Stats Chat

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.

Team Ratings for the Grand Final

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 200 matches played, 145 of which were correctly predicted, a success rate of 72.5%.
Here are the predictions for last week’s games.

Predictions for the Grand Final

Here are the predictions for the Grand Final. 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 9

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 23 matches played, 14 of which were correctly predicted, a success rate of 60.9%.
Here are the predictions for last week’s games.

Predictions for Round 9

Here are the predictions for Round 9. 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.

From David Hood on Twitter, this graph shows leaving-home-ness in Aotearoa and the West Island, based on Google’s phone mobility data

The most important point about the graph, to me, is that the black dots follow a horizontal line (and the blue dots mostly follow a set of three horizontal lines).  This says that level 4 restrictions (and level 3, in RoNZ) were not eroding over time.  People were staying home just as much at the end as the beginning, even after four weeks and a much reduced case load.

The second important point is that the cluster of blue dots in the middle is a bit below the rest of the middle. Level 3 is slightly more effective, in terms of people staying home, than the Victoria and NSW and ACT restrictions. Level 3 is still a risk: it relies on people being at least as careful about masks and distancing and not accidentally flying to Wanaka as in level 4. Experts seem to be worried that it might be a bad idea, but to pretty much agree it’s still an effort at elimination.

How is that possible, given all the news about level 4 breaks? Well, Auckland is a big place. If 1% of people committed some serious breach of the rules and 1% of that 1% were reported, you’d have 160 reports.

Team Ratings for Week 1

A caveat regarding these predictions. This is a competition where four teams have been added, and there is little information about the performance of those new teams against the existing teams. There is also little information concerning the effect of travel when the new teams are in a different continent. I have used previous form from the Pro14, Rainbow Cup, Super Rugby, and Super Rugby Unlocked but have not been able to tune model parameters using years of past data in the way I usually do, nor obtain initial ratings to my satisfaction. Particularly early in the competition, results may be erratic.

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.

Predictions for Week 1

Here are the predictions for Week 1. 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 21 matches played, 14 of which were correctly predicted, a success rate of 66.7%.
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.