Mega Focus Today: Peter Little attempts to interpret NSW Health statistics

Graeme Little Né Peter Pope - known to many of us by his Facebook identity of "Peter Little" styles himself as Australia's Pandemic Lawyer. Peter has recently been fascinated by the COVID-19 statistics that the NSW Health department is publishing. It turns out that on Tuesday 18th January, while Peter and his followers were still trying to cope as best they could with the deportation of Novak Djokavic, the NSW Health department released daily figures that showed that of the 36 reported COVID-19 deaths, 33 were fully vaccinated.

Our indefatigable health advocate was quickly on the case.

18th January at 15:07
RIGHT NOW IN AUSTRALIA - THIS is the MEGA FOCUS TODAY - the VACCINATED are CLOGGING UP the HOSPITALS and SADLY DYING - 33 deaths out of 36 today in NSW are AT LEAST DOUBLE SHOT!!!!!
Q Why is Victoria LYING that it is the unSHOT that are clogging hospitals and dying?
“Of the 36 people who died; 33 people had received at least two doses of a COVID-19 vaccine, and three people were not vaccinated. Older age is a significant risk factor for serious illness and death for COVID-19, particularly when combined with significant underlying health conditions.”
#chasetruth

Now Peter is not addressing the Statistical Society of Australia. He is talking to his paranoid demographic who have a rather different toolkit for numerical analysis at their disposal.

Gino Moore
They love that 33~ Masonic they are!

Kaploon Luke
Gino Moore yeh 33 out of 36 (3x6) 666

Some of his other fans suggested that these figures are going to lead to a new reporting standard or "goal post shifting" as they are want to call it.

Patricia Hatherly
The CHO in Qld on channel 9 last night gave the latest death figures here and said they were all "unvaccinated as they'd not yet had their booster"...now that's a significant goalpost shift and possibly explains why "unvaccinated" has a new meaning.

Nathan Hately
Patricia Hatherly yep exactly what i was gunna say. They will solve there vaxed died issue by saying they only had 2 shots and needed 3

Of course an eventual move to defining the vaccinated cohort as being vaccinated within a window of effectiveness is a sensible standard to adopt, but that is not the crux of the issue here with Peter's concerns.

There has been a day in NSW where only one in 12 people of the COVID-19 deaths was unvaccinated, so according to the logic of "Fight Pharma Corruption" the NSW Government is pushing an ineffective vaccination strategy.

What this pandemic has demonstrated to me is that our society is increasingly divided between the numerate and the innumerate. Plenty of people have minimal ability when it come to numeracy and prefer to leave it to the experts for their analysis and pronouncements, however there is a vocal segment of the innumerate population who lack insight into their functional innumeracy and conflate their mathematical inabilities with the belief that they have uncovered some statistical anomalies in the government health reporting that demolish the claims of the vaccination advocates and health authorities in general.

I also hear the same kind of flawed reasoning from problem gamblers, anti-helmet campaigners, a variety of science deniers who are convinced that they have uncovered some supposed evidence that the government is trying to conceal.

For most of us it would seem unremarkable if one in twelve road casualties were wearing a seatbelt given the near ubiquity of seatbelt wearing, but anti-vaxxers clearly fail to arrive at this basic mathematical intuition.

So let's take a look at the numbers and ask "If the COVID-11 vaccination regime was completely ineffective, what kind of mortality split would we expect to see in this daily cohort?"

To answer that we would start with looking at the statistics of vaccine coverage. I have picked data from NSW Health on the 4th January, because it is appropriate to be looking at vaccination rates at roughly the time that this cohort might have contracted COVID-19.

On 4th January 95% of people aged 16 and over had received at least one COVID-19 vaccination and 93.6% had received two vaccines. This means we can split the numbers up as follows. We aren't concerned with reporting on booster status as it is not typically included in the daily mortality figures.

So if COVID-19 vaccines were completely ineffectual we would expect to see the vaccination status in the mortality figures following about the same distribution as the vaccination status of the population at large. As 4.7% of 36 is about 1.692, if there was no vaccine effectiveness we'd expect to see one or two unvaccinated fatalities in the statistics. However, there are three unvaccinated deaths reported on 18th January. A total of 8.3% of the mortality figures.

So more unvaccinated people are turning up than by chance, but this reasonably obvious conclusion seems to be lost on Peter Little. Now, I don't believe that he is being knowingly deceptive. I believe that this basic fact eludes him because of his unfortunate intellectual limitations and exacerbated by him not having the self-awareness that he is engaging in an intellectual inquiry beyond his level of competency.

