Prior Risk Of Death (part 1)

I attempt to derive a more sophisticated measure for how sick in-patients are in the first instance and find something rather unexpected

OK, so I know this is going to sound crazy but I want to know exactly how sick people were before they died. Up to now I have been using a proxy called Diagnoses that is simply the number of diagnoses listed in the EPR, on a scale of zero to ten (there being a total of 10 diagnostic fields in the data dump I was given). This has done a decent job of accounting for case complexity prior to death and works alongside age, sex, disease prevalence, incidence of major non-respiratory morbidity, incidence of chronic respiratory disease, and probable COVID in helping level the playing field for a real world sample of cases so that we may more reliably assess vaccine harm/benefit using statistical modelling. Here’s my idea in three slices…

1. Establish the incidence of each of 11 primary diagnostic groupings across the entire sample of 57,557 in-hospital deaths over the period 2017 – 2021 in terms of a fractional value.

2. Sum the fractional values for each primary diagnostic group on a case-by-case basis to yield an aggregate value.

3. Transform aggregate values into risk scores on a scale of 0 – 100 to give prior risk of death (PROD).

To give you some idea of how this turned out for the entire sample of 57,557 deaths I shall reveal the mean score fetched-up at 22.4, with a median score of 20.2, minimum of 0.0 and maximum of 100.0. The distribution is positively skewed and looks like this if we use logarithmic graph paper:

There’s a decent-sized cohort hanging around zero, these being cases with no apparent chronic or acute health issues but who may well have been in the wrong place at the wrong time (road traffic accidents, knifings, shootings etc) including self-harm, poisoning and accidental intoxication. There’s a peak around a score of 20 and these are going to be cardiac cases not surviving acute myocardial infarction as well as those with organ failure of some kind. Complex cases will sit within the upper tail, as will the chronically ill.

There’s a fair few useful things we can do with this risk score and I guess the first is to compare it with the Diagnoses variable I’ve been using up to now. If I narrow the sample down to the 19,457 in-hospital deaths over the period March 2020 – September 2021 that I have been using for my logistic regression modelling we get this snazzy error bar plot:

Some curious readers are bound to ask how it is possible to have a zero diagnosis and the answer is invariably DOA (dead on arrival). If not DOA, then some poor soul who didn’t last very long as they came in on a blue light. If a consultant episode isn’t triggered in the system and casenotes prepped in time then they get wheeled over to the mortuary with not much of a patient record. Whatever the reason for lack of a final ICD-10 diagnosis within the EPR these folk are a different bunch. This might sound as though it offers a major analytical headache but in the 19,457 case sample I’m using for my main analyses there are only 35 such records.

If we ignore that quirky zero diagnosis situation we get a rather nice transition both in terms of case complexity and in terms of PROD. One will act as a darn good proxy for the other and I’m pleased to see such excellent correspondence after all that modelling!

That being said the PROD score, on a continuous scale from 0 – 100, is going to prove superior to the 10 discrete values of Diagnosis when it comes to serving as a covariate in a multivariate model. Instead of a variate that is distinctly ordinal in nature we’ve got a genuine scale-level variable to work with and this should yield more robust models when it comes to the tricky question of accounting for how sick patients were before they died. Level playing fields and all that.

Whoops-A-Daisies!

I did say that there’s a fair few useful things we can do with this new-fangled risk score and the first that sprung to mind is to plot the mean PROD against quinary age band. Try this:

Whoops-a-daisies indeed! I had expected PROD to increase steadily with age as health issues develop over time and cases become increasingly complex, frail and clinically vulnerable. This may be the case in the real world but that complexity, frailty and vulnerability is not transferred over to the diagnostic record. Ouch. We see a progression from the under 25’s right up to the 70 – 74y band as expected, but after this age band peak the PROD score declines markedly.

It is possible that elderly in-patients surviving the pandemic years were becoming less complex in their presentation, this being an expression of survivorship bias. It is also possible that diagnoses made for elderly patients were not as they should have been, with certain clinical features ignored or omitted in favour of something sweet and simple (like COVID-19, for instance).

Back when I acted as consultant in an audit of care of the elderly wards for my own Trust it became patently obvious that neglect abounded to save costs, especially with drugs. Not the happiest of audits, I confess, but at least it kicked a few managers up the Aga for a while. You can save on drugs by failing to diagnose illnesses, but then again many poor souls beyond a certain age simply don’t want to be tampered with, so the situation is not clear cut.

Back to the situation in hand…

I better roll the clock back and look at the situation prior to the pandemic. Here we go:

Aha! What we are looking at has got nothing to do with the pandemic and its fallout. We’re not looking at survivorship bias in terms of COVID, at least, but we may well be looking at survivorship bias in terms of general health. Then again we may be looking at failure to capture all possible diagnoses when it comes to care of the elderly. Whatever the reason this is a rather awkward finding.

I can now see why some logistic regression coefficients threw up some peculiar less-than-unity odds ratios for complex cases and/or the elderly, especially their interactions – these are attempting to level the playing field when it comes to roll-off in diagnosis rates for the elderly.

Right now I need to go away and have a jolly good think on how best to tackle this wrinkle, for in-patients aged 80 years and over are going to be misrepresented in terms of background health status and my mind is wondering what impact this will have on studies aimed at assessing vaccine benefit. Yet more bothersome bias to contend with!

Summary

• Prior risk of death (PROD) is a score derived from the frequency of 11 diagnostic groupings within the dataset. As applied to an individual it provides a proxy measure of base likelihood of death at admission.

• PROD provides evidence of diagnostic tail-off in the elderly, which will impinge on assessment of vaccine harm/benefit.

Kettle On!