Stats Chat

A few assorted issues:

First, the denominator questions — not the question of the actual population of NZ, which Henry Cooke is in charge of, but the eligibility and ethnicity questions.

Should we be quoting vaccination as a percentage of those eligible or as a percentage of the population? Yes, both. They answer two different important questions.  There’s a question of epidemic dynamics: are we getting to a point where enough people are vaccinated for Delta to be controllable more easily? What’s relevant there is vaccination as a percentage of the population; kids still count as unvaccinated, even though they aren’t eligible. There’s also a social question: are we providing the right access, information, and incentives to get people vaccinated? What’s relevant there is vaccination as a percentage of those eligible.

Next, ethnicity. I’ve seen people asking how ethnicity is counted in the MoH reports. Most of the NZ government tries to count people according to all the ethnicities they identify with — you can be in multiple categories. As a result, the categories add up to more than 100% of the population. The Ministry of Health does something different. If you give them multiple ethnicities, they pick one.  They prioritise: you’re Māori if that’s one of your ethnicities; you’re Pacific if that’s one of your ethnicities and Māori isn’t; you’re Asian if that’s one of your ethnicities and Māori and Pacific both aren’t, and so on. The advantage of this is that subgroups add up nicely: the number of vaccinations overall is the sum  of the numbers in each ethnic group. The disadvantage is that you may not be in the group or groups you expect.

Finally, pictures like this (this one is from @farmgeek on Twitter)

This is aiming to show the protective effect of vaccines. It’s a lot better than just reporting the % vaccinated among cases or hospitalised cases, because it shows the denominator.  The ratio of the red:green ratios in two bars is an estimate of one aspect of vaccine effectiveness; you can see it’s big.

It’s not a perfect estimate, for two reasons. The first is differences in exposure. If people who are unvaccinated are also more likely to be exposed, the vaccine will look more effective than it is; if people who are unvaccinated are less likely to be exposed the vaccine will look less effective than it is.  Both of these are likely: vaccination and exposure is broadly higher in Auckland than in the rest of the country, but within Auckland vaccination is  higher in areas where exposure is probably lower.

On top of any differences in exposure, a graph like this underestimates the impact of the vaccine because it misses out the reduction in unvaccinated cases due to the vaccine. Getting vaccinated protects you, but as the vaccination rates slowly rise, getting vaccinated also increasingly protects other people, regardless of their vaccination status.  Measles is a good example here: vaccinated people are almost never hospitalised for measles, because the vaccine protects us, but very few unvaccinated people are hospitalised for measles because community vaccination levels slow the outbreaks down enough for testing and tracing to control them.

Team Ratings for Week 3

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Performance So Far

So far there have been 16 matches played, 15 of which were correctly predicted, a success rate of 93.8%.
Here are the predictions for last week’s games.

Predictions for Week 3

Here are the predictions for Week 3. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Team Ratings for Round 6

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Performance So Far

So far there have been 35 matches played, 26 of which were correctly predicted, a success rate of 74.3%.
Here are the predictions for last week’s games.

Predictions for Round 6

Here are the predictions for Round 6. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Team Ratings for Round 4

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Performance So Far

So far there have been 18 matches played, 8 of which were correctly predicted, a success rate of 44.4%.
Here are the predictions for last week’s games.

Predictions for Round 4

Here are the predictions for Round 4. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Team Ratings for Round 10

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Performance So Far

So far there have been 27 matches played, 16 of which were correctly predicted, a success rate of 59.3%.
Here are the predictions for last week’s games.

Predictions for Round 10

Here are the predictions for Round 10. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Various people have created graphics showing the breakdown of vaccination rates across subpopulations of New Zealand.  They aren’t great (the vaccination rates, not the graphics), but they are improving.  As the graphics show, vaccination rates are lower in some subgroups than others.  Even when we get to 90% coverage on average, we could be well below 90% for some groups of people. This is a problem for two reasons.

The first reason is obvious: equity. People who haven’t been vaccinated yet aren’t just freeloading, they have reasons. For some people it’s harder to get to a vaccination (because of work hours or because they live somewhere remote). Others don’t trust the medical system — often for reasons that were well founded historically. It’s important to make sure everyone has a real opportunity to get vaccinated.