Relative Risk

We can go further with our analysis. When weighing up a health intervention it is worth knowing the relative risk of an intervention compared to not proceeding with an intervention. Any recommendations on vaccination should take these considerations into account. We don't want to simply be getting vaccinated if there is no significant benefit in doing so.

A simple formula that compares adverse outcomes in the intervention group to the control group determines the relative risk. The Wikipedia page gives a good overview, but there are plenty of online courses and resources on health statistics if you want to delve a bit deeper.

First of all a single day's worth of data is a somewhat small sample size. It could be there could be that there are some one off cases of data reporting - eg, sometimes a backlog of coronial data gets included into a single reporting day. Sometimes there are reporting patterns such as a cycle of weekday versus weekend figures that suggests that the working week of the health professionals has some influence over how data is reported. On the other hand we really don't want to look at six months worth of data as there have been several waves of infections and the pre-delta and pre-omicron statistics are best examined without being mixed in with the current wave. So, we will confine ourselves to the week of reporting figures from 12th January to 18th January 2022 in order to get a more representative snapshot of the current phase of the pandemic.

We can find this data in a uniform format on the NSW Health website on a page called 2022 media releases from NSW Health.

Putting this data into a spreadsheet we can use the vaccination rates listed above to derive the size of the population cohorts. We will use 6 500 000 as the number of people in NSW who are 16 years and over.

So the relative risk formula is:

RR  = (IE / (IE + IN)) / (CE / (CE + CN))

The terms in this formula are:

IE Intervention Event
IN Intervention Nonevent
CE Control Event
CN Control Nonevent

We will be calculating Relative Risk on mortality figures alone as that reflects the current focus of our inquiry.

For our purposes an Intervention Event is a vaccinated person who has died of COVID-19. A Control Event is a person an unvaccinated person who has died of COVID-19. Intervention and Control Nonevents make up the bulk of the NSW population - those who are either vaccinated or unvaccinated and have not died of COVID-19.

We can see in the spreadsheet that have been 122 deaths of fully vaccinated people (for our purposes this still double jabbed) and there are 41 deaths from unvaccinated people.

So we can calculate the Relative Risk of vaccination in this time period using the formula:

RR  = (IE / (IE + IN)) / (CE / (CE + CN))
= (vaccinated deaths / NSW fully vaccinated population) / (unvaccinated deaths / NSW unvaccinated population)
= (122 / 60840000) / (41 / 3055000)
= 0.149416302

A fully vaccinated person has a relative risk of about 15% of the unvaccinated person. Or another way of saying this is that an unvaccinated person has about 7 times the chance of dying from COVID-19 than an unvaccinated person.

These figures have been changes over time based on the type of virus strains in the population, the improvements in treatments and many other factors. If we did the same calculation on the single day figure of 18th January, we would get an RR = (33 / 60840000) / (3 / 3055000)) = 0.552350427.

So either way, even if we are just looking at the RR of the 18th January - the statistical outlier day) vaccinated people only have 55% of the risk of unvaccinated people.

References

The spreadsheet is available to view on Google Docs

These are the daily statements from NSW Health that were used to compile the spreadsheet above.

12 Jan 2022: Of the 21 people who died; 12 were vaccinated, eight were not vaccinated and one person had received one dose of a COVID-19 vaccine.https://www.health.nsw.gov.au/news/Pages/20220112_01.aspx

13 Jan 2022: Of the 22 people who died; 14 were vaccinated and eight were not vaccinated.
https://www.health.nsw.gov.au/news/Pages/20220113_00.aspx

14 Jan 2022: Of the 29 people who died; 19 people were vaccinated against COVID-19 and 10 people were not vaccinated.
https://www.health.nsw.gov.au/news/Pages/20220114_01.aspx

15 Jan 2022: Of the 20 people who died; 16 people were vaccinated against COVID-19 and four people were not vaccinated.
https://www.health.nsw.gov.au/news/Pages/20220115_00.aspx

16 Jan 2022: Of the 20 people who died; 14 people were vaccinated against COVID-19 and six people were not vaccinated.
https://www.health.nsw.gov.au/news/Pages/20220116_00.aspx

17 Jan 2022: Of the 17 people who died; 14 people were vaccinated against COVID-19, one person had received one dose of a COVID-19 vaccine and two people were not vaccinated.
https://www.health.nsw.gov.au/news/Pages/20220117_00.aspx

18 Jan 2022: Of the 36 people who died; 33 people had received at least two doses of a COVID-19 vaccine, and three people were not vaccinated.
https://www.health.nsw.gov.au/news/Pages/20220118_00.aspx