. Thus, positive-testing mothers-to-be in maternity units will become COVID ‘cases’, as will those unfortunate enough to require hospitalisation in a mental health facility.

Substantial bed loss paired with elevated PTB counts will result in impoverished hospitals that will be chock-a-block full of COVID ‘cases’ and little else. As one senior nurse remarked to a disgruntled family whose relative was being treated like a ping pong ball, “all wards are COVID wards”. And so it was, and absurd protocols will have ensured any remaining staff will have been stretched to the limit managing yet another positive test result rather than thinking about symptomatically sick folk (like we traditionally do with disease). This is not to say there weren’t any severe cases - there most certainly were - but this wasn’t the norm. Several nurses have confided that their unit tested patients endlessly until they got a positive result, after which the standard of care declined as newly found ‘cases’ were wheeled into a corner. Talk to a Senior House Officer about any of this and they’ll snort through their nose. Evidence-based medicine isn’t what it was.

Modelling Strategy

But I digress! Back in part 1 we considered cross-correlation function plots for BLF with both all cause and non-COVID death and discovered a delayed correlation of the order of 3 – 4 weeks. We cogitated on whether this was evidence of dangerous discharge given that the same lagged correlation was observed for non-COVID death. Whilst it is reasonable to assume non-COVID death rules out the possibility of SARS-tinted confounding factors, there is always that nagging doubt that non-COVID death doesn’t actually mean non-COVID death in much the same manner as COVID death doesn’t necessarily mean a death due to COVID (or even with COVID for that matter).

As an analyst with 38 years of experience I find myself in a strange and surreal landscape these days where nothing is as it seems, thus I am going to reach for my big spanner of ARIMA time series modelling again to see if this can shed any light. In this regard we shall start with a base model for the prediction of non-COVID death over the period 2020/w6 – 2022/w33, for that is the period for which I have 100% data capture.

There are two ways of going about this:

1. Modelling of the T4253H smoothed excess non-COVID weekly death count time series.

2. Modelling of the T4253H smoothed non-COVID weekly death count time series with the T4253H smoothed 5-year (2015-2019) mean baseline series as a covariate proxy for seasonal fluctuations.

I shall try both methods to see if agreement can be reached (this being a jolly good thing) and shall use the case detection rate series (rolling 7-day COVID cases per 100 virus tests, a.k.a. CDR) as an independent variable to test for reliability of non-COVID death classification. Once this confounding factor is nailed down I can enter BLF into the statistical models to see if this explains anything. If it does we’ll be a step closer to proof of dangerous discharge.

Bed Loss & Death – model #1

Herewith the best fitting ARIMA model for the prediction of T4253H smoothed excess non-COVID death that I can muster as things stand this morning. I appreciate that T4253H smoothed excess non-COVID death is a bit of a mouthful but it’s all very simple really… I’m having a look at non-COVID deaths since the pandemic began that have been adjusted for seasonality (hence excess) and administrative hiccoughs (hence smoothing):

The first feature to notice in this table is inclusion of the time series for CDR as a statistically significant predictor of excess non-COVID death (p<0.001). This means the designation of non-COVID is likely in error for a number of deaths since we’ve had to soak up a bit of variance using CDR as a proxy for disease prevalence. The coefficient of determination for the intermediate model (dependent + CDR) fetched-up at r-square = 0.064, which indicates that 6.4% of the variation in excess non-COVID deaths is explained by variation in the case detection rate. This gives us some idea of the level of erroneous certification, the positive coefficient of 50.315 suggesting that a number of non-COVID deaths were missed owing to false positive reporting (and thus need to be added back).

The second, and arguably most important feature to notice in this table, is inclusion of the time series for BLF as a statistically significant predictor of excess non-COVID death when assigned a lag of 2 weeks (p<0.001). The positive coefficient of +1774.312 gives us a handle on the impact of bed loss over the period 2020/w6 – 2022/w33, such that a 50% loss in beds is associated with 50% x 1774 = 887 additional weekly deaths some 2 weeks later. Even a 5% loss in beds will yield 89 additional weekly deaths, this giving us some idea of just how super-saturated the NHS is at the best of times. If we apply this coefficient to the BLF curve expressed in part 1, then run out cumulative additional non-COVID deaths associated with bed loss, we arrive at this slide:

My modest ARIMA model indicates that the cumulative count of additional deaths associated with bed loss is currently standing at just over 26,000 deaths. We should note that these are true excess deaths; that is, they’re deaths adjusted for both seasonal effects and certification error. We should also note these are non-COVID deaths so represent only part of the sorry picture.

Model #1 Pudding

Here’s how well that modest first model tracks excess non-COVID death over time:

Bed Loss & Death – model #2

That’s quite a convincing fit and quite a shocking result to boot so we better look at what the second method yielded:

Here we have the engine room of a model designed to predict (smoothed) weekly counts for non-COVID death rather than excess non-COVID death. In this approach seasonality isn’t accounted for by subtracting a prior 5-year mean baseline à la mode but by using the baseline series as a covariate. This pops up with a coefficient of 0.346 and p-value of p=0.015, which suggests around a third of the weekly variation we see within the baseline series overlaps with weekly variation for non-COVID death.

Again, there is a need to incorporate a proxy for disease prevalence (CDR), this being highly statistically significant at p<0.001, and the coefficient of 42.975 is pleasingly similar to that derived for the first model (50.315). Multiply these coefficients by the values of the CDR series and you get some idea of the number of misclassified deaths due to false positive test results or physicians jumping to the wrong conclusion and calling a non-COVID death a COVID death. I shall cover this wrinkle in a future article.

This brings us once again to the time series for bed loss fraction, which once again drops out as a highly statistically significant predictor of non-COVID death when lagged by 2 weeks (p<0.001). We should note the similarity of the associated coefficient (1842.084) with that derived from the first model (1774.312), which is most pleasing. The pudding is also equally tasty:

Yes, But Is It Robust?

Some sharp subscribers will ask if BLF pops up as a statistically significant predictor of non-COVID death for other delay values. I can report that this is indeed so, with the model yielding p=0.772 for zero delay, p=0.023 for a 1 week delay, p<0.001 for a 2 week delay, p=0.003 for a 3 week delay, p<0.004 for a 4 week delay and p=0.105 for a 5 week delay. The effect is thus robust from weeks 1 through 4 and something we need to pay attention to even if the government and NHS top brass try to sweep the issue under the carpet. Closing beds kills folk, plain and simple; it ain’t exactly rocket science and neither does it require any stretch of the imagination.

Kettle On!