In my trade, the well known term "literacy", i.e. the ability to effectively read and write a range of text, is paired with a less well known and used term, "numeracy". The word literacy is often coupled with other terms to mean that their level of comprehension and expression, for example, scientific literacy and digital literacy (both which are also frequent visitors to my discussions at work).
Numeracy is similar to literacy but instead of texts we have numbers. Both have a minimum standard to them: an illiterate person cannot read or write, even if they may have familiarity with the alphabet, while a functionally innumerate person would not be able to do much more than count or recognise numbers. But both have matters of degree. Most literate people can read e-mails, novels and blurbs, but they may have more difficulty with scientific literature. Averagely numerate people would have no trouble with handling money and percentages but not understand exponential growth, standard deviation and statistical significance, etc.
The pandemic has had plenty of numbers and as they enter the mainstream conversations and articles it is interesting to see how they are interpreted. Numbers can be counter-intuitive and also statistics famously can be used to create the wrong impressions, especially when mistakenly compared. One common misunderstanding is something like relative and absolute risk, two percentages that could differ significantly. Relative risk reduction through vaccination would be a comparison with a non-vaccinated person, i.e., if 100 unvaccinated people caught Covid-19 and ten were sick enough to go to the hospital, whereas 100 vaccinated people caught Covid-19 and only one was sick enough to go to hospital, the vaccination was 90% effective against hospitalisation. This is true even if the chance of any given unvaccinated person getting sick and going to hospital may be low. (A recent conversation I had touched on this kind of thing for running and cancer which I had casually raised in another conversation. There is some research findings
here. As a regular runner, I apparently have a 42% relative risk reduction of oesophageal cancer compared with a non-runner... but I have never known anyone with such a cancer.)
One of the numbers that is often asked is how many of the hospitalised cases were vaccinated. In the early days of Delta in NZ, it was a very strong selling point for the vaccine because it was like night and day, the vast majority of the hospitalisations were not vaccinated. But numbers can be deceptive, too, and the statistics from highly vaccinated countries have misled many. Vaccination after all reduces risk but does not eliminate it, so in a 100% vaccinated population, 100% of cases, 100% of hospitalisations and 100% of deaths will be in the vaccinated. There should be no room for shock at these outcomes, especially as in New Zealand any death of a positive case is recorded as a Covid death.
With the Delta variant, there was a blurring of the numbers at high levels of vaccination, like New Zealand, Australia and Canada as the vaccinated and the increasingly boosted majority presented more positive cases than the unvaccinated, even if their rate of becoming a case, hospitalised or dying would be significantly lower. In fact, even if the worst number, the death rate, were the same for vaccinated and unvaccinated, it would still be showing the huge benefit of vaccination as the vaccinated include the vast majority of the elderly and immunocompromised, while the unvaccinated would have a larger number of people who are younger or healthier.
The Delta strain in New Zealand, which was rather scary going in, has been muted for the most part by our vaccination policy. What had been a sharp, deadly wave for almost all countries has been an inconvenient but not terribly lethal interruption to normal life. With the "orange light" on, we are doing things more or less as usual with a tending down of transmission. But now we move on from the maths above of Delta and onto that for Omicron.
It is thankfully a "milder" variant but the sheer numbers potentially make it a short, sharp viral bullrush charge rather than the trench war of Delta, and New Zealand has had the best seats in the house to see how Omicron does its thing in other countries and adjust our approach in the absence of a hot war on our own turf. But the numbers are just bonkers. The case numbers are astronomically, making any meaningful association with previous records obsolete. Even in its earlier peaks, the global number of new daily cases only just broke 800,000. Now, still with many countries in the early days of their outbreaks, the average is almost two million a day. But the case number, apart from being ludicrously high is meaningless because:
- not all cases are being tested because of asymptomatic or minimally symptomatic infection (as was the case from the beginning)
- the testing system is overloaded in any Omicron dominant locality
- home-testing through Rapid Antigen Tests are being used and results are not often reported
The positivity rates for the officially recorded PCR tests are high, which usually means it is just too prevalent in the community, and that is really the only conclusion to take from it. The key takeaway is that it is a rampant variant that is easy to catch and easy to pass with neither previous infection nor vaccination standing up as much protection as they had with Delta.