The second reason is less obvious and more statistical: we need a higher vaccination rate if the unvaccinated are not evenly distributed through society.  A cluster of people with lower vaccination rate will not only be at risk of Covid themselves, they will be an opportunity for Covid to spread. This is true of ethnic groups, but also of churches, dog-walkers, soccer moms, fans of provincial rugby, or nerds at statistics conferences.

Modelling the full complexity of NZ society and Covid dynamics is beyond what I have the data and computation resources to do, so I coded up a very simplified model to show, qualitatively, the sorts of things that can happen.  This is a fairly common use of mathematical models: not just to predict what will happen, but to show the range of behaviours that are possible.

The model is a 100×100 grid, where people can only infect their neighbours (no-one accidentally flies to Wānaka or has a job as a truck driver).  Vaccination reduces your risk of being infected, and also reduces your risk of passing on the infection.  With a random 83% of the population vaccinated, the outbreaks can’t spread far (83% of the NZ population is about 95% of the 12+ population). Here are two random outbreaks. Blue is vaccinated, grey is unvaccinated; purple is vaccinated and infected, red is unvaccinated and infected

Now, suppose we have the same 83% vaccination on average, but there’s a high-risk group (lower left) who are less vaccinated and who cluster together. If we’re lucky, a random outbreak misses them; if we’re not, it hits them

Having a non-uniform spread of unvaccinated people increases the number of cases for them, and also for vaccinated people.

We can get more dramatic sorts of clustering, where a group of unvaccinated people are connected to each other and also across society. Again, if we’re lucky, the outbreak hits only vaccinated people; if we’re not lucky, it spread very widely and more vaccinated people are infected than with a uniform spread. Do you feel lucky?

And a more dramatic example, with criss-cross connections of unvaccinated people

These obviously aren’t realistic depictions of New Zealand society, which isn’t square or blue and has lots of long-distance connections. They are, though, depictions of the sort of impact that population structure is able to have on disease spread. These example all have the same overall, high, vaccination rate, but they have very different outbreaks.

It’s not enough to get good vaccine coverage on average. Every subgroup matters.

Academic journals keep expanding, especially with the growth of open-access journals. Some publishers have reacted to this by creating a bunch of new journals. A few of these publishers give all the journals related names. Nature has Nature Genetics and Nature Communications and Nature Scientific Reports. The BMJ has BMJ Open and BMJ Nutrition, Prevention and Healthcare. The Lancet has The Lancet Public Health and The Lancet Regional Health — Western Pacific and others.

These journals are not the same as the parent journal.  You might or might not think a paper published in Nature was especially reliable because it’s hard to publish in Nature; that’s much less true for Nature Scientific Reports. You might comment that research has been published “in prestigious medical journal The Lancet“, but that’s misleading if it was actually published in The Lancet Regional Health — Western Pacific. I think the importance of journal rankings is vastly overrated, but if you’re going to rely on it you need to get it right.

Back in November, the Trump Campaign held a famous press conference that was not exactly at the Four Seasons hotel.  The label Nature Total Landscaping for these additional journals is a bit unfair — Four Seasons Total Landscaping isn’t even trying to be in the posh hotel business — but it was irresistible to science social media.

Team Ratings for Week 2

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Performance So Far

So far there have been 8 matches played, 8 of which were correctly predicted, a success rate of 100%.
Here are the predictions for last week’s games.

Predictions for Week 2

Here are the predictions for Week 2. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Team Ratings for Round 5

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Performance So Far

So far there have been 28 matches played, 21 of which were correctly predicted, a success rate of 75%.
Here are the predictions for last week’s games.

Predictions for Round 5

Here are the predictions for Round 5. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Team Ratings for Round 3

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Performance So Far

So far there have been 12 matches played, 5 of which were correctly predicted, a success rate of 41.7%.
Here are the predictions for last week’s games.

Predictions for Round 3

Here are the predictions for Round 3. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.