Under Delta in a highly vaccinated country, it was taken that the metrics to follow were the number of hospitalisations and deaths, rather than cases. Vaccination does not prevent all infections and do not prevent transmission from those infected people. There had been a "decoupling" of cases and hospitalisation: before vaccination, case rises were always followed by hospitalisation rises and then deaths. With vaccination it weakened the delayed association.
Omicron has truly muddied the water with hospitalisations as well with a lot of people saying that vaccination was ineffective against the variant. Even in the early days in South Africa it was noted that the high case numbers were often incidental positive cases in the hospital. That is to say, there were patients who were coming to hospital for non-respiratory reasons, asymptomatic, but who turned out to be positive with the virus at the time of admission. If "hospitalised" for their other condition, they would be counted as hospitalised Covid positive cases (as they fit the categorisation, just like deaths of positive cases count, too). To be clear, even if you are in for a non-respiratory illness, an active viral infection is probably unhelpful and definitely something to keep away from those who were vulnerable within the hospital, and would be checked into a Covid ward. There were often the questions of hospitalisation "from" or "with" Omicron. Prepositions do matter to make sense of it but that kind of data is very hard to track for many practical reasons that you can imagine. While there would be admissions for clear-cut Covid, non-respiratory admissions with Covid could turn serious. It is hard to think about how this kind of data could be given easily without recreating a system that was fine pre-Omicron.
My sole contribution to the thinking for making sense of the numbers would be this. I'll take an example sent to me saying that in British Columbia in Canada, 44% of the Covid hospitalisations had been vaccinated. This is a lot of vaccinated people in hospital, but with a bit of thought we know that as a country in the league of Australia and New Zealand, it is actually a positive statistic. But under Omicron it is potentially even better than it looks. The key idea to note, which has been true in South Africa and the United Kingdom is that the virus is so prevalent that a huge number of hospitalised cases are "incidental", that is, they were hospitalised for another reason yet turned up a positive test. This really does mess with that once critical measure of hospitalisations. There are a couple of lenses to look at this number to get a better idea. For the first, I proffer two assumptions:
- those hospitalised for non-Covid reasons who are positive with the virus are there in proportion to the vaccination rate
- Omicron being the main reason for the majority of their hospitalisations as their Delta wave had passed
And for ease, let's assign some variables:
A = Hospitalised Covid-positive patients who are admitted for Covid who were vaccinated
B = Hospitalised Covid-positive patients who are admitted for Covid who were unvaccinated
C = Hospitalised Covid-positive patients who are admitted for other reasons who had been vaccinated.
D = Hospitalised Covid-positive patients who are admitted for other reasons who had not been vaccinated.
The 44% would have a numerator of A+C, and the demoninator would be A+B+C+D, when what we want to know is A/(A+B), the hospitalisation rate for vaccinated people. But with 79% of the total population double vaccinated, it is easy to know that C would outnumber D with the conservative assumption that asymptomatic infection is just as probable (it probably isn't). This addition of a number to both the numerator and denominator reduces an extreme number towards the middle. For example, if A = 5, B = 20, C = 20, D = 5, the apparent percentage of vaccinated hospitalised patients would be 25/50 (50%) when the actual percentage of vaccinated hospitalised would be 5/20, i.e. 25%.
The 44% statistic might well discourage the vaccination effort or, worse, be weaponised by those want to draw more attention to the inefficacy of vaccines. If it were known that the percentage of vaccinated people hospitalised for Covid reasons were between 20%-30%, and that they are from not just a majority of the population, but the segment that included the elderly and immune-compromised for whom the vaccine would have the least effect and, conversely, the unvaccinated minority was still producing the vast majority of hospitalised Omicron cases, it is rather positive news!
The other lens to look at it from is that just as cases are not an accurate measure, ICU/HDU admission is the new critical number. For New Zealand's reference, probably the most useful numbers to look at are here: Daily Cases Admitted to Hospital - COVID Live for Australia. The numbers will shortly exceed anything from Australia's previous waves, although this particular wave takes the proverbial cake as its with all states now contributing (aside from Western Australia which is still more or less Covid-zero).
The awkward thing about the currency of numbers and statistics that are that without some base numeracy they are misunderstood and applied. The dilemma for any of the public health communicators is to not deny such numbers or interpret them skipping the analysis, but to "show their working" in a simple way, preferably with graphics. Otherwise, people feel dissonance between what is being claimed (vaccines are preventing hospitalisations) and the seemingly concrete numbers (44% of hospitalisations are in the vaccinated!).
